V.S.B. ENGINEERING COLLEGE, KARUR DEPARTMENT OF …€¦ · 6 Cut off region: The collector and...
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1 S.NO SUBJECT CODE SUBJECT NAME PAGE NO 1 EC8353 Electron Devices and Circuits 2 2 EE8301 Electrical Machines-I 19 3 EE8391 Electromagnetic Theory 46 4 ME8792 Power Plant Engineering 65 5 EE8351 Digital Logic Circuits 86 6 MA8353 Transforms and Partial Differential Equations 112 CLASS II YEAR/ III SEMESTER 2 MARK AND 16 MARK QUESTION BANK DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING V.S.B. ENGINEERING COLLEGE, KARUR
Transcript of V.S.B. ENGINEERING COLLEGE, KARUR DEPARTMENT OF …€¦ · 6 Cut off region: The collector and...
1
S.NO SUBJECT CODE SUBJECT NAME PAGE NO
1 EC8353 Electron Devices and Circuits 2
2 EE8301 Electrical Machines-I 19
3 EE8391 Electromagnetic Theory 46
4 ME8792 Power Plant Engineering 65
5 EE8351 Digital Logic Circuits 86
6 MA8353 Transforms and Partial Differential
Equations 112
CLASS II YEAR/ III SEMESTER
2 MARK AND 16 MARK QUESTION BANK
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
V.S.B. ENGINEERING COLLEGE, KARUR
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V.S.B ENGINEERING COLLEGE, KARUR
Department of Electrical and Electronics Engineering
ELECTRONIC DEVICES AND CIRCUITS
Two marks Question and answers
UNIT -I
1. What are conductors? Give examples?
Conductors are materials in which the valence and conduction band overlap each
other so there is a swift movement of electrons which leads to conduction. Ex. Copper, silver.
2. What are insulators? Give examples?
Insulators are materials in which the valence and conduction band are far away from
each other. So no movement of free electrons and thus no conduction. Ex glass, plastic.
3. What are Semiconductors? Give examples?
The materials whose electrical property lies between those of conductors and
insulators are known as Semiconductors. Ex germanium, silicon.
4. What are the types of Semiconductor?
1. Intrinsic semiconductor
2. Extrinsic semiconductor.
5. What is Intrinsic Semiconductor?
Pure form of semiconductors are said to be intrinsic semiconductor.
Ex: germanium, silicon
6. What is Extrinsic Semiconductor?
If certain amount of impurity atom is added to intrinsic semiconductor the resulting
semiconductor is Extrinsic or impure Semiconductor.
7. What are the types of Extrinsic Semiconductor?
1. P-type Semiconductor 2. N- Type Semiconductor.
8. What is P-type Semiconductor?
The Semiconductor which are obtained by introducing pentavalent impurity atom
(phosphorous, antimony) are known as P-type Semiconductor.
9. What is N-type Semiconductor?
The Semiconductor which is obtained by introducing trivalent impurity atom
(gallium, indium) are known as N-type Semiconductor.
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10. What is doping?
Process of adding impurity to a intrinsic semiconductor atom is doping. The impurity
is called dopant.
11. Define drift current.
When an electric field is applied across the semiconductor, the holes move towards
the negative terminal of the battery and electron move towards the positive terminal of the
battery. This drift movement of charge carriers will result in a current termed as drift current.
12. Give the expression for drift current density due to electron.
Jn = q n μnE
Where,
Jn - drift current density due to electron
q- Charge of electron
μn - Mobility of electron
E - applied electric field
13. Define the term diffusion current.
A concentration gradient exists, if the number of either electrons or holes is greater in
one region of a semiconductor as compared to the rest of the region. The holes and electron
tend to move from region of higher concentration to the region of lower concentration. This
process in called diffusion and the current produced due this movement is diffusion current.
14. What is recovery time? Give its types.
When a diode has its state changed from one type of bias to other a transient
accompanies the diode response, i.e., the diode reaches steady state only after an interval of
time “tr” called as recovery time. The recovery time can be divided in to two types such as
(i) forward recovery time (ii) reverse recovery time
15. Define storage time.
The interval time for the stored minority charge to become zero is called st2orage
time. It is represented as t s.
16. Define transition time.
The time when the diode has normally recovered and the diode reverse current
reaches reverse saturation current I0 is called as transition time. It is represented as t t.
17. What is zener breakdown?
When a small value of reverse bias voltage is applied , a very strong electric field is
set up across the thin depletion layer. This electric field is enough to break the covalent
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bonds. Now extremely large number of free charge carriers are produced which constitute the
zener current. This process is known as zener break down.
18. What is avalanche break down?
When bias is applied, thermally generated carriers which are already present in the
diode acquire sufficient energy from the applied potential to produce new carriers by
removing valence electron from their bonds. These newly generated additional carriers
acquire more energy from the potential and they strike the lattice and create more number of
free electrons and holes. This process goes on as long as bias is increased and the number of
free carriers gets multiplied. This process is termed as avalanche multiplication. Thus the
break down which occurs in the junction resulting in heavy flow of current is termed as
avalanche break down.
19. What is rectifier? What are its types?
Rectifier is an electronic device which converts an alternating (ac) voltage or current
into a unidirectional (dc) voltage or current.
Types of rectifier:
1. Half wave rectifier
2. Full wave rectifier
i. Full wave rectifier with center tapped transformer
ii. Full wave bridge rectifier
20. Define rectifying efficiency.
Rectifying efficiency is defined as the ratio of DC output power into AC input power
of a rectifier.
21. What is the function of filters?
Filter is used to reduce the ripple contents in the output of a rectifier to obtain a pure
dc.
22. List the advantages of Zener regulator.
1. Simple circuits
2. Only 2 or 3 components are required to be used
3. Low cost.
23. What is PN junction diode?
A PN junction diode is a two terminal device consisting of a PN junction formed
either in germanium or silicon crystal. A PN junction is formed from a piece of
semiconductor by diffusing P-type material to one half sides and N type material to other half
side.
24. What is depletion region in a PN junction diode?
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The region around the junction from which the charge carriers are depleted is called
as depletion region. When a PN junction is forward biased, the depletion region width
decreases When a PN junction is reversed biased the depletion region width increase.
25. Define the term transition capacitance CT of a diode.
When a PN junction is reverse biased the depletion layer acts like a dielectric material
while P and N type region on either side have low resistance acts as the plates. In reverse
biased PN junction may be regarded as parallel plate capacitor. This junction capacitance is
called transition capacitance. It is denoted by CT and is also called as space charge
capacitance or depletion layer capacitance.
26. List the application of PN junction diode.
Used as rectifier diodes in dc power supplies
Used as signal diodes in communication circuits for modulation and demodulation
Used in clipped and clamper circuits
Used as a switch in logic circuits used in computers
UNIT-II
1. What is bipolar junction transistor?
A bipolar junction transistor (BJT) is a three terminal semiconductor device in which
the operation depends on the interaction of both majority and minority carriers and hence the
name bipolar.
2. What are the different configurations of BJT?
Common emitter configuration
Common collector configuration
Common base configuration
3. What is thermal runaway?
The continuous increase in collector current due to poor biasing causes the
temperature at collector terminal to increase. If no stabilization is done, the collector leakage
current also increases. This further increases the temperature. This action becomes
cumulative and ultimately the transistor burns out. The self destruction of an un stabilized
transistor is known as thermal runaway.
4. Define the different operating region of transistor.
Active region: The collector junction is reverse biased and emitter junction is forward biased.
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Cut off region: The collector and emitter junction are both reverse biased.
Saturation region: The collector and emitter junction are forward biased.
5. List the uses of emitter follower (common collector configuration) circuit.
It is widely used in electronic instruments because of low output impedance and high
input impedance.
It is used of impedance matching.
6. Define alpha and beta of the transistor.
The ratio of change in collector current IC to the change in emitter current IE at
constant collector base voltage VCB ( α = IC/ IE)
Base current amplification factor (β)
The ratio of change in collector current IC to the change in base current IB ( β = IC/
IB)
7. What is meant by early effect?
When the collector base voltage is made to increase, it increase the depletion region
across the collector base junction, with the result that the effective width of base terminal
decreases. This variation of effective base width by collector base voltage is known as base
width modulation or early effect.
8. Explain the significance of early effect or base width modulation.
It reduces the charges recombination of electron with holes in ht base region, hence
the current gain increase with increase in collector base voltage. The charge gradient is
increased within the base; hence the current due to minority carriers across emitter junction
increases.
9. Which configuration provides better current gain?
CB configuration
10. What is the significance of VBE and ICO?
VBE and ICO are significant because any changes in VBE and ICO cause a drastic
change in temperature and collector current IC. It leads to thermal runaway problem.
11. List out the different types of biasing.
Voltage divider bias.
Base bias
Emitter feedback bias
Collector feedback bias.
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12. Why is the transistor called a current controlled device?
The output characteristics of the transistor depend on the input current. So transistor
is called a current controlled device.
13. Define current amplification factor.
It is defined as the ratio of change in output current to the change in input current at
constant other side voltage.
14. What are the requirements for biasing circuits?
The q point must be taken at the Centre of the active region of the output
characteristics.
Stabilize the collector current against the temperature variations.
Make the q point independent of the transistor parameters.
When the transistor is replaced, it must be of same type.
15. When does a transistor act as a switch?
The transistor acts as a switch when it is operated at either cutoff region or saturation
region.
16. What is biasing?
To use the transistor in any application it is necessary to provide sufficient voltage
and current to operate the transistor. This is called biasing.
17. What is operating point?
For the proper operation of the transistor a fixed level of current and voltages are
required. This values of currents and voltages defined at a point at which the transistor
operate is called operating point.
18. What is stability factor?
Stability factor is defined as the rate of change of collector current with respect to the
rate of change of reverse saturation current.
19. What is d.c load line?
The d.c load line is defined as a line on the output characteristics of the transistor
which gives the value of Ic & Vce corresponding to zero signal condition.
20. What are the advantages of fixed bias circuit?
This is simple circuit which uses a few components. The operating point can be fixed
anywhere on the Centre of the active region.
21. Explain about the various regions in a transistor.
The three regions are active region, saturation region and cutoff region.
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22. Explain about the characteristics of a transistor.
Input characteristics: it is drawn between input voltage & input current while keeping
output voltage as constant.
Output characteristics: It is drawn between the output voltage &output current while
keeping input current as constant.
23. What is the necessary of the coupling capacitor?
It is used to block the c signal to the transistor amplifier. It allows ac &blocks the d c.
24. What is reverse saturation current?
The current due to the minority carriers is called the reverse saturation current.
25. What is a FET?
A field effect (FET) is a three terminal semiconductor device in which current
conduction takes place by one type of carriers (either holes or electron) and is controlled by
an electric field.
26. Why FET is called an unipolar device?
The operation of FET depends upon the flow of majority carriers only (either holes or
electrons) the FET is said to be unipolar device.
27. Why the input impedance of FET is more than that of a BJT?
The input impedance of FET is more than that of a BJT because the input circuit of
FET is reverse biased whereas the input circuit of BJT is forward biased.
28. What is meant by gate source threshold voltage of a FET?
The voltage at which the channel is completely cur off and the drain current becomes
zero is called as gate source threshold voltage.
29. Why N channel FET’s are preferred over P channel FET’s?
In N channel FET the charge carriers are the electrons which have a mobility of about
1300 cm2/ VS, whereas in P channel FET’s the charge carriers are the holes which have a
mobility of about 500 cm2 /VS. the current in a semiconductor is directly proportional to
mobility. Therefore the current in N channel FET is more than that of P channel FET.
30. What is JFET? And What are the terminals and types in JFET?
JFET- Junction Field Effect Transistor. And the terminals are Gate, Drain and Source
and the types are N- Channel JFET and P- Channel JFET.
31. What are all the types of MOSFET?
i) Enhancement type ii) Depletion type
32. Differentiate Enhancement and Depletion MOSFET.
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Enhancement MOSFET Depletion MOSFET
Positive voltage at the gate Negative voltage at the gate
Inversion layer is made Depletion of majority carriers happens
Negative charges are formed Positive charges are formed
UNIT-III
1. What is an amplifier?
An amplifier is a device which produces a large electrical output of similar
characteristics to that of the input parameters.
2. How are amplifiers classified according to the input?
1. Small– signal amplifier
2. Large – signal amplifier.
3. How are amplifiers classified according to the transistor configuration?
1. Common emitter amplifier
2. Common base amplifier
3. Common collector amplifier.
3. What is the different analysis available to analyze a transistor?
1. AC analysis. 2. DC analysis.
4. How can a DC equivalent circuit of an amplifier be obtained?
By open circuiting the capacitor.
5. How can a AC equivalent circuit of a amplifier be obtained?
By replacing dc supply by a ground and short- circuiting capacitors.
6. What is an amplifier?
An amplifier is a device which produces a large electrical output of similar
characteristics to that of the input parameters.
7. How are amplifiers classified according to the input?
1. Small – signal amplifier 2. Large – signal amplifier
8. How are amplifiers classified according to the transistor configuration?
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1. Common emitter amplifier. 2. Common base amplifier. 3. Common collector amplifier.
9. List out the biasing schemes available to achieve the required bias in a FET.
Voltage divider bias, Base bias, Emitter feedback bias, Collector feedback bias,
Emitter bias.
10. Mention the parameters of JFET.
A.C. drain resistance
Transconductance
Amplification factor
11. What is transconductance in JFET?
It is the ratio of small change in drain current to the corresponding change in drain to
source voltage.
12. What is amplification factor in JFET?
It is the ratio of small change in drain to source voltage to the corresponding change
in Gate to source voltage.
13. Why do we choose q point at the center of the load line?
The operating point of a transistor is kept fixed usually at the center of the active
region in order that the input signal is well amplified. If the point is fixed in the saturation
region or the cut off region the positive and negative half cycle gets clipped off respectively.
14. Define MOSFET and what are all the terminals.
Metal oxide semiconductor field effect transistor. The terminals are gate, Drain and
source.
15.Why bypass and coupling capacitor are used in amplifier circuits?
Bypass capacitor CE:
The capacitor connected in parallel with the emitter resistor RE is called as the emitter bypass
capacitor.
This capacitor offers a low reactance to the amplified ac signal. Therefore the emitter resistor
RE gets bypassed through CE.
16. How does the MOSFET has high input impedance?
The input impedance of a MOSFET is higher than that of FET since the gate is
insulated from the channel by thin layer of silicon di oxide.
17. Define stability factor of an amplifier? What is its ideal value.
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It is rate of change of collector current with respect to the reverse saturation current
ICO or β or V be. This is the factor which is used to monitor the thermal stability of the
amplifier circuit. The ideal value of stability factor 1.
18. What is the advantage of using emitter resistance in the context of biasing?
It is used to increase the stability by providing negative feedback.
19. What is bandwidth of an amplifier?
The range of frequencies between the upper cutoff frequency and lower cutoff
frequency is known as bandwidth.
20. What are the features of cascode amplifier?
It is another type of wide band amplifier where the first stage is a CE amplifier and
the second stage is the CB amplifier stage. This arrangement is designed to provide high
input impedance with lower voltage gain to ensure that the miller capacitance is at a
minimum with the CB stage providing good high frequency operation.
UNIT-IV
1. What is a differential amplifier?
An amplifier that has two inputs and produces on output signal that is a function of
the difference between the two given output.
2. What are the applications of difference amplifier?
Medical electronic field
Input stage in the measuring instruments
Analog computation
Linear integrated circuit
3. What are the advantages of differential amplifier?
It uses no frequency dependent coupling or bypassing capacitors.
It can compare any tow signals and detect the difference.
It gives higher gain than two cascaded stages of ordinary direct coupling.
4. What is operational amplifier?
An op amp to perform mathematical operation like summation, multiplication,
differentiation and integration etc. in analog computers. It is very high directly couple
negative fee back amplifier, which can amplify signals having frequency ranging from 0Hz to
1 MHz.
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5. What are the specifications for an ideal operational amplifier?
Open loop gain = ∞, Input impedance = ∞
Output impedance = 0, Band width = ∞, CMRR = ∞
6. What is common mode voltage swing?
The common mode voltage swing is defined as the maximum peak input voltage
which may be applied to either input terminal without causing abnormal operation or
damage.
7. Define slew rate.
It measure of an operational amplifier’s switching speed defined as the maximum
time rate of change of the output voltage when subjected to a square wave input signal when
the closed loop gain is unity. Unit is V/msec.
8. Define input off set voltage.
The algebraic difference between the currents into the (-) input and (+) input is
referred to as input offset current.
9. Is the practical op-amp on ideal op-amp?
A practical op-amp is not ideal and has finite value of input offset voltage input offset
current and input bias current. These produce a dc offset voltage at the output.
10. Can op-amp be used to amplify AC as well as DC output?
Op amp can be used to amplify AC and DC for amplifying AC .we use a capacitance
coupled amplifier.
11. What is phase shift distortion?
If the phase shift introduced by the amplifier for different input frequencies are not
proportional to frequency then phase distortion will take place. The phase distortions are not
detectable by the human ears as they are insensitive to the phase changes.
Therefore, phase shift distortion takes place due to unequal phase shifts of the input
signal at different frequencies.
12. What is difference between voltage amplifier and power amplifier?
Small signal amplifiers are also known as “Voltage amplifiers”. This is because
these amplifiers are used primarily for voltage amplification but they are not capable of
supplying a large power to the loads such as loud speakers. The large signal amplifier (power
amplifier) will increase the current sourcing and sinking capability. So at its output we get a
high voltage, high current signal that means a high power signal. Thus the power amplifier is
basically a current amplifier.
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13. What are the types of bias method?
1. Fixed bias circuit (single base resistor biasing)
2. Collector to base bias circuit
3. Voltage divider bias (self-bias) circuit.
14. Define pinch off voltage.
The drain source voltage(VDS) at which the drain current (ID )reaches to its constant
saturation level is called as “pinch off voltage, VP”
VP = (q ND a2)/2є
15. Why thermal runaway not present in FET?
Thermal runaway does not exist in JFET, because drain resistance rd increases with
the temperature, which reduces ID. Thus with the reduction of ID the temperature of the
device is reduced.
16. What is meant by monostable, bistable, astable multivibrator?
Bistable multivibrator-It has two stable states. The multivibrator can exist indefinitely
ineither of the two stable states .It requires an external triggering pulse to change from one
state to another.
Monostable Multivibrator: It has one stable state and one quasi state. The
multivibratorremains in a stable state and when external triggering is applied, then
multivibrator goes to quasi state .After some time interval, the circuit automatically returns to
normal state.
Astable Multivibrator-The astable multivibrator has both the states as the quasi stablestates.
None of the state is stable. Due to this, the multivibrator automatically makes the successive
transition from one quasi stable state to other, without any triggering pulse
17. Mention few applications of UJT.
1. Phase control 2.Saw – tooth generators 3.Non-sinusoidal oscillators 4.Triggering
device for SCR and DIAC.
18. List the various square wave generator circuits.
Astable multivibrator.
Monostable multivibrator.
Bistable multivibrator.
Schmitt trigger
19. List the various saw tooth generator circuit.
Exponential charging
Miller circuit.
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Bootstrap circuit.
Phantastron circuit.
Inductor circuit
20. How the frequency of oscillation varied in an astable multivibrator?
1/T = 1/ 1.38RC, so by varying the value of R or C, the frequency of oscillation can
be varied.
UNIT-V
1. Define positive feedback.
If the feedback signal is in phase with input signal, then the net effect of the feedback
will increase the input signal given to the amplifier. This type of feedback is said to be
positive or regenerative feedback.
2. Define negative feedback.
If the feedback signal is out of phase with the input signal then the inputvoltage
applied to the basic amplifier is decreased and correspondingly the output isdecreased. This
type of feedback is known as negative or degenerative feedback.
3. Define sensitivity.
Sensitivity is defined as the ratio of percentage change in voltage gain with feedback
to the percentage change in voltage gain without feedback.
4. What are the types of feedback?
i. Voltage-series feedback
ii. Voltage-shunt feedback
iii. Current-series feedback
iv. Current-shunt feedback
5. Define feedback.
A portion of the output signal is taken from the output of the amplifier and is
combined with the normal input signal. This is known as feedback.
6. Give an example for voltage-series feedback.
The Common collector or Emitter follower amplifier is an example for voltage series
feedback.
7. Give the effect of negative feedback on amplifier characteristics.
i. Negative feedback reduces the gain
ii. Distortion is very much reduce
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8. What is Oscillator circuit?
A circuit with an active device is used to produce an alternating current is called an
oscillator circuit.
9. What are the classifications of Oscillators?
Based on wave generated:
(i) Sinusoidal Oscillator (ii)Non-sinusoidal Oscillator or Relaxation Oscillator
Ex: Square wave, Triangular wave, Rectangular wave etc.
10. Give the properties of negative feedback.
i. Negative feedback reduces the gain
ii. Distortion is very much reduced.
11. What are the types of feedback oscillators?
i. RC-Phase shift Oscillator
ii. LC-Oscillators
a. Tuned collector Oscillator
b. Tuned emitter Oscillator
c. Tuned collector base Oscillator
d. Hartley Oscillator
e. Colpits Oscillator
f. Clap Oscillator.
12. What are the conditions for oscillation?
The total phase shift of an oscillator should be 360o. For feedback oscillator i should
satisfies Barhausen criterion.
13. What is Miller crystal oscillator? Explain its operation.
It is a Hartley oscillator its feedback Network is replaced by a crystal. Crystal
normally generate higher frequency reactance due to the miller capacitance are in effect
between the transistor terminal.
14. Define Oscillator.
A circuit with an active device is used to produce an alternating current is called an
oscillator circuit.
15. What is feed back?
It is the process of injecting some energy from the output and then returns it back to
the input.
16. What is the disadvantage of negative feedback?
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Reduces amplifier gain
17. Define Blocking Oscillator.
A special type of wave generator which is used to produce a single narrow pulse or
train of pulses.
18. What are the two important elements of Blocking Oscillator?
Transistor and pulse transformer.
19. What are the applications of blocking Oscillator?
It is used in frequency dividers, counter circuits and for switching the other circuits.
21. Define Hartley oscillator.
A LC oscillator which uses two inductive reactance and one capacitive reactance in
its feedback network is called Hartley Oscillator.
22. Define Colpitts oscillator.
A LC oscillator which uses two capacitive reactance and one inductive reactance in
its feedback network is called Hartley Oscillator.
23. What are the main advantages of crystal oscillator?
The main advantages of crystal oscillator are frequency accuracy, stability and low
power consumption.
24. What do you mean by Multivibrators and mention its types?
The Multivibrators are used to produce the non – sinusoidal input signal. Types:
(1)Astable multivibrators (2) Monostable multivibrators (3 ) Bistable multivibrators
16 Marks Questions
UNIT-I
1. Explain the forward and revere bias operation and VI characteristics of a PN
junction diode.
2. Explain the working of centre-tapped full wave rectifier (with and without filter)
with neat diagrams.
3. Discuss the effect of temperature on VI characteristics of a diode.
4. Explain the characteristics and applications of Zener diode.
5. Explain the mechanism of avalanche and Zener break down.
6. Define and derive the expression for diffusion capacitance of a PN diode.
7. Discuss the effect of doping on depletion region.
8. Define regulator. Explain the operation of any one type of regulator.
9. Explain about filters and also explain the operation of CLC and LC filter.
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10. Explain about LED,LCD and its applications.
11. Draw the circuit diagram of half wave rectifier and explain its operation with
necessary waveform.
UNIT-II
1. Explain the operation of PNP& NPN transistor.
2. Explain input and output characteristics of CE configurations in NPN transistors.
3. Explain the operation of NPN transistor in CE configuration with its input and
output Characteristics. Also define active, saturation and cut –off regions.
4. How could transistor act as a switch?
5. Compare JFET and MOSFET. Also give a detailed description of construction and
operation of JFET.
6. Explain the principle of operation of a unijunction transistor.
7. Explain how D-MOSFETs and E-MOSFETs differ.
8. Explain the construction, principle of operation, Characteristics and applications of
Thyristor.
9. Explain the construction, principle of operation, Characteristics and applications of
IGBT.
10. Compare pinch off and cutoff in JFET. Also discuss how voltage controls the
current in JFET.
UNIT-III
1. With the hybrid equivalent circuit define the various h parameters of the CE
transistor configuration and derive the analytical expression for each of them.
2. A common base transistor amplifier is driven by a voltage source Vs and internal
resistance RS=1200Ω. The load impedance is a resistor RL OF 1000Ω. The ‘h’
parameters are given below: hib = 220Ω; hrb =3*10-4 ; hfb= -0.98; hob=0.5µA/V
Compute, current gain (Ai), Input impedance (Ri), Voltage gain Av, input
impedance (Ro) and Power gain Ap.
3. Explain in detail on voltage and current gain expressions for CB configuration
using hybrid model.
4. Discuss on the following (i) JFET Small signal model (ii) Darlington
connection.
5. Explain how different hybrid parameters are found out using CB configuration.
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6. Explain About Thermal Runaway and Thermal Stability.
7. Derive the relations among ά, β, γ of a transistor.
8. What are called h-parameters? Explain the analysis of CE small signal amplifier
using h-parameter.
9. Draw the small signal equivalent circuit of FET amplifier in CS connection and
derive the equations for voltage gain, Input Impedance and output impedance.
10. Compare CB, CE and CC amplifiers.
UNIT-IV
1. Explain the different amplifier with common mode and differential mode of
operations.
2. Explain the biasing techniques of JFET under different conditions.
3. Discuss the working of various types of power amplifiers.
4. What do you understand by Differential amplifiers? Draw the circuit diagram and
explain the Working of differential amplifier. Explain the circuit operation of CM
and DM.
5. Draw the circuit diagram and explain the working of differential amplifier. Explain
the circuit Operation at CM and DM.
6. Draw the drain and transfer characteristics of A N-Channel JFET and explain.
7. Explain about i) CS amplifier ii) CD amplifier iii) CG amplifier.
8. Derive the voltage gain, input resistances of CS, CD, CG amplifiers.
9. Write short notes on cascade and cascode amplifiers.
10. Write short notes on Darlington connections.
UNIT-V
1. Explain the effects of negative feedback in amplifiers.
2. Explain the operation of crystal oscillator with neat diagram and write the
expression of its frequency of oscillations.
3. Describe the characteristics i) positive feedback ii) negative feedback.
4. With the suitable block diagrams, derive the expression for input and output
resistances for i) voltage series amplifier ii) voltage shunt amplifier iii) current
series & shunt amplifier.
5. Explain the concept of oscillators.
6. Explain the principle of operation and derive the expression for Wein Bridge
oscillator.
7. Explain the principle of operation and derive the expression for Colpitts oscillator.
8. Derive the expression and characteristics of i) RC phase shift oscillator ii) Hartley
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oscillator.
9. What is Barkhausen criterion? Explain in detail?
10. Explain the principle of operation and derive the expression for any one LC
oscillator.
ELECTRICAL MACHINES-I
Two Marks Questions and Answers
UNIT-I MAGNETIC CIRCUITS AND MAGNETIC MATERIALS
1. Mentionthetypes ofelectricalmachines.
Therearethree basicrotatingmachinestypes, namely
a.Thedcmachines
b. the polyphasesynchronousmachine(ac),and
c.Polyandsingle phaseinductionmachine(ac)andastationarymachine,namely
Transformer.
2. Define magneto motive force?
MMF is the cause for producing flux in a magnetic circuit. the amount of flux setup in the
core decent upon current(I)and number of turns(N).the product of NI is called MMF and it
determine the amount of flux setup in the magnetic circuit
MMF=NI ampere turns (AT).
20
3. Defineleakageflux
Thefluxsetupintheair pathsaroundthemagneticmaterialisknownasleakageflux.
4. Definemagneticreluctance
Theoppositionofferedbythemagneticcircuitforthemagneticfluxpathisknownas
magnetic reluctance.Itisanalogoustoelectricresistance.
5. Drawthetypicalnormalmagnetizationcurve of ferromagneticmaterial.
B(T) Saturationzone
Linear Zone (const μ)
Initialnonlinearzone H(A/m) 6. Whatisfringing? In the air gap the magnetic flux fringes out into neighboring air paths due to thereluctanceofair gap which causesa non uniform flux densityin the air gap of amachine.Thiseffectiscalledfringing effect.
7. Statestackingfactor.
Thestackingfactorisdefinedastheratioofthenetcrosssectionalareaofamagneticcoretothe
grosscrosssectionalareaofthemagneticcore.Duetolaminationnetcrosssectionalarewillbealways
lessthangrosscrosssectionalarea.Thereforethevalueofstackingfactor isalwayslessthanunity.
8. Mentionsomemagneticmaterials.
Alnicos,chromiumsteels,copper–nickelalloy,nickel,cobalt,tungstenandaluminum
21
9. Whatismagnetostiction?
Whenferromagneticmaterialsaresubjectedtomagnetizingmmf,thesemayundergosmall
changes indimension;this phenomenonisknownasmagnetostriction.
10. Definestaticallyinducedemf.
Thecoilremainsstationarywithrespecttoflux,butthefluxthroughitchangeswithtime.Theemfindu
cedisknownasstaticallyinducedemf.
11.Definedynamicallyinducedemf.
Fluxdensitydistributionremainsconstantandstationarybutthecoilmovesrelativetoit. The
emfinducedisknownasdynamicallyinducedemf.
12.StateFleming’sright handrule.
Extendthethumb,foreandmiddlefingeroftherighthandsothattheyaremutuallyperpendicular
toeachother. If the thumb represents the direction of movement
ofconductorandtheforefingerthedirectionofmagneticflux,thenthemiddlefingerrepresents the
directionof emf.
13. StateFleming’sLefthandrule.
Extendthethumb,foreandmiddlefingeroftherighthandsothattheyaremutuallyperpendicular
toeachother.Iftheforefingerrepresentsthedirectionoffluxandthemiddlefingerthedirectionofcurrent,the
nthemiddlefingerrepresentsthedirectionofmovementofconductor.
14. Whatarethelossescalledascoreloss?
Hysteresis lossandeddy currentloss. 15. Definecoercivity.
Itisthemeasureofmmfwhich,whenappliedtothemagneticcircuitwouldreduceitsfluxdensitytoze
ro,i.e.,itdemagnetizesthemagneticcircuit.
16. What are the magnetic losses?
1. Eddy current loss
2. Hysterisis loss
17. Types of induced emf?
1. Dynamically induced emf
2. Statically induced emf
18. Define self inductance?
The property of a coil that opposes any change in the amount of current flowing through it is called
self inductance
19. Define mutual inductance?
The property of a coil to produce emf in a coil due to change in the value of current or flux in it is
called mutual inductance
20. Define coefficient coupling?
It is defined as the fraction of magnetic flux produced by the current in one coil that links the other
coil.
22
21. State faradays law of electromagnetic induction
Whenever a flux linking in the coil changes emf always induced in the conductor the
magnitude of induced emf is proportional to rate of change flux linkage
e = NdФ/dt
22. State Lenz law?
The law states that induced emf always opposite to applied voltage source.
23. What is magnetic circuit?
The closed path followed by magnetic flux is called magnetic circuit.
24. Define magnetic flux?
The magnetic lines of force produced by a magnet is called magnetic flux it is denoted as Ф and its
unit is Weber
25. Define magnetic flux density?
It is the flux per unit area at right angles to the flux it is denoted by B and unit is Weber/m2.
26. Define reluctance?
The opposition that the magnetic circuit offers to flux is called reluctance. It is defind as the ratio of
MMF to flux. It is denoted by S and its unit is AT/m
27. What is retentivity?
The property of magnetic material by which it can retain the magnetism even after the removal of
inducing source is called retentivity
28. Define permeance?
It is the reciprocal of reluctance and is a measure of the cause the ease with which flux can pass
through the material its unit is wb/AT
29. Define magnetic flux intensity?
It is defined as the mmf per unit length of the magnetic flux path. it is denoted as H and its unit is
AT/m
H=NI/L.
30. Define permeability?
Permeability of a material means its conductivity for magnetic flux. Greater the permeability of
material, the greaters its conductivity for magnetic flux and vice versa.
31. Define relative permeability?
It is equal to the ratio of flux density produced in that material to the flux density produced in air by
the same magnetizing force
μr=μ/μ0
23
Unit–II Transformers
1. Mentionthe differencebetweencoreandshelltypetransformers.
Incoretypethewindingssurroundthecoreconsiderablyandinshelltypethecoresurroundthewin
ding.
2. What isthe purposeoflaminating thecoreintransformers?
Toreduceeddy currentloss.
3. Givetheemf equationofatransformer anddefineeachterm.
EmfinducedinprimarycoilE1=4.44fΦmN1volt
Emf induced insecondarycoil E2 =4.44fΦmN2 volt
Where f isthefrequencyofACinput
Φmisthemaximum value offluxinthecore
N1,N2 arethe numberofprimary andsecondaryturns.
4. Doesthetransformerdrawanycurrentwhensecondaryis open? Why?
Yes,
it(primary)willdrawthecurrentfromthemainsupplyinordertomagnetizethecoreandtosupplyiron
andcopperlossesonnoload. Therewillnotbeanycurrentinthesecondarysincesecondaryisopen.
5. Definevoltageregulationofatransformer.
Whenatransformerisloadedwithaconstantprimaryvoltage, thesecondaryvoltagedecreasesfo
r laggingpowerfactorload,andincreasesforleadingPfloadbecauseofitsinternal
resistanceandleakagereactance. Thechangeinsecondaryterminalvoltagefromnoloadtofull
loadexpressedasapercentageofnoloadsorfullloadvoltageistermedasregulation.
%regulationdown =(0V2-V2)x100/0V2
%regulationup =(0V2-V2)x100/V2
6. Fullloadcopperlossinatransformer is1600 watts.Whatwill bethelossathalf load?
Ifxistheratioofactualloadtofullloadthencopperloss=x2(fullloadcopperloss).Here
Wc=(0.5)2
x1600=400watts
7. Defineallday efficiency ofatransformer.
Itisthecomputedonthebasisofenergy consumedduring acertainperiod, usuallyadayof
24hrs.
ηallday=outputinkWh/inputin kWhfor 24hrs.
8. Whytransformersare ratedinkVA?
Copperlossofatransformerdependsoncurrentandironlossonvoltage. Hencetotallosses
depends on Volt- Ampereand not on the power factor. That iswhythe
ratingoftransformersisinkVAandnotinkW.
9. Whatarethetypicalusesof autotransformer?
24
(i)Togivesmallboosttoa distributioncabletocorrectfor the voltagedrop.(ii)As
inductionmotorstarters.
(iii)Asfurnacetransformers
(iv)Asinterconnecting transformers
(v)Incontrolequipmentforsingle phaseand3phaseelectivelocomotives.
10.Whataretheapplications of step-upandstep-downtransformers?
Step-
uptransformersareusedingeneratingstations.Normallythegeneratedvoltagewillbeeither11kVor
22kV.Thisvoltageissteppedupto110kVor220kVor400kVandtransmittedthroughtransmissionli
nes.(Inshortitmaybecalledassendingend).Step-down
transformersareusedinreceivingstations.Thevoltageareagainsteppeddownto11kVor22kVandtr
ansmittedthroughfeeders.(Inshortitmaybecalledasreceivingend).Furtherthese
11kVor22kVaresteppeddownto3phase400Vbymeansofadistributiontransformerandmade
ava ilableat consumer premises . The
t ransfo rmersusedatgenerat ingstat ionsandreceivingstationsarecalledpower
transformers.
11.Howtransformersareclassifiedaccordingtotheirconstruction?
Or
Mentionthedifferencebetween“CORE”and“SHELL”typetransformers.
Or
Whatarethetwotypesofcores used? Comparethem.
Transformersareclassifiedaccordingtotheirconstructionas,
(i)Core type (ii) Shelltype (iii)Spirakoretype.
Spira coretypeisalatesttransformerandisusedinbigtransformers. In“core”type,the
windings (primaryandsecondary)
surroundthecoreandin“shell”type,thecoresurroundsthewindings.
12.Explainon thematerialusedforcoreconstruction.
Thecoreisconstructedoftransformersheetsteellaminationsassembledtoprovideacontinuou
smagneticpathwithaminimumofairgapincluded.Thesteelusedisofhighsiliconcontentsometimes
heat-
treatedtoproduceahighpermeabilityandalowhysteresislossattheusualoperatingfluxdensities.Th
eeddycurrentlossisminimizedbylaminatingthecore;thelaminationsbeinginsulatedfromeachoth
erbylightcoatofcore-platevanishorbyanoxide
layeronthesurface.thethicknessoflaminationsvariesfrom0.35mmforafrequency of59Hzand
0.5mm fora frequency of25Hz.
13.WhenwillaBucholzrelay operateinatransformer?
Bucholzrelyisaprotectivedeviceinatransformer.Ifthetemperatureofthecoilexceeds
itslimit,Bucholzrelayoperatesandgivesanalarm.
14.Howdoeschangeinfrequencyaffectthe operationofagiventransformer?
Withachangeinfrequency,ironloss,copperloss,regulation,efficiencyandheatingvariesandt
hereby efficiency reduces.
15.What istheanglebywhichno-loadcurrentwilllag theidealappliedvoltage?
25
Inanidealtransformer,therearenocopperlossandnocoreloss,(i.e.lossfreecore).
Thenoloadcurrentisonlymagnetizingcurrent.Thereforetheno-loadcurrentlagsbehind
byanangleof90˚.Howeverthewindingspossessresistanceandleakagereactanceandtherefore
theno-loadcurrentlagstheappliedvoltageslightlylessthan90˚.
16.Listtheadvantages ofsteppedcorearrangementinatransformer.
(i) Toreducethespaceeffectively.
(ii) Toobtainreducedlengthof meanturnof thewindings.
(iii) ToreduceI2
Rloss.
17.Whyarebreathersused intransformers?
Breathersareusedtoentraptheatmosphericmoistureandtherebynotallowingittopass
ontothe transformer oil.Also topermittheoilinsidethetank
toexpandandcontractasitstemperatureincreasesanddecreases.Alsotoavoidsledgingofoili.e.decom
positionofoil.Additionof8partsofwaterin1000000reducestheinsulationsquantityofoil.Normall
ysilicagelisfilledinthebreatherhavingpinkcolour.Thiscolourwillbechangedtowhiteduetocontinuo
us use, which isanindicationof badsilicagel;itis normallyheatedandreused.
18.What isthefunctionof transformer oilinatransformer?
Nowadaysinsteadofnaturalmineraloil,syntheticoilsknownasASKRELS(tradename)a
reused.Theyarenoninflammable;underanelectricarcdonotdecomposetoproduce
inflammablegases.PYROCOLORoilpossesseshighdielectricstrength.Henceitcanbesaidthattra
nsformer oil provides,(i)goodinsulationand(ii) cooling.
19.A1100/400V,50Hzsinglephasetransformerhas100turnsonthesecondarywinding.
Calculatethe number of turns onits primary.
Weknowthat V1/V2=k =N2/N1
Substituting inaboveequation400/1100 =100/N1
N1 =100/400 x1100
=275turns.
20.Whatarethe functions of no-loadcurrentinatransformer?
No-loadcurrentproduces fluxandsuppliesironlossandcopper lossonno-load.
21.Howwillyou transferthequantitiesfromonecircuittoanother circuitinatransformer?
1. Secondary toprimary 2.Primarytosecondary
Symbol
V2
Value
V2/k
Symbol
VL
Value
kV1
26
I2
R2
X2
ZL
kI2
R2/k2
X2/k2
ZL/k2
IL
RL
XL’
I1 /k
k2
R1
k2X1
22.Canthe voltageregulationof atransformergoto negative?Ifsounderwhatcondition?
Yes.If theloadhasleadingpower factor.
23.Distinguishbetweenpowertransformeranddistributiontransformer.
PowertransformershaveveryhighpowerratingsintheorderofMVA.Theyareused
ingeneratingandreceivingstations.Sophisticatedcontrolsarerequired.Voltagerangeswillbe
veryhigh.Distributiontransformersareusedinconsumerside.Voltagelevelswillbemedium.Power
ranging willbesmallinorderofkVA.Complicatedcontrolsare notneeded.
24.What isthe purposeof providing‘taps’ intransformerandwheretheseareprovided?
Inorder toattaintherequiredvoltage, ‘taps’ areprovided.Normallyitwillbeprovidedat
lowvoltagesides
25.Givethe methodof reducing iron lossinaTransformer (Oct–98)
Theiron lossesareminimizedbyusing high-
gradecoremateriallikesiliconsteelhavingverylow hysteresisloopandby
manufacturingthecoreintheformof laminations.
26.Statetheconditionfor maximum efficiency(Oct–97)
Copperlosses=Ironlosses.
27. What is the turns ratio and transformer ratio of transformer?
Turns ratio = N2/ N1
Transformer = E2/E1 = I1/ I2 =K.
28. Mention the difference between core and shell type transformers?
In core type, the windings surround the core considerably and in shell type the core
surrounds the windings i.e winding is placed inside the core.
29. Does transformer draw any current when secondary is open? Why?
Yes, it (primary) will draw the current from the main supply in order to magnetize the core
and to supply for iron and copper losses on no load. There will not be any current in the
secondary since secondary is open.
30. What are the applications of step-up & step-down transformer?
27
Step-up transformers are used in generating stations. Normally the generated voltage will
be either 11kV. This voltage (11kV) is stepped up to 110kV or 220kV or 400kV and
transmitted through transmission lines (simply called as sending end voltage).
Step-down transformers are used in receiving stations. The voltage are stepped down to
11kV or 22kV are stepped down to 3phase 400V by means of a distribution transformer and
made available at consumer premises. The transformers used at generating stations are called
power transformers.
31.How does change in frequency affect the operation of a given transformer?
With a change in frequency, iron and copper loss, regulation, efficiency & heating varies so
the operation of transformer is highly affected.
32. What is the angle by which no-load current will lag the ideal applied voltage?
In an ideal transformer, there are no copper & core loss i.e. loss free core. The no load
current is only magnetizing current therefore the no load current lags behind by angle
900.However the winding possess resistance and leakage reactance and therefore the no load
current lags the applied voltage slightly less than 900
33. List the arrangement of stepped core arrangement in a transformer?
1. To reduce the space effectively
2. To obtain reduced length of mean turn of the winding
3. To reduce I2R loss.
Unit–III ELECTROMECHANICAL ENERGY CONVERSION AND CONCEPTS IN
ROTATING MACHINES
1. Writedowntheequationfor forceinmagneticfieldsystem.
2. Whatisanelectromechanicalsystem?
The system in which the electromechanical energy conversion takes palace via the
mediumofamagneticorelectricfieldiscalledelectromechanicalsystem.
3. Describemultiplyexcitedmagneticfieldsystem.
The specially designed transducers have the special requirement of producing
anelectrical signalproportionaltoforcesorvelocitiesofproducingforceproportionalto
electricalsignal.
Suchtransducersrequiretwoormoreexcitationcalledasmultiplyexcitedmagneticfieldsyste
m.
4. Definecoenergy.
Coenergyisanenergyusedforalinearsystemcomputationkeepingcurrentasconstant.
Itwillnotbe appliedtothe nonlinear systems.
5. Howenergyisstored?
28
Energycanbestoredofretrievedfromthemagneticsystembymeansofanexcitingcoilconne
ctedtoanelectricsource.
6. Write theequationformechanicalforce.
7. Definefieldenergy.
a. Theenergydrawnbyvirtueofchangeinthedistancemovedbytherotorinelectricalm
achines infieldconfigurationisknownasfieldenergy.
8. Drawthegraphicalrelationbetweenfieldenergyandcoenergy
-axis
Wf
=fielden
ergy
I- curveforfixedx
29
f
W’ =coenergy
a. I-axis
9. Writetheexpressionforthe principleofenergy conversion.
Mechanicalenergyoutput(workdonebythefieldforce)=Electricalenergyinput–increased
infieldenergy.
10. Whatisthesignificanceofcoenergy?
Thecoenergyhasnophysicalsignificancebutitisimportantinobtainingmagneticforces.
11. Howtheenergy stored inmagneticfield?
Whenthemovingpartofanyphysicalsystemisheldfixed,andthentheentireelectricalenergy
inputgetsstored inthemagneticfield.
12. Giveanyfourexamplesifsingleexcitedmagneticsystem.
(i)ElectromagneticRelay
(ii) Reluctancerelay(iii)MIinstruments(iv)Hysteresismotor.
13. Writetheapplications of singlyexcitedanddoubly excitedmagneticsystem.
Singly excited magnetic system – EM Relays, Reluctance motor, MI
instruments,Hysteresis motor.
Double exc it ed magnet ic s ys t e m–Alternator, Synchronous motor, loud
speakers,tachometers,DCmachines.
14. Statethenecessaryconditionsforthe productionofsteadytorquetheinteractionof
statorandrotorfields inanelectricmachine.
(i) Thetwofieldsmusthavethesame number ofpoles
(ii) Thetwofieldsshallberelativelystationary.
15.Definethetermpolepitch
Thedistancebetweenthecentresoftwoadjacentpolesis
calledpolepitch,onepolepitchisequalto180electricaldegrees.Itisalsodefinedasthenumbe
rof slots per pole.
16. Define pitchfactor
Itis definedastheratioof resultantemfwhencoilisshort pitchtothe resultantemfwhen coil
isfullpitched. Itisalwayslessthanone.
Pitchfactor isalwaystermedascoilspan(Kc)factor.
kc =cosα/2whereα=angle of shortpitch.
17. Definethetermbreadthfactor
Thebreadthfactorisalsocalleddistributionfactororwindingfactor.
30
Thefactorbywhichthereis
areductionintheemfduetodistributionofcoiliscalleddistributionfactordenotedaskd.
18. Writedowntheadvantages of short pitchedcoil. (i)Thelengthrequiredfortheendconnectionofcoilsislessi.e.,inactivelengthofwindingis
less.So lesscopperisrequired.Henceeconomical.
(ii)Short pitchingeliminated highfrequencyharmonicswhich distortthe sinusoidal
natureofemf.Hencewaveformofaninducedemfismoresinusoidalduetoshort pitching.
(iii)Ashighfrequencyharmonicsgeteliminated,eddycurrentandhysteresislosseswhichdep
endonfrequency alsogetminimized.Thisincreasestheefficiency. 19. Writedowntheadvantages of short pitchedcoil.
(i)Thelengthrequiredfortheendconnectionofcoilsislessi.e.,inactivelengthofwindingis
less.So lesscopperisrequired.Henceeconomical.
(ii)Short pitchingeliminated highfrequencyharmonicswhich distortthe sinusoidal
natureofemf.Hencewaveformofaninducedemfismoresinusoidalduetoshort pitching.
(iii)Ashighfrequencyharmonicsgeteliminated,eddycurrentandhysteresislosseswhichdep
endonfrequency alsogetminimized.Thisincreasestheefficiency.
20. Whatis distributedwinding?
Id‘x’conductorsperphasearedistributedamongstthe3slotsperphaseavailableunder
pole,thewindingiscalleddistributedwinding.
21. Explainthefollowingtermswithrespecttorotating electricalmachines.a)Polepitch&b)
Chording angle.
Polepitch:Thedistancebetweenthecentersoftwoadjacentpolesiscalledpolepitch.Onepol
epitchisequalto180electricaldegrees.Itisalsodefinedasthenumberofslots perpole.
Chordingangle:Itisdefinedasthatanglebywhichthecoilpitchdepartsfrom180electricald
egrees.
22. Writetheexpressionsforthesynchronousspeed.
Thespeedofrotating magneticfieldiscalledsynchronousspeed.
WhereNs =Synchronousspeedf=FrequencyinHz
P=numberof poles. 23. Write themmfequationofdcmachine.
Thefundamentalcomponentofmmfwaveisgivenby Whereθ=electricalanglemeasuredfromthemagneticaxisofthecoilwhichcoincideswiththe
positivepeak ofthefundamentalwave.
31
24. Whatismeantby electromagnetictorque?
Whenthestatoradrotorwindingsofthemachinebothcarrycurrents,theyproducetheir
ownmagneticfieldsalongtheirrespectiveaxeswhichsinusoidallydistributedalongthe air-
gaps.Torqueresultsfromthetendencyof thesetwofieldstoalignthemselves.
25. Statethetorqueequationfor roundrotormachine. Where P=No.pole
D=Averagediameterofairgap
l=Axiallengthifairgap
µo=Permeabilityoffreespace=4x10-7
H/mg=airgaplength
F1 = Peak valueofsinusoidal mmfstatorwave
F2 =peak valueofsinusoidal mmfrotorwave Α=Angle betweenF1 andF2 calledtorqueangle
26.Define rotating magneticfield.
Whenabalancedthreephasewindingwithphasedistributedinspacesothattherelativespacea
ngleis120 i s fedwithbalanced3phasecurrent,resultantmmfrotatesinairgapat speed.
32
Unit– IVDC GENERATOR
1. What do you meant by Electric Generator?
Electricity does not occur naturally in usable form and it also cannot be stored in
usefully large quantities. Therefore, it must be generated continuously to meet the
demand at all times. An efficient and convenient way to generate electric power is by
conversion of mechanical power into electrical form in rotating device called Generator
2. Define Electric Motor. (May 2011)
The major use of electric energy is made by converting it back to run the wheels of
industry as well as tiny household appliances. The electromechanical energy conversion
process is a reversible one and simple adjustment of mechanical shaft and electrical
conditions reverses the flow of power. In this mode of operation, the electromechanical
device, in general called the electric machine, is known as the motor and the machine is
said to be in the motoring mode.
3. Draw the cross sectional view of DC machine. (April – 98)
4. What are all the main parts of a DC machine? (Oct – 97)
1. Stationary member called stator
2. Rotating member called rotor
3. Field winding wound on field poles to produce uniform magnetic
33
flux
4. Armature winding used to interchange current with the external
electric system depending upon the circuit conditions
5. Commutator – a mechanical rectifier
6. Brushes – used to collect the current
5. Write down the EMF equation of a DC Generator (April – 98)
Ea = (ZnP) / (60A) Volts
Where - the magnetic flux/pole in Wb
n - The armature speed in rpm
Z - Total armature conductors
A – Number of parallel paths
P – Number of poles
6. Write down the torque equation of a DC motor? (Nov 2010)
T=KaIa Nm
Where Ka = (1/2)Z(P/A)
- Magnetic flux / pole in Wb
Ia – Armature current in amps
7. Write the formula to find the magnitude of the induced e.m.f? (May 2011)
The magnitude of the Induced e.m.f is given by,
E=B * l * v
Where l=Active length of conductor in m
v=Relative velocity component of conductor in m/s in the direction
perpendicular to direction of the flux.
8. Write the functions of yoke? (Nov 2009)
Various functions are
i) It serves the purpose of outermost cover of the d.c. machine. So that
insulating materials get protected from harmful atmospheric elements like
moisture, dust and various gases like SO2, acidic fumes etc.,
ii) It provides mechanical support to the poles.
iii) It forms a part of the magnetic circuit. In provides a path of low reluctance
for magnetic flux. The low reluctance path is important to avoid wastage of
power to provide same flux.
9. Write the functions of field winding? (Dec 2011)
The main functions of field winding is
i) To carry current due to which pole core, on which the field winding is
placed, behaves as an electromagnet, producing necessary flux.
ii) As it helps in producing the magnetic field i.e. exciting the pole as an
electromagnet it is called field winding or exciting winding
10. Write the functions of Armature winding? (May 2011)
Various functions of armature winding is
34
i) Generation of e.m.f takes place in the armature winding in case of
generators.
ii) To carry the current supplied in case of d.c motors.
iii) To do useful work in the external circuit.
11. Write the functions of Commutator? (Nov 2010)
Various functions arte
i) To facilitate the collection of current from the armature conductors.
ii) To convert internally developed alternating e.m.f. to unidirectional e.m.f.
iii) To produce unidirectional torque in case of motors.
12. Mention the types of armature winding. (Dec 2011)
Armature winding has basically two types namely,
i) Lap winding
ii) Wave winding
13. Write down the comparison of lap and wave type winding? (Apr 2010)
S.No Lap winding Wave winding
1. Number of parallel paths(A) =
Poles (P)
Number of parallel paths (A) = 2
2. Number of brush sets required is
equal to number of poles
Number of brush sets required is
always equal to 2
3. Preferable for high current, low
voltage capacity generators
Preferable for high voltage, low current
capacity generators
4. Normally used for generators of
capacity more than 500A
Preferred for generators of capacity less
than 500A
14. Define commutation. (May 2007)
The reversal of current is likely to take place in short interval when a coil is short
circuited by a brush so that transfer of current from one direction to other is carried out
without any sparking. This process is called commutation.
15. Mention the methods of improving commutation. (Nov 2009)
There are two practical ways by which commutation may be improved. These
methods are
I. Resistance commutation
II. E.M.F commutation
16. Draw the symbolic representation of dc generator. (Nov 2010)
35
17. Underwhat circumstances does a dc shunt generator fail to build up? (Dec 2011)
1. Absence of residual flux.
2. Initial flux set up by the field winding may be in opposite direction to residual flux
3. Shunt filed circuit resistance may be higher than its critical field resistance
4. Load circuit resistance may be less than its critical load resistance
18. Define critical field resistance in dc shunt generator(Nov 2009)
Critical field resistance is defined as the resistance of the field circuit which
will cause the shunt generator just to build up its e.m.f at a specified field.
19. Why is the e.m.f not zero when the field current is reduced to zero in a dc
generator?
Even after the field current/magnetizing force is reduced to zero the machine
is left out with some flux as residue. E.m.f due to this residual flux is available when
field current is zero.
20. Define the term ‘critical speed’ in dc shunt generator. (Nov 2010)
Critical speed is defined as the speed at which the generator is to be driven to
cause self-excited generator to Build up its e.m.f for the given field circuit resistance.
21. Define the term armature reaction in dc machines. (Dec 2011)
The interaction between the fluxes set up by the current carrying armature
conductors with the main field flux is defined as armature reaction.
22. What are the two unwanted effects of armature reaction? (Nov 2009)
Cross magnetizing effect / Distorting effect
Demagnetizing effect
1. Differentiate between geometric neutral axis (GNA) and magnetic neutral axis
(MNA). (Nov 2010) GNA is the axis, which is situated geometrically or physically in the mid way
between adjacent main poles. MNA is the axis, which passes through the zero crossing
of the resultant magnetic field waveform in the air gap.
24.Does a d.c motor differ from d.c generator in construction? (Nov 2009)
Generators are normally placed in closed room, accessible only to skilled
operators. Therefore on ventilation point of view they may be constructed with large
opening in the frame. Motors on the other hand, have to be installed right in the place of
use which may have dust, dampness, inflammable gases, chemical fumes etc . To
36
protect the motors against these elements, the motor frames are made either partly
closed or totally closed or flame proof etc.
25.Does a d.c motor differ from d.c generator in construction? (Dec 2011)
Generators are normally placed in closed room, accessible only to skilled
operators. Therefore on ventilation point of view they may be constructed with large
opening in the frame. Motors on the other hand, have to be installed right in the place of
use which may have dust, dampness, inflammable gases, chemical fumes etc . To
protect the motors against these elements, the motor frames are made either partly
closed or totally closed or flame proof etc.
26. To what polarity are the interpoles excited in dc generators? (Nov 2010)
The polarity of the interpoles must be that of the next main pole along the
direction of rotation in the case of generator.
27.Why are carbon brushes preferred for dc machines? (May 2012)
The high contact resistance carbon brushes help the current in the coil undergoing
commutation to attain its full value in the reverse direction at the end of commutation.
The carbon brushes also lubricate and give less wear and tear on Commutator surface.
28. Draw the diagram of separately excited DC generator.
29. What are the conditions to be fulfilled for a dc shunt generator to build up
e.m.f?
1. The generator should have residual flux
2. The field winding should be connected in such a manner that the flux set up by the
3.field winding should be in the same direction as that of residual flux
4. The field circuit resistance should be less than critical field resistance
5. Load circuit resistance should be above its critical load resistance.
Unit–VDC MOTOR
Part–A
1.What is primemover?
37
Thebasicsourceofmechanicalpower,whichdrivesthearmatureofthegenerator,iscalled
primemover. 2.Givethe materialsused inmachinemanufacturing
Threematerialsareusedinmachinemanufacturing.(i)steel–toconductmagneticflux
(ii) Copper–toconductelectriccurrent
(iii)Insulation 3.Howwillyouchangethedirectionof rotationofad.cmotor?
Eitherthe directionofthe mainfieldorthedirectionofcurrentthrough
thearmatureconductors is tobereserved. 4.What is back emf ind.cmotors?
As themotorarmaturerotates, thesystemof conductor
comeacrossalternateNorthandSouthPolemagneticfieldscausinganemf
inducedintheconductors. Thedirectionofthe emf inducedintheconductors.
Thedirectionoftheemfinducedisinthedirectionopposite tothecurrent.As
thisemfalwaysopposestheflowofcurrentinmotoroperationitis calledbackemf. 5.Under whatconditionthemechanicalpowerdevelopedinadcmotorwill bemaximum?
Conditionformechanicalpowerdevelopedtobemaximumis
Eb =Ua /2
or Ia= Ua /2Ra 6.What isthefunctionof ano-voltagereleasecoilprovidedina dcmotorstarter?
AslongasthesupplyvoltageisonhealthyconditionthecurrentthroughtheNVRcoil
produceenoughmagneticforceofattractionandretainthestarterhandleintheONposition
againstspringforce.Whenthesupplyvoltagefailsorbecomeslowerthanaprescribedvalue,
theelectromagnetmay nothaveenoughforceandthehandlewillcomebacktoOFFposition due
tospringforceautomatically.Thusano-voltageorundervoltageprotectionsgiventothemotor.
7.Namethetwotypesofautomaticstartersusedfordcmotors.
Backemftypestarter
Time delaytypestarter.
8.Enumeratethefactorsonwhichthespeedofadcmotordepends.
N=1/CE (Ua-IaRm)/ф Thespeedofdcmotor depends onthreefactors. Fluxintheairgap
Resistanceofthearmaturecircuit
Voltageappliedtothearmature
9.Listthe differentmethodsofspeedcontrolemployedfordcseriesmotor(APR’04,AU)
Fielddivertermethod
38
Regroupingoffieldcoils Tappedfieldcontrol
Armatureresistancecontrol
Armaturevoltagecontrolfor singlemotor
Seriesparallelcontrolformultiple identicalmotors.,
10.DrawtheNVsEb characteristics of a dcmotorfortwodifferentfieldcurrents.
11.Namethedifferentmethodsof electricalbreakingof dcmotors.
(i) Dynamicbraking (ii) Regeneratingbraking
(ii) Countercurrentbrakingorplugging
12. Towhat polaritytheinterpolesexcitedindcmotors?
Formotoroperationthepolarityof theinterpolesmustbethat of the
previousmainpolealongthedirectionofrotation.
14.Drawthetorquecharacteristics ofashuntmotor..(NOV’03,AU) N Ia
15. Drawthetorquecharacteristicsofaseries motor.
N (RPM)
39
I (amps)
16.Nameany four applicationsofDCseriesmotor.Electric traction
Mixies
Hoists
Drillingmachines
17. Why DCmotorsarenot operatedtodevelopmaximum powerinpractice?
Thecurrent obtainedwillbemuchhigher thantheratedcurrent. Theeffiency ofoperationwill
be below50%.
18. Namethestartersusedfor seriesmotors.Face platetype.
Drum typecontroller.
19.NameDifferenttypesof starters.
1. Three pointstarter
2. Four pointstarter.
20.NametheProtectivedevicesinastarter.
1, Novoltrelease
2. OverloadRelease.
21.Drawtorquecharacteristics of shuntmotor
T
Ig
22. WhatarethemodificationinwardLeonardlinger system?
1. Smallermotorandgenerator set
2. Additionof flywheelwhosefunction istoreducefluctuationsinthe power
demandfromthesupplycircuit.
23. Whattype of DCmotorsaresuitablefor varioustorqueoperations?
1. DCseriesmotor
2. DCcumulativelycompoundmotor.
40
24. Definespeedregulation.
%Speedregulation=NL speed-FLspeedx100
FLspeed
25. Whatarethe performancecurves?
OutputVstorque
OutputVscurrent OutputVsspeedOutputVsefficiency
26. Towhatpolarity aretheinterpolesexcitedindcgenerators?
Thepolarityoftheinterpolesmustbethatofthenextmainpolealongthedirectionofrotationint
he caseofgenerator.
27. Whyarecarbonbrushespreferredfor dcmachines?
The high contact resistance carbon brushes help the current in the coil
undergoingcommutation
toattainitsfullvalueinthereversedirectionattheendofcommutation.Thecarbon
brushesalsolubricate andgivelesswear andtearoncommutator surface.
28. Whatarethevarioustypes ofcommutation?
Linear commutation
Sinusoidalcommutation.
29. Namethetwomethodsofimproving commutation.
(i) Emfcommutation.
(ii) Resistance commutation
30. Whatisreactanceemfindcmachine?
Theself-
inducedemfinthecoilundergoingcommutationwhichopposesthereversalofcurrentisknownasre
actanceemf.
31. Definethetermcommutationindcmachines.
Thechangesthattakeplaceinwindingelementsduringtheperiodofshortcircuitbya brushiscalled
commutation.
32. Howandwhythecompensating winding indcmachineexcited?
41
Asthecompensationrequiredisproportionaltothearmaturecurrentthecompensatingwindingis
excitedby thearmaturecurrent.
16 Marks Important Questions
UNIT-I
MAGNETIC CIRCUITS AND MAGNETIC MATERIALS
1. In arectangular electromagneticrelay, the exciting coil has 1200 turns.
2. CrosssectionalareaofthecoreisA=6cm×6cm.neglectthereluctanceofthemagnetic
circuitandfringingeffects. With coilcurrentkeptconstantat2A,
deriveexpressionforforceonarmatureasafunctionofairgapoflengthx.Findtheworkdone
bythemagneticfieldwhenxdecreasesfrom1 cmto0.5cm byintegrating theforce.
3. Comparestatically induced emf anddynamicallyinducedemf?
4. Discussthe originof hysteresisandeddy currentlossesinelectricalmachines.
5. Astraightconductorof2mlengthcarriesacurrentof20A.Itislyingatrightanglestoa
uniformmagneticfluxdensityof0.8T.Find:(1)theforcedevelopedontheconductor(2)the
powerrequiredtodrivetheconductoratauniformspeedof25m/sand(3)theemfinducedint
heconductor.
6. ExplaintheACoperationof magneticcircuitinelectricalmachines.
7. Compare the various magnetic materials?
8. Derive the expression of the flux, reluctance of the magnetic material with air
gap.
9. Derive the inductance, energy and power of a magnetic circuit with two
windings.
10. Differentiate between Electric and magnetic circuits.
11. Explain with a neat diagram the B-H curve.
UNIT II
TRANSFORMERS
1. Whatarethetestsrequiredtodrawtheequivalentcircuitof
aSinglephaseTransformer?Howtheyare Conducted?(Nov–02)
2. Draw phasordiagramtorepresentconditionsinasingle-phasetransformer-supplying
loadat
1.Unityp.f, 2.Lagging p.f 3.Leading p.f(Nov-02).
3. ExplaintheBacktobackmethodof testingof twoidenticalsingle phasetransformers
4. Explaintheconstructionandprincipleofoperationof single phasetransformer.
5. Deducetheequivalentcircuitof aTransformer.
6. Derivetheemf equationoftheTransformer.
7. Listthelosses,whichoccurinaloaded transformer.Deducethe relationshipbetween
lossesfor
maximumefficiency.
42
8. Derivetheconditionformaximum efficiencyof a Transformer .
9. Explainthetypesof testing of transformer.
10. ExplaintheConstructionof3phaseTransformer.
11. Describethevariousthree phasetransformer connections.
12. Explain the operation of transformer in no load and loaded condition with phasor
diagram.
13. Draw the equivalent circuit of a transformer and derive the components with respect
to primary side.
14. What is sumpner’s test? Draw the circuit diagram to conduct the test.
15. What are the various losses of the transformers and give its efficiency.
16. A 120kVA, 6000/400V, Y/Y, 3-phase, 50Hz transformer has a iron loss of 1800W.
The maximum
efficiency occurs at ¾ full loads. Find the efficiency of the transformer at
a. Full load and 0.8 pf
b. The maximum efficiency at unity pf.
17. The emf per turn of a single phase, 6.6kV/440V, 50 Hz transformer is
approximately 12V. Calculate the number of turns in the HV and LV windings and
the net cross sectional area of the core for a maximum flux density of 1.5T.
18. Obtain the equivalent circuit of a 200/400V, 50Hz, single phase transformer from
the following test
data:
a. OC test: 200V, 0.7A, 70W on LV side
b. SC test: 15V, 10A, 85W on HV side.
19. The maximum efficiency of a single phase 250kVA, 2000/250 V transformer
occurs at 80% of full load and is equal to 97.5% at 0.8 pf .determine the efficiency
and regulation on full load at 0.8pf lagging if the impedance of the transformer is
9%.
20. A11000/230 V,150 KVA ,1-phase ,50 Hz transformer has core loss of 1.4kW and
F.L cu loss of 1.6 Kw .determine the kVA load for maximum efficiency and the
value of maximum efficiency at unity p.f and the efficiency at half F.L 0.8 pf
leading.
UNIT III
ELECTROMECHANICAL ENERGY CONVERSION AND
CONCEPTS IN ROTATING MACHINES
1. Derive the expression for field energyproduced in a doublyexcited magnetic
fieldsystem?
43
2. Themagneticfluxdensityonthesurfaceofanironfaceis1.6Twhichisatypicalsaturationle
velvalueforferromagneticmaterial.Findtheforcedensityon theironface.
3. Whatarethespecialapplicationswheretheelectricfieldisusedasacouplingmedium for
electromechanicalenergyconversion?Alsoexplainwhyelectricfieldcouplingis
preferredinsuchapplications?
4. Findanexpressionfortheforceperunitareabetweentheplatesofaparallelplatecondenserintermsoftheelectricfieldintensity.Useboththeenergyandcoenergymethods.FindthevalueoftheforceperunitareawhenE=3x10
6 V/m,thebreakdownstrength ofair.
5. Explainwithneatdiagramandsufficientexpressions,themultiplyexcitedmagneticfields
ystems.
6. Explain the i-λ characteristics of a magnetic system .also derive expression for co
energy density assume the i-λ relationship of the magnetic circuit is linear
7. Explaintheconcept of singly–excitedmachinesandderivetheexpressionfor the
electromagnetictorque.
8. Two coupled coils have self and mutual inductance of L11=2+1/(2x); L22=1+1/(2x):
L12= L21=1/(2x). Over a certain range of linear displacement x. The first coil is
excited by a constant current of 20A and the second by a constant current of -10A.
a. Mechanical work done if x changes from 0.5to1m
b. Energy supplied by each electrical source in part 1
c. Change in field energy in part1
Hence verify that the energy supplied by the sources is equal to the increase in field
energy plus the mechanical work done.
9. Consider an attracted armature relay is exited by an electric source. Explain about
the mechanical force developed and the mechanical energy output with necessary
equations. For linear and non linear cases.
10. Two coupled coils have self and mutual inductance of L11 = 3+0.5 x ;L22 = 2+0.5x
; L12= L21=0.3x Over a certain range of linear displacement x. The first coil is excited by
a constant current of 15A and the second by a constant current of -8A.
(i)Mechanical work done if x changes from 0.6 to 1m
(ii)Energy supplied by each electrical source in part 1.
11. Derivetheexpressionforthe r.m.svalue of emf inducedina.c.machines
12. Provethatmmfwaveofasinglephaseacwinding is pulsatingorstanding
13. Provethattheresultantmmfwaveofthreephaseacwindingisrotatinginspacewithspeed
butitsmagnitude isconstant.
14. Derivethetorqueequationfor roundrotormachine
15. Explainthe variousconceptsofmagneticfieldsinrotating machines
16. Explainwithneatdiagramtheconcept ofmmfspacewaveofasinglecoil.
17. Write indetailaboutmmfspacewave ofthree phase distributedwinding.
18. 18. A 50 Hz , 400v, 4-pole cylindrical synchronous generator has 36slots, two –
layer Winding with full pitch coils of 8 turns each. The mean air –gap diameter is
0.16m, axial length 0.12m and a uniform air gap of 2mm. calculate the value of the
resultant AT/pole and the peak air gap flux density. The machine is developing an
electromagnetic torque of 60 Nm as a generator at a torque angle of 260. What
44
should be the rotor AT/pole? What is the stator AT and the angle it makes with the
resultant AT? Also find the stator current.
19. A 3-phase 50 kW, 4-pole, 50 Hz induction motor has a winding (ac) designed for
delta connection. The winding has 24 conductors per slot arranged in 60 slots. The
rms value of the line current is 48A. find the fundamental of the mmf wave of phase
–A when the current is passing through its maximum value . What is the speed and
peak value of the resultant mmf/pole?
20. 3-phase ,400 kVA ,50 Hz star connected alternator (synchronous generator)
running at 300 rpm is designed to develop 3300 V between terminal .the
armature consists of 180 slots , each slot having one coil side with 8
conductors. Determine the peak value of the fundamental mmf in AT/pole
when the machine is delivering full load current.
UNIT IV
DC GENERATORS
1. Explain various methods of commutation.(AU,APR’03)
2. Derive the emf equation of a generator.(AU,NOV’03)
3. Draw the performance characteristics of different types of DC generator.
(AU,NOV’03).
4. Explain the constructional details of DC generator.(AU,APR’04)
5. Draw the circuit diagrams for separately excited and self excited series generator.
(AU,APR’04)
6. How armature reaction takes place in DC generator.
7. Explain the DC generator parallel operation with neat diagrams.
8. Explain the different types of excitation in DC generator.
9. Draw the performance characteristics of DC series generator.
10. Draw the performance characteristics of compound DC generator.
11. A 4 pole, lap wound 750 r.p.m. d.c shunt generator has an armature resistance of
0.4
ohm and field resistance of 200 ohm. The armature has 720 conductors and the flux
per
pole is 30mWb. If the load resistance is 15 ohm, determine the terminal voltage.
UNIT V
DC MOTORS
1. Draw the diagram of a 3 point starter and explain.(NOV’03,AU)
2. Explain the different methods of speed control.(NOV’04,AU)
3. What is meant by speed control of a DC motor? Explain the various methods in detail.
(NOV’03, AU)
4. With neat sketch, explain the function of 3 point starter.(APR’06,AU)
45
5. Explain the principle of operation of DC motor.
6. Classify the types of DC motor and write the voltage equation for the same.
7. Draw and explain the characteristic of DC series motor and shunt motor.
8. Draw and explain the characteristic of DC compound motor.
9. Draw the diagram of a 4-point starter and explain.
10. Mention the main parts of DC motor and explain each part with neat sketch.
11. A 230V, DC shunt motor, takes an armature current at 3.33A at rated voltage and at
a no load speed of 1000RPM. The resistances of the armature circuit and field circuit
are 0.3 Ώ and 160 Ώ respectively. The line current at full load and rated voltage is
40A. Calculate, at full load, the speed and the developed torque in case the armature
reaction weakens the no load flux by 4%.
12. A 220V, Dc shunt motor with an armature resistance of 0.4 Ώ and a field resistance
of 110 Ώ drives a load, the torque of which remains constant. The motor draws from
the supply, a line current of 32A when the speed is 450 RPM. If the speed is to be
raised to 700RPM, what change must be effected in the value of the shunt field
circuit resistance? Assume that the magnetization characteristics of the motor are a
straight line.
13. Determine developed torque and shaft torque of 220V, 4 pole series motor with 800
conductors wave-connected supplying a load of 8.2 kW by taking 45A from the
mains. The flux per pole is 25m/Wb and its armature circuit resistance is 0.6Ώ.
14. A 4-pole, 50 kW, 250 V, wave wound shunt generator has 400 armature conductors.
Brushes are given a lead of 4 Commutator segments. Calculate the demagnetization
ampere-turns per pole if shunt field resistance is 50 ohm. Also calculate extra shunt
field turns per pole to neutralize the demagnetization.
15. A 4-pole, lap connected DC machine has 540 armature conductors. If the flux per
pole is .03 Wb and runs at 1500 RPM, determine the emf generated. If this machine
is driven as a shunt generator with same field flux and speed, calculate the line
current if the terminal voltage is 400V.Given the RSH=450Ώ and RA=2 Ώ.
ELECTROMAGNETIC THEORY
UNIT I
INTRODUCTION
1. Define scalar field?
46
A field is a system in which a particular physical function has a value at
each and every point in that region. The distribution of a scalar quantity with a
defined position in a space is called scalar field.
Ex: Temperature of atmosphere.
2. Define Vector field?
If a quantity which is specified in a region to defined a field is a vector
then the corresponding field is called vector field.
3. Define scaling of a vector?
This is nothing but, multiplication of a scalar with a vector. Such a multiplication
changes the magnitude of a vector but not the direction.
4. What are co-planar vector?
The vectors which lie in the same plane are called co-planar
vectors.
5. What is an identical vector?
Two vectors are said to be identical if there difference is zero.
Thus A and B are
identical if A B 0, i.e, A B . Such two vectors are also called as equal
vectors.
6. Define base vectors?
The base vectors are the unit vectors which are strictly oriented along the directions
of the coordinate axes of the given coordinate system.
7. What is a position vector?
Consider a point p(x, y, z) are Cartesian coordinate system. Then the position
vector of point p is represented by the distance of point p from the origin directed from
origin to point. This is also called as radius vector.
8. Define scalar product of vectors?
The scalar of the two vectors Aand B is denoted as A.B and defined as the
product of the magnitude of A and magnitude of B and the cosine of angle between
them.
47
A.B A B cos AB
9. Define Divergence.
Divergence is defined as the net outward flow of the flux per unit volume
over a closed incremental surface.
10. State Divergence Theorem.
The integral of the normal component of any vector field over a closed surface is
equal to the integral of the divergence of this vector field throughout the volume enclosed
that closed surface.
13. What is physical significance of curl of a vector field?
Curl gives rate of rotation. Curl F gives work done per unit area.
14. What is physical significance of divergence?
Divergence of current density gives net outflow of current per unit volume
.Divergence of flux density gives net outflow per unit volume. In general, divergence
of any field density gives net outflow of that field per unit volume.
15. State the conditions for a field to be a) solenoidal b) irrotational.
a) Divergence of the field has to be zero.
b) Curl of the field has to be zero.
16. Define scalar and vector quantity?
The scalar is a quantity whose value may be represented by a single real
number which may be positive or negative.e.g, temperature, mass, volume,
density
A quantity which has both a magnitude and a specified direction in space is
called a vector.e.g.force, velocity, displacement, acceleration.
17. How to represent a vector.
A vector can be represented by a straight line with an arrow in a plane. The length
of the segment is the magnitude of a vector while the arrow indicates the direction of a
vector. OA
18. What is a unit vector? What is its function while representing a vector?
48
A unit vector has a function to indicate the direction. Its magnitude is always
unity, irrespective of the direction which it indicates and the coordinate system under
consideration.
19. Name 3 coordinate systems used in electromagnetic engineering?
1) Cartesian or rectangular coordinate system.
2) Cylindrical coordinate system.
3) Spherical coordinate system.
20. How to represent a point in a Cartesian system?
A point in rectangular coordinate system is located by three coordinates namely x,
y and z coordinates. The point can be reached by moving from origin, the distance x in x
direction then the distance y in y direction and finally z in z direction.
21. What is separation of vector?
The distance vector is also called as separation vector. Distance vector is nothing
but the length of the vector.
22. State the relation between Cartesian and cylindrical coordinate system?
x r cos
y r sin
z z
23. Show how a point p represented in a spherical coordinate system.
The point p can be defined as the intersection of three surfaces in
spherical coordinate system.
r - Constant which is a sphere with centre as origin
θ – Constant which is a right circular cone with apex as origin and axis as
z axis. Φ – Constant is a plane perpendicular to xy plane.
24. State the relationship between Cartesian and spherical system?
x=r sin θ cos Φ
y= r sin θ sin
Φ z=r cos θ
Now r can be expressed as
49
x2 + y2 + z2 = r2 sin2 θ cos2 Φ + r2 sin2 θ sin2 Φ + r2 cos2 θ
= r2 sin2 θ [sin2 Φ + cos2 Φ] + r2 cos2 θ
= r2 [sin2 θ + cos2 θ]
= r2
25. What is dot product?
Dot product is also called as scalar product. It is defined as the product of the
magnitude of A and magnitude of B and cosine of the smallest angle between them.
A.B | A || B | cos ABan
26. State dot product properties.
1) It obeys commutative law. A.B B.A
2) It obeys distributive law. A.( B C) A.B A.C
3) If the dot product with itself is performed the result is square of the magnitude
of that vector A.A | A | 2
4) Any unit vector dotted with itself is unity. ax.axay.ay 1
27. What is called as cross product?
Cross product is also called as vector product. It is defined as the product
of the magnitude of A and magnitude of B and sine of the smallest angle between
them.
A B |A || B | sin ABan
28. State cross product properties.
1) Cross product is not
cumulative i.e. A B B A
2) Reversing the order of vectors, reverse its
direction. A B | B || A |
29. Give the application of dot products.
1. To determine the angle between the two vectors,
cos A.B
50
| A || B |
2. To find the component of a vector in a given direction.
30. Give the application of cross product.
1) The cross product is used to determine the direction of force.
2) Another physical quantity which can be represented by cross product is moment
of force.
31. State scalar triple product properties.
1) The scalar triple product is distributive.
2) If two of the three vectors are equal then the result of the scalar triple product is
zero.
32. Define vector triple product.
The vector triple product of the three vectors A, B, C are mathematically defined
as,
33. Convert Cartesian to cylindrical system.
Ar cos sin 0 Ax
A sin cos
0 A
y
1z
Az 0 0
A
34. Transform the Cartesian system into spherical system.
Ar sin cos sin sin cos Ax
A cos cos cos sin sin Ay
sin cos
51
Az 0 Az
35. What are the types of integral related to electromagnetic theory?
1. Line integral
2. Surface integral
3. Volume integral
UNIT II
ELECTROSTATICS
1. Define point charge.
A point charge means that electric charge which is separated on a surface or space
whose geometrical dimensions are very very small compared to other dimensions, in
which the effect of electric field to be studied.
2. Define one coulomb.
One coulomb of charge is defined as the charge possessed by (1/1.602x10-9) i.e
6x1018 number of electrons.
3. State Coulomb’s law.
The coulomb’s law states that force between the two point charges Q1 and Q2
i) Acts along the line joining the two point charges
ii) is directly proportional to the product of the charges
iii) is inversely proportional to the square of the distance between them.
F=Q1Q2
R 2
4. Define constant of proportionality (K).
52
It is defined as k41 where is the permittivity of medium in which charges are located.
where 0 r. Where p-position of any other charge around Q1
5. What is an equipotential surface?
An equipotential surface is an imaginary surface in an electric field of a
given charge distribution, in which all points on the surface are at the same
electric potential.
6. What is an electric flux?
The total number of lines of force in any particular electric field is called electric
flux.
It is represented by the symbol Similar to the charge, unit of electric flux is also Coulomb.
7. Define electric flux density.
The net flux passing normal through the unit surface area is called electric flux
density. It
is denoted as D . It has a specified direction which is normal to the
surface area under consideration hence it is a vector field.
8. State Gauss’s Law.
The electric flux passing through any closed surface is equal to the total
charge enclosed by that surface.
9. State the application of Gauss’s law.
1) The Gauss’s law can be used to find E and D for symmetrical charge
distributions.
2) It is used to find the charge enclosed or the flux passing through the closed
surface.
10. State the applications of Poisson’s equation and Laplace’s equation.
1) To obtain potential distribution over the region.
2) To obtain E in the region.
3) To check whether given region is free of charge or not.
4) To obtain the charge induced on the surface of the region.
53
11. Define current density.
The current density is defined as the current passing through the unit surface area,
when
the surface is held normal to the direction of the current. The current density is
measured in A/m2.
12. Define a current and its unit Ampere.
The current is defined as the rate of flow of charge and is measured as Ampere’s.
A current of 1 Ampere is said to be flowing across the surface when the
charge of 1 coulomb is passing across the surface in 1 second.
13. What is drift current and convection current?
The current constituted due to the drifting of electrons in metallic conductor
is called drift current.
While in dielectrics, there can be flow of charges, under the influence of
electric field intensity. Such a current is called convection current.
14. What is Polarization?
The applied field E shifts the charges inside the dielectric to induce the electric
dipoles.
This process is called Polarization.
15. What is Polarization of Dielectrics?
Polarization of dielectric means, when an electron cloud has a centre separated
from the nucleus. This forms an electric dipole. The dipole gets aligned with the applied
field.
16. State the point form of Ohm’s law.
The relationship between JandE can also be expressed in terms of conductivity of
the material. Thus for metallic conductor,
Where - conductivity of material. And the equation is called point form of Ohm’s law.
17. What is Boundary conditions means?
The conditions existing at the boundary of the two media when field
passes from one medium to other are called boundary conditions.
54
18. How is electric energy stored in a capacitor?
In a capacitor, the work done in charging a capacitor is stored in the form of
electric energy.
19. What is a capacitor?
A capacitor is an electrical device composed of two conductors which are
separated through a dielectric medium and which can store equal and opposite
charges ,independent of whether other conductors in the system are charged or not.
20. Define dielectric strength of a dielectric?
The minimum value of the applied electric field at which the dielectric breaks
down is called dielectric strength of that dielectric.
UNIT III
MAGNETOSTATICS
1. Define Magnetic flux density.
The total magnetic lines of force i.e. magnetic flux crossing a unit area in a plane
at right angles to the direction of flux is called magnetic flux density. It is denoted as B
.Unit Wb/m2.
2. State Ampere’s circuital law.
The line integral of magnetic field intensity H around a closed path is exactly
equal to the direct current enclosed by that path.
The mathematical representation is H.dL I .
3. Define Magnetic field Intensity.
Magnetic Field intensity at any point in the magnetic field is defined as the
force experienced by a unit north pole of one Weber strength, when placed at that
point. Unit: N/Wb
(or) AT /m.It is denoted as H .
4. Define Inductance.
In general, inductance is also referred as self inductance as the flux
produced by the current flowing through the coil links with the coil itself.
55
5. What is fringing effect?
If there is an air gap in between the path of the magnetic flux, it spreads and bulges
out.
This effect is called fringing effect.
6. What are boundary conditions?
The conditions of the magnetic field existing at the magnetic field existing at the
boundary of the two media when the magnetic field passes from one medium to other
are called boundary conditions.
7.Define self inductance.
Self inductance is defined as the rate of total magnetic flux linkage to the currentthrough
the coil.
8. State Biot Savart Law.
The Biot Savart law states that, The magnetic field intensity dH produced at a point
p due to a differential current element IdL is
1) Proportional to the product of the current I and differential length dL
2) The sine of the angle between the element and the line joining point p to the
element
3) And inversely proportional to the square of the distance R between point p and
the element
9. What is Magnetostatics?
The study of steady magnetic field, existing in a given space, produced due to
the flow of direct current through a conductor is called Magnetostatics.
10. What is Magnetic Field?
The region around a magnet within which influence of the magnet can be
experienced is called Magnetic Field.
11. What are Magnetic Lines of Force?
The existence of Magnetic Field can be experienced with the help of compass
field. Such a field is represented by imaginary lines around the magnet which are
called Magnetic Lines of Force.
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12. Give the relation between Magnetic flux and Flux density.
The relation between Magnetic flux and flux density is obtained through the
property of medium and permeability . This is given by,
13. Give Gauss’s law in differential form for magnetic fields.
The divergence of magnetic flux density is always zero.
14. Define scalar magnetic Potential.
The scalar magnetic potential Vm can be defined for source free region
where J i.e. current density is zero.
15. Define Mutual inductance.
The mutual inductance between the two coils is defined as the ratio of flux linkage
of one coil to the current in other coil. Thus the mutual inductance between circuit 1 and
circuit 2 is given by
16. What is Magnetization?
The field produced due to the movement of bound charges is called Magnetization
represented by M .
17. Define Reluctance.
Reluctance R is defined as the ratio of the magneto motive force to the total flux.
R em And it is measured as Ampere-turn/Weber.
18. What is Lorentz force equation?
Lorentz force equation relates mechanical force to the electrical force. It is
given as the total force on a moving charge in the presence of both electric and
magnetic fields.
F Fe Fm N .
19. Define Moment of force.
The Moment of a force or torque about a specified point is defined as the vector
product of the moment arm R and the force F . It is measured in Nm.
T R FNm .
U
57
20. Define Magnetic dipole moment.
The Magnetic dipole moment of a current loop is defined as the
product of current through the loop and the area of the loop, directed normal
to the current loop.
21. Give any two dissimilarities between electric and magnetic circuits.
1) In electric circuit the current actually flows i.e. there is a movement of
electrons whereas in magnetic circuit, due to m.m.f, flux gets established and doesn’t
flow in the sense in which current flows.
2) The electric lines of flux are not closed. They start from positive charge and
end on negative charge and the magnetic lines of flux are closed lines.
22. Define current density.
Current density is defined as the current per unit area.
J= I/A Amp/m2
UNIT IV
ELECTRODYNAMIC FIELDS
1. State Ampere’s Circuital law.
The line integral of magnetic field intensity H around a closed path is exactly
equal to the direct current enclosed by that path.
The mathematical representation is
2..State Maxwell equation I.
The MMF around a closed path is equal to the sum of the conduction current and
displacement current enclosed by the path.
3.State Maxwell’s Equation II.
The EMF around a closed path is equal to the magnetic displacement(flux density)
through that closed path.
4.Define Electric Gauss law.
It states that electric flux through any closed surface is equal to the charge
enclosed by the surface.
5. State Maxwell’s Equation III.
The total electric displacement through the surface enclosing a volume is equal to
the total charge within the volume.
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6.Define Magnetic Gauss law.
It states that the total magnetic flux through any closed surface is equal to zero.
7.Define conduction current density.
The conduction current current per unit area is known as conduction current density.
8.What is displacement flux density?
The electric displacement per unit area is known as electric displacement flux density or
electric flux density.
9.State poynting Theorem.
The net power flowing out of a given volume is equal to the time rate of decrease of the
energy stored within the volume conduction losses.
10.Define pointing Vector.
The poynting vector is defined as rate of flow of energy of a wave as it propagates.
P=ExH
UNIT V
ELECTROMAGNETIC WAVES
1. Define a wave.
If a physical phenomenon that occurs at one place at a given time is
reproduced at other places at later times , the time delay being proportional to
the space separation from the first location then the group of phenomena
constitutes a wave.
2. Mention the properties of uniform plane wave.
i) At every point in space ,the electric field E and magnetic field H are
perpendicular to each other.
ii)The fields vary harmonically with time and at the same frequency
everywhere in space. 3.Define intrinsic impedance or characteristic impedance.
It is the ratio of electric field to magnetic field. or It is the ratio of
square root of permeability to permittivity of medium.
3.Define propagation constant.
Propagation constant is a complex number, Where is propagation constant
59
4.Define skin depth
It is defined as that depth in which the wave has been
attenuated to 1/e or approximately 37% of its original value.
5.Define Poynting vector.
The pointing vector is defined as rate of flow of energy of a
wave as it propagates. P =E X H
6. State Poyntings Theorem.
The net power flowing out of a given volume is equal to the time rate of decrease
of the the energy stored within the volume- conduction losses.
7. State Maxwell’s fourth equation.
The net magnetic flux emerging through any closed surface is zero.
8. State Maxwell’s Third equation
The total electric displacement through the surface enclosing a volume is
equal to the total charge within the volume.
9. Define loss tangent.
Loss tangent is the ratio of the magnitude of conduction current
density to displacement current density of the medium.
10.What will happen when the wave is incident obliquely over dielectric –
dielectric boundary?
When a plane wave is incident obliquely on the surface of a perfect dielectric
part of the energy is transmitted and part of it is reflected .But in this case the
transmitted wave will be refracted, that is the direction of propagation is altered.
11.What is the fundamental difference between static electric and
magnetic field lines?
There is a fundamental difference between static electric and magnetic field
lines. The tubes of electric flux originate and terminates on charges, whereas
magnetic flux tubes are continuous.
12.What are uniform plane waves?
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Electromagnetic waves which consist of electric and magnetic fields that are
perpendicular to each other and to the direction of propagation and are uniform in plane
perpendicular to the direction of propagation are known as uniform plane waves.
13.What is the significant feature of wave propagation in an imperfect dielectric ?
The only significant feature of wave propagation in an imperfect dielectric
compared to that in a perfect dielectric is the attenuation undergone by the wave.
14. Define power density.
The power density is defined as the ratio of power to unit area.
Power density=power/unit area.
15. What is called wave velocity?
The velocity of propagation is called as wave velocity. It is denoted as .
For free space it is denoted by c and its value is 3x108m/s.
16. What is called as intrinsic impedance?
The ratio of amplitudes of EandH of the waves in either direction is called
intrinsic impedance of the material in which wave is travelling. It is denoted by .
17. Why dielectric medium is lossless dielectric.
For perfect dielectric medium, both the fields EandH are in phase. Hence
there is no attenuation .Hence there is no loss.
18. What is mean by lossy dielectric?
The presence of attenuation indicates there is a loss in the medium. Hence such
medium is called as lossy dielectric.
19. What is mean by skin depth?
The distance through which the amplitude of the travelling wave decreases to
37% of the original amplitude is called skin depth or depth of penetration.
20. What is called skin effect?
For the frequencies in the microwave range, the skin depth or depth of penetration
is very small for good conductors and all the fields and currents may be considered as
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confined to a thin layer near the surface of the conductor. This thin layer is nothing but
the skin of the conductor and hence it is called skin effect.
21. What is Normal Incidence?
When a uniform plane wave incidences normally to the boundary
between the media, then it is known as normal incidence.
22. What is normal Incidence?
When a uniform plane wave incidences obliquely to the boundary
between the media, then it is known as normal incidence.
23. What is called attenuation constant?
When a wave propagates in the medium, it gets attenuated. The amplitude of
the signal reduces. This is represented by attenuation constant . It is measured in neper
per meter (NP/m). But practically it is expressed in decibel (dB).
24. What is phase constant?
When a wave propagates, phase change also takes place. Such a phase
change is expressed by a phase constant . It is measured in radian per meter
(rad/m).
25. Define standing wave ratio.
The standing wave ratio is defined as the ratio of maximum to minimum amplitudes of
s
E
voltage.
1s m
ax .
E
1s m
in
26. What is the condition for practical dielectric?
Fir practical dielectric, there is some conductivity, that is its value is not zero
and hence there is some loss in practical dielectric but its value is very small.
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QUESTION BANK
UNIT-I INTRODUCTION
1. What are the different types of Coordinate systems? Explain any one of them.
2. Define Divergence Theorem and Prove the Theorem.
3. Define Stokes Theorem and Prove the Theorem.
4. Explain briefly about the Sources and effects of electromagnetic fields.
5. i) Show that the Vector H 3y4za2x 4x3z2ay 3x2y2azis solenoid .
ii) Show that the Vector 2xy ax+(x2 +2yz) ay+(y2 +1) az is irrotational.
6 i) Prove that . xH 0
ii) Prove that x V0
7. Prove the identity x xH( .H)2H ,Where H is a Vector.
8. Transform the vector field W10 ax- 8ay6az to cylindrical coordinate system at point P
(10,-8, 6).
UNIT-II ELECTROSTATICS
1. Derive the expression for electric field intensity due to infinite line charge.
2. Derive the expression for electric field intensity due to infinite charge.
3. Derive the expression for electric field intensity due to infinite circular ring of charge.
4. State Gauss‟ s law and explain any two applications.
5 .i) Derive the expression for energy stored in a Capacitor.
ii) Explain Poisson‟ s and Laplace equations.
6. Derive the boundary conditions at the charge interface of two dielectric media.
7. The charge is distributed along the z-axis from z=-5 m to -∞ and from z=+5 m to +∞
with a charge density of 20nC/m. Find electric field intensity at (2,0,0)m.
8. Four point charges each of 10µC are placed in free space at the points (1, 0, 0),
63
(-1,0,0),(0,1,0) and (0,-1,0)m respectively. Determine the force on a point charge o 30
µC located at a point (0,0,1)m.
9. Derive the expression for composite parallel plate capacitor.
10. Derive the expression for energy stored and energy density in electrostatic fields.
11. Derive the expression for capacitance between two co-axial cylinders of radii
“a”(inner) and “b” (outer) respectively.
UNIT-III MAGNETOSTATICS
1. Derive an expression for the magnetic field intensity at a point „P‟ in a medium of
permeability „ „due to an infinitely long current carrying conductor at a distance „r‟
meters from the point.
2. State Ampere‟ s Circuital law and explain any two applications.
3. Obtain the boundary conditions of normal and tangential components of magnetic
field at the interface of two media with different dielectrics.
4. Explain Biot‟ s Savart law in vector form.
5. Derive the expression for Magnetic Scalar and Vector Potential.
6. Derive the expression for inductance of solenoid and toroid.
7. Derive the expression for magnetic force between two parallel conductors.
8. Derive the expression for energy stored in magnetic fields and its energy.
UNIT-IV ELECTRODYNAMIC FIELDS
1. Briefly explain Maxwell‟ s Equation-I
2. Explain the Maxwell‟ s Equation derived from Faraday‟ s Law
3. Explain Maxwell‟ s Equation-III and Maxwell‟ s Equation-IV.
4. Compare Field Theory and Circuit Theory.
5. Derive the expression for Displacement Current .
6. Derive the Maxwell‟ s Equations in Free space.
7. Derive the Maxwell‟ s Equations in phasor form.
8. For 1A conductor current in copper wire find the corresponding displacement current
at 100MHz.Assume for copper 5.8x107mho/m .
UNIT-V ELECTROMAGNETIC WAVES
1. Derive the electromagnetic wave equation for electric fields and magnetic fields.
2. Explain the Wave propagation in Lossy medium.
3. Explain the Wave propagation in Lossless medium.
4. State and prove Poynting theorem.
5. Define Brewster angle and derive its expression.
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6. Obtain the expression for the reflection co-efficient and transmission coefficient for
a wave normally incident on the surface of the dielectric.
7. Find the skin depth at a frequency of 2MHz in aluminum where
38.2x106mho / mand µr=1.
8. Obtain the expression for the reflection co-efficient and transmission coefficient for
a wave incident obliquely on the surface of the dielectric.
65
POWER PLANT ENGINEERING
UNIT-1THERMALPOWER PLANTS
1.Statethermodynamiclaw:
1. Zerothlawreferstothermodynamicequilibriumandtemperature
2.Firstlawreferstoheat,workandenergy
3.Secondlawreferstoentropy
2.Statezerothlawof thermodynamics:
“Twosystemsinthermal equilibriumwithathirdsystemareinthermal
equilibrium witheachother”
3. StateFirstlawof thermodynamicsandenergyconversion.
Thefirstlawofthermodynamicsisoften called asLawofconversionofenergy.This
lawsuggeststhat energycanbetransferredfromonesystemto
anotherinmanyforms. Also,itcannotbedestroyedorcreated.
4.Statesecondandthirdlawof thermodynamics:
Thesecondlawofthermodynamicsanotherstatevariablecalled entropy. Inany
closedsystem,theentropyofthesystemwill
eitherathermodynamicprocess,thesystem
cannevercompletelyreturnpreciselythesamestateitwasinbefore.
Thethirdlawofthermodynamicsstatesthat if all thethermalmotionof
molecules(kineticenergy)couldberemoved,astatecalled
absolutezerowilloccur. Absolutezeroresultsinatemperatureof0kelvinor-
273.15celcius.
5.Whatis thermodynamiccycle?
AThermodynamiccycle
isaseriesofthermodynamicprocessestransferringheat
andwork,whilevaryingpressure,temperature,andotherstatevariables,eventu
ally returningasystemtoitsinitial state.
66
6.Listthevariousthermodynamicprocesses:
1.Adiabaticprocess-aprocesswithnoheat transferintooroutofthesystem
2.Isochoricprocess-aprocesswithnochangeinvolume,insuchcasethesystem
doesnowork
3.Isobaricprocess-aprocesswithnochangeinpressure
4.Isothermalprocess-aprocesswithnochangeintemperature
7.Whatismeantbypowerplant? Powercanbedefinedastherateof flowofenergyandstatethat apowerplantisa
unitbuilt forproductionanddeliveryof a flowof mechanicalworkandelectrical
energy. Amachineor assemblingofequipmentthat producesanddeliversa
flowofmechanical andelectrical energyisapowerplant.
8.Listthefactorsof powerplantperformance.
Theperformanceofapowerplantcanbeexpressedthroughsomecommo
n performancefactors as
1.Heat rate
2.Capacityfactor
3.Economicefficiency
4.Load factor
5.Operationalefficiency
9.Whatareavailableenergysourcesforvariouspowerplants?
1.Conventionalenergysourcesor Non-renewableenergysources
2.NonconventionalenergysourcesorRenewableenergysources
10.Whatarethe majorpowerlimitationsof conventionalenergysources?
1.Resourcesforpowergenerationi.e, coal,gasetc., arelimited
2.Thehydropowerisseasonalandvariesdependingupontherainfallinth
e catchmentareas
3.Submersionoflandareadueto raiseinwaterlevel
4.Centralizedpowergenerationanddistributionofthesametolongdistanceswi
ll resultinhighlosses.
5.Theenergyconversionprocessfromthermalpowerprojectsresultsinemission
of greenhousegases
11.Listoutthevariousconventionalandnon conventionalpowerplant: Typesofconventionalpowerplant:
1.Hydropowerplant
2.Steampowerplant
67
3.Nuclearpowerplant
4.Gasturbinepowerplant
Typesofnon-conventionalpowerplant:
1.Tidalpowerplant
2.Windpowerplant
3.Geothermalpowerplant
4.Solarpowerplant
5.Wavepowerplant
6.MHDGeneration
12.Whatishydraulic/Pneumatictypeashhandlingsystem?
Thehydraulicsystemcarriedtheashwiththeflowofwaterhighvelocitythrougha
channelandfinallydumpsintoasump.Thehydraulicsystemisdividedintoalow
velocityandhighvelocitysystem.The advantagesofthissystemarethat its
clean,large ashhandlingcapacity,
considerabledistancecanbetraversed,absenceofworkingparts in contactwithash
Inpneumatictypeashhandlingisthemostpopularmethodusedinmediumlevel
powerplants.It
usesdensephaseconveyingsystemforconveyingashistotallyenclosed
withoutanyleakage.Thesystemcan conveymaterialsuptodistanceofaround200-250
mts.
13.Listthechallengesofashhandling: 1.Indiancoal containshighashcontentgenerallywhichtendstobeinconsistent.
2.Designofthesystemhasto adequatelycover
anticipatedvariationsandbecapable ofhandlingtheworstscenario
3.Systemhastobeenvironmentallyfriendly
4.Systemhastobeenergyefficient
14.Whatis crusheranditscrushingmethod? Acrusherisamachinedesignedtoreducelargesolidchunksofrawmaterialsiinto
smallerchunks.Crushersarecommonlyclassifiedbythedegreetowhichtheytragmen
t thestartingmaterial.
CrushingMethods:
1.Impact
2.Shear
3.Attrition4.Compression
15.Whatareall thetypesof Mechanicaldrafts? There arethreetypesof mechanicaldrafts:Theyare:
1.Induceddraft
2.Forceddraft
3.Balanceddraft
16.WhatisDeaeration?
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Mechanicalandchemicalldeaearationis
anintegralpartofmodernboilerwater
protectionandcontrol.Deaerationcoupledwithotheraspectsofexternal
treatment,providesthebest andhighestqualityfeedwaterforboileruse.
17.Whatis thepurposeof deaeration?
Thepurposeofdeaerationare:
1.Toremoveoxygen,carbondioxideandothernoncondensablegasesfr
om feedwater.
2.Toheat theincomingmakeupwaterandreturn condensateto
anpptimum temperature
3.Minimizingsolubilityofundesirablegases
4.Providingthehighesttemperaturewaterforinjectiontotheboiler.
18.Whatarethetypesof deaerators?
1.Tary-TypeDeaeratingheaters
2.Spray-TypeDeaeratingheaters
19.WhatismeantbycoolingTowers?
It isatowerorbuildinglikedeviceinwhichatmosphericaircirculatesindirector
indirectcontactwithwarmerwaterandwateristherebycooled.Coolingtowersmay
eitherusetheevaporationofwatertoremoveprocessheatandcooltheworkingfluid.
20.Listthetypesof coolingtowers: 1.Evaporativeor wet coolingtower
2.Nonevaporativeordrycoolingtower
(a)Air cooledcondensers(b)Aircooled exchangers
21.Listthetypesof coolingfunctionstocondensethesteam:
1.Once-throughwet cooling
2.Recirculatingwetcooling3.Drycooling
22.Listthefactorstobeconsideredwhilechoosingasiteforsteampowerstation: 1.Supplyoffuel
2.Availabilityofwater
3.Transportationfacilities
4.Costandtypeofland
5.Nearnesstoloadcentres
6.Distancefrompopulatedarea
23.Listthethermalpowerplantin Tamilnadu.
Alathiur(2*18MW),Tamilnadu,Madrascements
Ennore(2*60MW,3*110MW)TamilnaduElectricityBoard
Neyveli(6*50MW,2*100MW)TamilnaduNeyvelilignitecor
p Ltd.
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24.Definesuperheater: ASuperheaterisadeviceusedto convertsaturatedsteamintoadrysteam used
forpowergenerationorprosessessteamwhichhasbeensuperheatedisknownas
superheatedsteam.
25.Listthetypesof superheaters: 1.Radientsuperheater- absorbheat byradiation
2.Conventionsuperheater-absorbheat viaa fluid
3.Separatelyfixedsuperheaters-it istotallyseparatedfromtheboiler
UNIT-IIHYDRO ELECTRIC POWER PLANT
1.Writetheformulatocalculatethehydraulicpowerproducedbya
hydroturbine: Thehydraulicpowerisgivenbytheformula:
P=GpQH
WhereP isthehydraulicenergyinwatts
Gis
accelerationduetogravity(9.81M/s2)
P iswaterdensity
Qistheflowordischarge
Histheheightof fall of waterorheadinmeter.
2.Listanyfouradvantagesof hydropower:
1.Watersourceisperenniallyavailable
2.Runningcostisverylow
3.Non-polluting
4.Powergenerationcanbeswitchedonandoffinaveryshortperiod.
3.Listanyfourdisadvantagesof hydropower:
1.Highcapital investmentandlowrateof return
2.Gestationperiodisverylarge
3.Powergenerationdependsonavailabilityofwater
4.Transmissioncost andlossesarehigh
4.Listthefactorstobeconsideredfortheselectionof siteforhydropowerplant:
1.Availabilityofwaterandwaterhead
2.Accessibilityofsite
3.Waterstoragecapacity
4.Distancefromtheloadcenter
5.Typeofland
5.Listtheclassificationof dams:
70
1.Basedontheirfunc
tions:
(a)storagedams
(b)Diversiondams
(c)Detentiondams
2.Basedontheirshape:
(a)Trapezoidaldams
(b)Archdams
3.Basedonthematerialsofconstruc
tion:
(a)Earthdams(b)Rockpiecesdams
(c)Stonemasonarydams (d)concretedams
(e)RCCdams(f)TimberandRubberdams
4.Basedonhydraulicd
esign:
(a)Overflowtypedam
(b)Non-overflowtypedam
5.BasedonstructuralD
esign: (a)Gravitydam
(b)Archdam
(c) Buttressesdam
6.Whatisasurgetank?
Asurgetankisasmallreservoirinwhichthewaterlevel risesor fallsto reduce
thepressureswingsduringopeningandclosingof inlet
valve.Thesurgetankisnot requiredforrunoffplantsandmediumheadplants.
7.WhatisaDrafttube? Thedrafttube allowsthe turbinetobeset abovethetailraceto facilitateinspection
andmaintenance. It alsoregainsthemajorportionofthekineticenergyattherunner
outletbydiffuseraction.Thedrafttube canbeastraight conicaltubeoranallowtube.
8.Listtheequipmentspresentin apowerhouse:
1.Hydraulicturbines
2.Electric generators
3.Governors
4.Gatevalves andrehetvalves
5.Watercirculatingpumps
6.Airduct
7.Switchboardandinstruments
8.Storagebatteries andcranes
9.Listthetypesof hydropowerplantsbasedonavailabilityofhead; 1.Highheadpowerplant(head>100m)
2.Mediumheadpowerplant(30m-100m)
71
3.Lowheadpowerplants(head<30m)
10.Listtheadvantagesof pumpedstoragepowerplants:
1.Increasesthepeakloadcapacityat lowcost
2.Highoperatingefficiency
3.Betterloadfactor
4.Independenceofsteam flowconditions
11.Listtheadvantagesof impulseturbine:
1.Greatertoleranceofsandandotherparticlesinthewater
2.Betteraccesstoworkingparts
3.Nopressuresealsaroundtheshaft
4.Easierto fabricate and maintain
5.Betterpart-flowefficiency
12.Listanyfourpumpedstoragehydropowerplantsin India:
1.Bihar,Maharastra,150MW
2.Kadamparai,Coimbatore,Tamilnadu,400MW
3.NagarjunaSagarPH,AndhraPradesh,810MW
4.Puruliapumpedstorageproject,Avodhvahills,WestBengal,900MW
5.SrisailamLeft BankPH,AndhraPradesh,900MW
6.TehriDam,Uttranchal,1000MW
13.Whataretheessentialelementsof hydropowerplant? 1.Catchmentarea
2.Reservation
3.Dam
4.Surgetanks
5.Drafttubes
6.Powerhouse
7.Switchedfortransmissionofpower
14.Whatismeantbycatchmentareaandexplainitsfunction:
Thewholeareabehindthedamis calledthecatchmentarea.Therainwaterinthe
areawillbedrainedinto thedamthroughadamorriver.
15.ExplainReservoir:
Areservoirmaybenatural,likealakeonamountainorartificiallybuiltby
erectingadamacrossa river.
16.Definesurgetank:
ASurgetankisasmallreservoirinwhichthewaterlevel risesswingsduring
openingandclosingofinlet valve.
17.Whatispowerhouse?
72
Apowerhouseisastablestructurewhichhousestheequipmentinthepowerplant
18.Whatismeantbypumpedstoragepowerplant?
Thepumpedstorageplantsareusedforloadbalancing.Duringpeakloadwateris
usedtoworkonturbinestoproduceelectricity.Waterafterworkinginturbinesisstored
inthetailracereservoir.
19.WhatisminiHydroplants? Theminipowerplantsoperatewith5m-20mheadandproduceabout1MWto5
MWofpower.
20.Whatismicrohydroplants? Themicropowerplantsrequireaheadlessthan5mandproduce0.1MWto1
MW.
21.Defineturbines:
Aturbineconvertsenergyintheformoffallingwaterintorotatingshaftpower.
Theselectionofbestturbineforanyparticularsitedependsonthesitecharacteristics.
22.Whatarethedisadvantagesof impulseturbine? Theyareunsuitableforlow-headsitesbecauseof theirlowspecificspeeds.
23.Whatispeltonturbine?
Apeltonturbineconsistsofaset ofspeciallyspreadbucketsmountedona
peripheryof a circulardisc. It isturnedbyjetsof waterwhich
aredischargedfromoneor morenozzles.
24.Whatismeantbyreactionturbines? Francisturbineandpropellerturbinesarethereactionturbines.Thereacti
on turbinesrotatefasterthan impulseturbine.
25.Whatismeantbypropellerturbine? Thebasicpropellerturbineconsistsofapropeller.Insideitconsistof
a continuationofthepenstocktube.
26.Whatismeantby Kaplanturbine? Thepitchofthepropellerbladestogetherwithwicketgateadjustment,enables
reasonableefficiencytobemaintainedunderpartflowconditions.Suchturbinesar
e called asKaplanturbines.
27.Definetwinrunners:
Tworunnerscanbeplacedonthesameshafteithersidebysideoronopposite
sidesofthegenerator.Thisconfigurationisunusualandwouldonlybeusedifthe
numberofjetsper runnerhadmaximized.
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28.Statetheadvantagesof impulseturbineoverreactionturbine: Impulseturbineareusuallycheaperthenreactionturbinebecausethereisnonee
d foraspecialistpressurecasing.
29.Explainimpulseturbinein termsof heads? Highhead-peltonTurgo
Mediumhead-Multijetpeltonturgo
Lowhead- crossflow
30.Explainreactionturbinein termsof head: Highhead-
Francis
Mediumhead-
Propeller
Lowhead-
Kaplan
UNIT-IIINUCLEAR POWER PLANTS
1.Whatismeantbyradioactivity?
It referstothegermannameofRadio-Activitat.Radioactivityisthespontaneous
disintegrationof
atomicnuclei.Thenucleusemitsparticlesorelectromagneticrays
duringthisprocess.
2.Whatis theunitof Radioactivity?
1.Roentgen2.RAD(RadiationAbsorbedDose)
3.RBE(RelativeBiologicalEffectiveness)4.REM(RoentgenEquivalentinMan)
5.Gray(GY)-100rads6.Sievert(SV)
3.WhatarethetypesofRadioactivedecay?
1.Alphadecay2.Betadecay
3.Gammadecay4.Poistronemission(Betapositivedecay)
5.Electroncapture
74
4.Define-Decaytiming.
Thenumberofdecayevents–dNexpectedtooccurinasmallintervaloftimedt is
proportionaltothenumberofatomspresent.If N isthenumberofatoms,thenthe
probabilityofdecay(-dN/N)isproportionaltodt.
5.WhatisUraniumenrichment? Inmosttypesof reactor, ahigherconcentrationofuraniumisusedtomake fuel rod.
Thisproducedbyaprocesstermedenrichment.Theenricheduraniumcontainingmor
e thannatural0.7%U-235.
6.Whatarethetwowaysof uraniumenrichment? 1.Gascentrifugeprocess
2.Gasdiffusion
7.Whatis thepurposeof reprocessingof nuclearwaste? Theusedfuelcontains96%uranium,1%plutoniumand3%radioactivewastes.
Reprocessingisusedtoseparatethewastefromtheuraniumandplutoniumwhichcanbe
recycledinti newfuel.Thereprocessingeffectivelyreducesthevolumeof wasteand
limitstheneedtominenewsuppliesofuranium,sothat extendingthetimeofresources.
8.DefineNuclear Fission. Anatom’snucleuscanbesplit apart.Whenthisisdoneatremendousamountof
energyis released.Theenergyisbothheat andlight
energy.Thisenergy,whenletout slowlycanbeharnessedtogenerateelectricity.
9.DefineNuclear Fusion.
Fusionmeansjoiningsmallernucleitomakealargernucleus.Thesunusesnuclear
fusionofhydrogenatomsintoheliumatoms.Thisgivesoffheatandother radiation.
10.WhatisNeutronlifetime?
Thepromptneutronlifetime,istheaveragetimebetweentheemissionofneutronsan
d eithertheir absorbtioninthesystemortheir
escapefromthesystem.Thetermlifetimeisusedbecausetheemissionofaneutroniso
ftenconsidereditsbirth,andthe subsequentabsorptionis considereditsdeath.
11.WhatisUranium-235chainReactor?
Ina chainreaction,particlesreleasedbythesplittingoftheatom gooffandstrike
otheruraniumatomssplittingthose.Thoseparticlesgivenoffsplitstill otheratomsina
chainreaction.If anleastoneneutronfromU-235fissionstrikesanothernucleusand
causesit to fission,Thenthechainreactionwill continue.
12.Whatisfourfactorformula?
Thefourfactor formulaisusedinnuclear engineeringtodeterminethe
multiplicationofanuclearchainreactionin
aninfinitemedium.Theformulais:
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-ReproductionFactor-Thethermalutilizationfactor
-Theresonanceescapeprobability-Thefast fissionfactor
13.Listthefourtypesofradiationassociatedwithnuclearfission. 1.Alpharadiation
2.Beta radiation
3.Gammaradiation
4.Neutronradiation
14.DefineAlpharadiation. Thisisbasicallytheatomicnucleusoftheelement(He)consistingoftwoprotons
andtwoneutrons.It isnotverypenetrativeandthedangertomanarisesifan alpha
emittingelement,suchasplutonium,thenthealpharadiationbeverydamaging.
15.DefineBetaradiation.
Beta radiationconsistsof
electronsortheirpositivelychargedcounterparts.This
canpenetratetheskin,butnotveryfar.
16.DefineGammaradiation. GammaradiationispenetrativeinamannersimilartoX-raysandhassimilar
physicalproperties.Itcanbestoppedonlybythickshieldsofleadorconcrete.
17.DefineNeutronradiation. Neutronradiationconsistsoftheneutronsemitted
duringthefissionprocess.
Neutronsarealsoverypenetrative,butlesssothengamma-radiation.
18.Definewaterasmoderator.
Neutronsfromfissionhaveveryhighspeedsand mustslowedgreatlybywater
moderationtomaintainthechainraction.TheUranium-235is enrichedto2.5-3.5%to
allowordinarywatertobethemoderator.Enoughspontaneouseventsoccurtoinitiatea
chainreactionifthepropermoderationandfueldensityisprovided.
19.Listthetypesof Nuclearreactors.
Thereactorsareclassifiedbasedonthefollowing:
1.Typeoffuelused
2.Neutronflux spectrum
3.Thecoolant
20.Listthevariouswidespreadpowerplantreactortypes.
1.Pressurizedwaterreactor(PWR)
2.Bolingwater reactor(BWR)
3.PressurizedHeavywaterreactor(PHWR)
4.Liquidmetalfast BreederReactors(LMFBR)
5.HightemperatureGas cooledreactors(HTGCR)
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21.Whatispressurizedwaterreactors(PWR)?
ThePWRbelongstothelidhtwatertype.Themoderatorandthecoolant areboth
lightwater(H2O).Thecoolingwatercirculatesintwoloops,whicharefullyseparated
fromoneanother.PWRkeepwaterunderpressure,sothewaterheatsbutdoesnotboil
evenat thehighoperatingtemperature.
22.Whatisboilingwaterreactor(BWR)?
Inaboilingwaterreactor, Lightwaterplaystheroleofmoderatorandcoolantas
well.Partofthewaterboilsawayinthereactorpressurevessel,thusamixtureofwater
andsteamleavesthereactorcore.
23.Whatis MoltenSaltReactor(MSR)? Amoltensalt reactorisatypeofnuclearreactorwheretheprimarycoolantisa
moltensalt.Moltensalt referstoasalt that isintheliquidphasethat isnormallyasolidat
standardtemperatureionicliquid,althoughtechnicallymoltensaltsarea classofionic
liquids.
24.NuclearPowerplantsafety. Radiationdosescanbecontrolledthroughthefollowingprocedures:
1.Thehandlingofequipmentviaremoteinthecoreofthereactor
2.Physicalshielding
3.Limitonthetimeaworkerspendsinareaswithsignificantradiationlevels
4.Monitoringofindividualdosesandoftheworkingenvironment
5.Safetymechanismof aNuclearpowerreactor
25.ListtheNuclearpowerplantsin India. 1.Kaiga(3*22MWPHWR),Karnataka
2.Kakrapar(2*22MWPHWR),Gujarat
3.Kudankulam(2*100MWPWR),Tamilnadu
4.Madras(2*17MWPHWR),Tamilnadu
26.Definemeangenerationtime. It istheaveragetimefromaneutronemissiontoa captureresultsin fission.The
mean
generationtimeisdifferentfrompromptneutronlifetimebecausethemean
generationtimeonlyincludesneutronabsorptionthat leadsto fissionreaction.
UNIT IV GAS DIESEL POWER PLANT
1.Listtheadvantagesofgasturbinepowerplant.
1.Lowcapital cost
2.Highreliability
3.Flexibilityinoperation
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4.Capabilitytoquickstart
5.Highefficiencye.t.c.
2.Listthe majorcomponentsof gasturbine. 1.Compressor
2.Combustionchamberand
3.Turbine
3.Listthetypesof gasturbinepowerplants. 1.Opencyclegasturbinepower plant
2.Closedcyclegasturbinepowerplant
4.Listthedisadvantagesof gasturbinepowerplant. 1.NoloadandPartialloadefficiencyislow
2.Highsensitiveto componentefficiency
3.Theefficiencydependsonambientpressureandambienttemperature
4.Highair rateisrequiredtolimitthemaximuminlet
airtemperature.Henceexhaust lossesarehigh
5.Airandgasfilterisrequiredtopreventdustintothecombustionchambers.
5.Defineregeneratorefficiency. Theregeneratorefficiencyisdefinedas:
=Actualtemperaturerise ofair/ Maximumtemperaturerisepossible
6.Listthefactorswhichaffecttheperformanceof gasturbinepowerplants. 1.Partloadefficiency
2.Fuelconsumption
3.Airmassflowrate
4.Thermalefficiency
5.Regeneration
7.Whataretheworkingfluidsin gasturbine?
1.Air
2.Helium
3.Argon
4.Carbondioxide
8.Listthevarioustypesof dieselplants.
Basedonnumberofstr
okes:
(a)Twostrokediesel
engine
(b)Foursrtokediesele
ngine
Basedonorientation:
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(a)Horizontaldiesel
engine (b)
Verticaldiesel engine
Basedonnumberof
cylinders:
(a)singlecylinder
(b)Multicylinder
Andothertypelikenaturallyaspirated,superheatedetc.,
9.Listthecomponentsof dieselpowerplant.
1.Dieselengine
2.Airintakesystem
3.Exhaustsystem
4.Fuelsystem
5.Coolingsystem
6.Lubricatingsystem
7.Startingofengine
10.Listthevariousfunctionsoffuelinjectionsystem. 1.Itfiltersthefuel
2.Monitorthecorrectquantityoffueltobeinjected
3.Timingoftheinjectionprocess
4.Regulatesthefuelsupply
5.Fineatomizationoffueloil
6.Distributestheautomizedfuelproperlyinsidethecombustionchamber
11.Listtheclassificationof oilinjectionsystem. (a)Commonrail injectionsystem
(b)Individualpumpinjectionsystem
(c)Distributorsystem
12.Listthereasonwhythecoolingsystemisnecessaryforadiesel engine.
1.Toavoiddetemiationoflubricatingoil
2.Toavoiddamagesandoverheatingofpiston
3.Toavoidunevenexpansionwhichresultsin craking
4.Toavoidpre-ignitionanddetonationorknocking
5.Toavoidreductioninvolumetricefficiencyandpoweroutputoftheengine
13.Whatarethe methodsof coolingsystemused? 1.Aircooling
2.Watercooling
14.Listthemethodsadoptedforcirculatingthewaterin a coolingsystem. 1.Thermosiphoncooling
2.Forcedcoolingbypump
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3.Thermostatcooling
4.Pressurisedwatercooling
5.Evaporativecooling
15.Whataretheimportantfunctionsof alubricatingsystem?
1.Lubricating
2.Cooling
3.Cleaning
4.Sealing
5.Noiseabsorption
16.Listthevarioustypesof lubricatingsystemusedin diesel engine.
1.Mistlubricatingsystem
2.Wetsumplubricationsystem
3.Drysumplubricationsystem
17.Whatarethestartingmethodsof diesel engine? 1.Byanauxiliaryengine
2.Byanelectricmotor
3.Bycompressedair
18.Listanyfouradvantagesof dieselpowerplant.
1.It iseasytodesignand install
2.It iseasilyavailableinstandardcapacities
3.Theycanrespondtoloadchanges
4.Theyhavelessstandbylosses
19.Listanyfourdisadvantagesof dieselpowerplant.
1.Highoperatingcost
2.Highmaintenanceand lubricationcost
3.Capacityisrestricted
4.Noisepollution
20.Listanyfourapplicationsof dieselpowerplant.
1.Usedaspeakloadplants
2.Suitableformobileplants
3.Usedasstandbyunits
4. Usedas emergencyplant
UNIT-V NON CONVENTIONAL POWERGENERATION
1.Whatarethecomponentsof solarenergy? 1.Collector
2.Storageunit
2.Whatis concentrationratio?
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Concentrationratioisdefinedastheratiobetweentheapertureareaandthereceiver
absorberareaofthecollector.
3.Listthevarioustypesof solarenergycollectors. 1.Stationarycollectors(or)Non-concentrating
(a) Flateplatecollectors
(b)Compoundparaboliccollectors
(c)Evaculatedtube collectors
2.Suntrackingconcentratingcollector
(a)singleaxistracking
(b)Two-axistracking
4.Listanyfourapplicationsof solarcollectors. 1.Solarwaterheating
2.Solarspaceheatingsystems
3.Solarrefrigeration
4.Industrialprocessheatsystems
5.Listthefourimportantsolarsystems. 1.Lowtemperaturecyclesusingflat plat collectororsolarpond
2.Powertowerorcentralreceiversystem
3.Distributedcollectorsystem
4.Concentratingcollectorsformediumandhightemperaturecycle
6.ListtheadvantagesofsolarEnergy. 1.Solarenergyisfree frompollution
2.Theycollect solar energyopticallyandtransferit
toasinglereceiver,thus minimizingthermal-
energytransportrequirements
3.Theytypicallyachieve
concentrationratiosof300to1500andsoarehighly efficientbothin
collectingenergyandconvertingit to electricity.
4.Theplant requireslittlemaintenanceorhelpaftersetup
5.It iseconomical
7.Listanyfourdisadvantagesof solarenergy.
1.Avilableindaytimeonly
2.Needstoragefacilities
3.Itneedsabackuppowerplant
4.Keepingbackupplantshotincludesan energycostwhichincludescoal burning
8.Listtheclassificationof OTECbasedonlocation.
1.Landbasedplant
2.Shelfbasedplant
3.Floatingplant
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9.Listtheclassificationof OTECbasedoncycle. 1.Opencycle
2.Closedcycle
3.Hybridcycle
10.Listanyfourbenefitsof OTEC.
1.Airconditioning
2.Chilledsoil agriculture
3.Aquaculture
4.Desalination
11.Listanyfourdisadvantagesof OTEC. 1.Degradationofheatexchangerperformanceasdissolvedgases.
2.Degradationofheatexchangerperformancebymicrobialfouling
3.Impropersealing
4.Parasiticpowerconsumptionbyexhaustcompressor
12.Listthevariouscomponentsofwindenergysystem. 1.Rotor
2.Gearbox
3.Enclosure
4.Tailvane
13.Whatarethetwobasicdesignof turbines? 1.Verticalaxis(or)Eggbeaterstyle
2.Horizontalaxis(propellerstyle)machines
14.Writedownthevarioustypesofwindpowerplants. 1.Remote
2.Hybrid
3.Gridconnected
15.Listanyfouradvantagesof windturbine.
1.Inexhaustiblefuelsource
2.Nopollution
3.Excellentsupplementtootherrenewablesource
4.Itsfree
16.Listthedisadvantagesof windpowergeneration.
1.Lowenergyproduction
2.Expensivemaintenance
17.Whatarethevariouswaysof creatingtidalenergy?
1.TidalBarrager
2.Tidalfences
3.Tidalturbines
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18.Listthevarioustypesof turbinesusedin tidalpowerstation. 1.Buldturbine
2.Rimturbine
3.Tubularturbines
19.Whatarethecomponentsof tidalpowerstation?
1.Barrage
2.Turbines
3.Sluices
4.Embankments
20.Listanyfouradvantagesof tidalpowergeneration. 1.Renewableandsustainableenergy
2.NoliquidorSolidpollution
3.Littlevisualimpact
4.Reducesdependenceuponfossilfuels
21.Listthelimitationsof tidalenergy. 1.Orientationproblem
2.Requiresstoragedevices
3.Availableatalowerratingandtime
4.Highcapital cost
22.Whatarethe mainpartsof geothermalpowerplant? 1.Productionwell
2.Vaporizer
3.Circulatingpump
4.Expansionturbine
5.Generator
6.Condenser
7.Transformer
23.Whataretheclassificationsof geothermalenergyconversionsystem?
1.Singlecyclegeothermalpowerplant
2.Binarycyclepowerplant
24.Whataretheapplicationsof geothermalenergy?
1.Generationofelectricpower
2.Spaceheatingforbuilding
3.Industrialprocessheat
25.Whataretheadvantagesof geothermalenergy? 1.Cheaper
2.Versatileinitsuse
3.Deliversgreater amountofenergy
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26.Whatarethedisadvantagesof geothermalenergy?
1.Drillingoperationisnoisy
2.Itneedslargeareasof exploitationof geothermalenergy
3.Lowoverallpowerproductionefficiency.
27.Whataretheclassificationof MHDsystem? 1.Opencyclesystems
2.Closedcyclesystems
(a)Seededinertgassystems
(b)Liquidmetalsystems
28.Whataretheadvantagesof MHDsystems? 1.Largeamountofpowerisgenerated
2.Nomovingparts,somorereliable.
3.Closedcyclesystemproducespower,freeofpollution
4.Abilitytoreachits fullpowerassoonasstarted.
29.Listtheclassificationof oilinjectionsystem. (a)Commonrail injectionsystem
(b)Individualpumpinjectionsystem
(c)Distributorsystem
30.Listthedisadvantagesof MHDsystems.
1.Needsverylargemagnets(highexpenses)
2.Veryhighfrictionandheat transferlosses
3.Itsuffersfromthereverseflowof
electronsthroughtheconductingfluidsaround theendsofthemagneticfield.
PART B 16 MARKS
UNIT – 1: THERMAL POWER PLANTS
1. Draw a general lay out of a thermal power plant and explain the working of different
circuits. 2. What factors are considered for selecting a site for a big thermal power plant?
3. How much coal, cooling water and combustion air are required for a thermal power
station of 500 MW capacity per hour. 4. How much ash and SO2 are produced per day from a plant of Koradi size if Indian low
grade coal is used. 5. What is the importance of thermal power plant in the national power grid?
6. What is meant by overfeed and underfeed principles of coal firing? Which is preferred
for high volatile coal and why. 7. What are the advantages of burning the fuels in pulverized form? 8. Why ash and dust handling problem is more difficult than coal handling problems.
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9. What are different ash handling systems? Discuss the relative merits and demerits. 10. How the ash produced carries the importance in the selection of thermal power plant
site 11 Draw a general lay out of a thermal power plant and explain the working of different
circuits. 12 What factors are considered for selecting a site for a big thermal power plant?
13 How much coal, cooling water and combustion air are required for a thermal power
station of 500 MW capacity per hour. 14 How much ash and SO2 are produced per day from a plant of Koradi size if Indian low
grade coal is used. 15 What is the importance of thermal power plant in the national power grid?
16 What is meant by overfeed and underfeed principles of coal firing? Which is preferred
for high volatile coal and why. 17 What are the advantages of burning the fuels in pulverized form? 18 Why ash and dust handling problem is more difficult than coal handling problems. 19 What are different ash handling systems? Discuss the relative merits and demerits. 20. How the ash produced carries the importance in the selection of thermal power plant
site.
UNIT – 2: HYDROELECTRIC POWER PLANTS
1. What are the different factors to be considered while selecting the site for hydroelectric
power plant? 2. How the hydroelectric power plants are classified. 3. How the most economical capacity of hydroelectric power plant is decided. 4. What do you understand by run-off river power plant and how its performance is
increased by introducing a pondage in the plant? 5. Explain in detail about pump storage plant. 6. Draw a neat diagram of storage type hydroelectric power plant and describe the function
of each component used in the plant. 7. Mention the advantages and disadvantages of hydroelectric power plants compared with
thermal power plants.
8. Why the combined operation of hydro and thermal plants is more economical than
individual operation of the plant. 9. What do you understand by pump storage plant and what are the advantages and
limitations of this plant. 10. What are the specific advantages of storage reservoir type power plant? How they differ
from other types of hydro power plant?
UNIT – 3: NUCLEAR POWER PLANTS
1. Why uranium oxide is preferred over uranium as fuel. 2. Why cladding is necessary. What are the requirements of a good cladding material? 3. What properties are required for a good coolant? Which gases are used as coolant?
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4. What are the desirable properties of a good moderator? Compare H2O, D2O and C as
moderators. 5. What are the desirable properties of control rod materials? Compare the merits and
demerits of different control rod materials. 6. Why shielding of a reactor is necessary. What do you understand by thermal shielding? 7. Compare the properties of stainless steel and zirconium for use as reactor fuel element
cladding. 8. How induced radioactivity affects the cost of shielding. 9. Considering the problem of induced radioactivity which coolant among water and
sodium is more desirable and why. 10. Discuss the advantages and disadvantages of Lithium, Bismuth and sodium as coolants
for nuclear reactors.
UNIT – 4: GAS AND DIESEL POWER PLANTS
1. What are the main advantages of a combined cycle system in the present power picture
of the world? 2. Draw the line diagrams of repowering system using steam turbine only and boiler only.
Discuss the merits and demerits also. 3. What is the gasification of coal and explain in detail. 4. What are the merits and demerits of using air or O2 in a gasification plant when the
gasification plant is integrated with closed cycle? 5. What do you understand by PFBC, Explain in detail? 6. Draw the line diagrams of two different PFBC systems which are commonly used and
discuss their merits and demerits. 7. What are the main difficulties faced in developing the combined cycles with PFBC. 8. Why and when organic fluid is preferred over water in the bottoming cycle. What are its
advantages? 9. Discuss the part behavior of combined cycle plant and compare with conventional gas
turbine plant of the same capacity. 10. What future developments are expected in combined cycle plants?
UNIT – 5: NON-CONVENTIONAL POWER GENERATION 1. What are the non-conventional sources of energy and why are they seriously thought
throughout the world. 2. What are the different sources of geothermal energy? 3. Discuss the different systems used for generating the power using geo-thermal energy. 4. What are the specific environmental effects if the geothermal source of energy is used for
power generation? 5. What factors are considered for selecting a suitable site for tidal power plants? 6. Differentiate with neat sketches the difference between single basin and double basin
systems.
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7. List out the advantages of tidal power plants over the conventional hydel power plants. 8. What are the basic requirements for locating a wind power plant? What factors affect
them? 9. What methods are used to overcome the fluctuating power generation of a wind mill? 10. Explain the working of a fuel cell and list out its advantages over other non-
conventional systems of power generation.
V.S.B ENGINEERING COLLEGE, KARUR
DEPARTMENT OFELECTRICALAND ELECTRONICS ENGINEERING
II YEAR / III SEMESTER
DIGITAL LOGICCIRCUITS TWO MARK QUESTION AND ANSWER
UNIT I
NUMBER SYSTEMS AND DIGITAL LOGIC FAMILIES
1. What is meant by parity bit?
A parity bit is an extra bit included with a message to make the total number of 1’s
either even or odd. Consider the following two characters and their even and odd parity:
with even parity with odd parity.
ASCII A = 1000001 01000001 11000001
ASCII T = 1010100 11010100 01010100
In each case we add an extra bit in the left most position of the code to produce an
even number of 1’s in the character for even parity or an odd number of 1’s in the character
for odd parity. The parity bit is helpful in detecting errors during the transmission of
information from one location to another.
2. What are registers?
Register is a group of binary cells. A register with n cells can store any discrete
quantity of information that contains n bits. The state of a register is an n-tuple number of
1’s and 0’s, with each bit designating the state of one cell in the register.
3. Define binary logic?
Binary logic consists of binary variables and logical operations. The variables are
designated by the alphabets such as A, B, C, x, y, z, etc., with each variable having only
two distinct values: 1 and 0. There are three basic logic operations: AND, OR, and NOT.
4. Convert (4021.2)5 to its equivalent decimal.
(4021.2)5 = 4 x 53 + 0 x 52 + 2 x 51 + 1 x 50 + 2 x 5-1
= (511.4)10
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5. Represent binary number 1101 - 101 in power of 2 and find its decimal equivalent.
N = 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 + 1 x 2-1 + 0 x 2-2 + 1 x 2-3
= 13.625 10
6. Convert (634)8 to binary.
6 3 4
110 011 100
Ans = (110 011 100)2
7.Convert (9 B 2 - 1A) H to its decimal equivalent.
N = 9 x 16 2 + B x 16 1 + 2 x 16 0 + 1 x 16 -1 + A (10) x 16 -2
= 2304 + 176 + 2 + 0.0625 + 0.039
= 2482.1 10
8.What are the different classifications of binary codes?
Weighted codes
Non - weighted codes
Reflective codes
Sequential codes
Alphanumeric codes
Error Detecting and correcting codes.
9. Convert 0.640625 decimal number to its octal equivalent.
0.640625 x 8 = 5.125
0.125 x 8 = 1.0
Ans. = 0.640 625 10 = 0.51
10. Convert 0.1289062 decimal number to its hex equivalent.
0.1289062 x 16 = 2.0625
0.0625 x 16 = 1.0
Ans. = 0.21 16
11. Convert decimal number 22.64 to hexadecimal number. 22/ 16=6
1/ 16 =1
0.64 x 16 = 10.24
0.24 x 16 = 3.84
0.84 x 16 = 13.44
0.44 x 16 = 7.04
Ans. = (16.A3D7)16.3
12. What are the two steps in Gray to binary conversion?
The MSB of the binary number is the same as the MSB of the gray code number.
So write it down. To obtain the next binary digit, perform an exclusive OR operation
between the bit just written down and the next gray code bit. Write down the result.
13. Convert gray code 101011 into its binary equivalent.
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Gray Code: 1 0 1 0 1 1
Binary Code:1 1 0 0 1 0
14. Convert 10111011 is binary into its equivalent gray code.
Binary Code: 1 0 1 1 1 0 1 0 1 1
Gray code: 1 1 1 0 0 1 1 0
15. Find 2’S complement of (1 0 1 0 0 0 1 1) 2
0 1 0 1 1 1 0 0 1 1’s Complement
+ 0 1
0 1 0 1 1 1 0 1 0 2’s Complement.
16. What are the advantages of 1’s complement subtraction?
The 1’s complement subtraction can be accomplished with an binary adder.
Therefore, this method is useful in arithmetic logic circuits.
The is complement of a number is easily obtained by inverting each bit in the
number
17.Classify thelogicfamily by operation?
TheBipolarlogicfamilyis classified into
Saturated logic
Unsaturated logic.
TheRTL,DTL, TTL,I2
L, HTLlogiccomes underthesaturated logicfamily.
TheSchottkyTTL,andECLlogic comes undertheunsaturated logicfamily.
18.State the classifications ofFET devices. FET is classifiedas
1.Junction Field EffectTransistor (JFET)
2.Metal oxidesemiconductor family(MOS).
19.Mentiontheimportant characteristics ofdigital IC’s?
Fan out
Powerdissipation
Propagation Delay
NoiseMargin
FanIn
Operatingtemperature
Powersupplyrequirements
20.DefineFan-out?
Fanoutspecifiesthenumberofstandardloadsthattheoutputofthegatecan drive without
impairment ofits normal operation.
21.Definepowerdissipation?
Powerdissipationismeasureofpowerconsumedbythegatewhenfullydriven byall its
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inputs.
22.Definenoisemargin?
Itisthemaximumnoisevoltageaddedtoaninputsignalofadigitalcircuitthat does not
causean undesirable changein the circuit output.It is expressed in volts.
23.Definefanin?
Faninisthenumberofinputsconnectedtothegatewithoutanydegradationin
thevoltagelevel.
24.Whatis Operating temperature?
Allthegatesorsemiconductordevicesaretemperaturesensitiveinnature.The
temperature in which the performance of the IC is effective is called as operating
temperature. OperatingtemperatureoftheICvaryfrom 00
Cto 700
c.
25.Whatis HighThreshold Logic? Somedigitalcircuitsoperateinenvironments,whichproduceveryhighnoise
signals.ForoperationinsuchsurroundingsthereisavailableatypeofDTLgatewhich
possessesahighthresholdtonoiseimmunity.ThistypeofgateiscalledHTLlogicor High
ThresholdLogic.
26.Whatare the typesofTTL logic? 1.Open collectoroutput
2.Totem-Pole Output
3.Tri-stateoutput.
27.Whatis depletionmodeoperationMOS?
Ifthechannelisinitiallydopedlightlywithp-typeimpurityaconductingchannel exists
atzero gatevoltage and thedeviceis said to operatein depletion mode.
28.Whatis enhancementmodeoperationofMOS?
Iftheregionbeneaththegateisleftinitiallyunchargedthegatefieldmustinduce achannel
beforecurrentcanflow.Thusthegatevoltageenhancesthechannelcurrent and such adeviceis
saidto operatein the enhancement mode.
29.List thedifferentversions ofTTL
TTL(Standard TTL)
LTTL (Low PowerTTL)
HTTL(High Speed TTL)
STTL(ScottyTTL)
LSTTL(LowpowerSchottkyTTL)
30.Stateadvantages and disadvantages ofTTL
Advantages:
Easilycompatible with otherICs
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Low output impedance
Disadvantages:
Wired output capabilityis possibleonlywith tristate and open collectortypes
Special circuits in Circuit layout and system design arerequired.
31.Convert(4021.2)5 to its equivalentdecimal. (4021.2)5 =4 x53 +0 x 52 +2 x51 +1 x50 +2x5-1
=(511.4)10
UNIT II
COMBINATIONAL CIRCUITS
1.Whatareregisters?
Registerisagroupofbinarycells.Aregisterwithncellscanstoreanydiscrete
quantityofinformationthatcontainsnbits.Thestateofa registerisann-tuplenumberof
1’s and 0’s, with each bit designatingthestateofone cell in the register.
2.Whatis meantby register transfer?
Aregistertransfer operationisabasicoperationindigitalsystems.Itconsistsof
transferofbinaryinformationfromonesetofregistersintoanothersetofregisters.The
transfermaybedirectfromoneregistertoanother,ormaypassthroughdataprocessing circuits to
performan operation.
3.Definelogicgates?
Logicgatesareelectroniccircuitsthatoperateononeormoreinputsignalsto producean
output signal.Electrical signals such as voltages or currents exist throughout a
digitalsystemineitheroftworecognizablevalues.Voltage-operatedcircuitsrespondto two
separatevoltagelevels that representabinaryvariable equal to logic1orlogic0.
4. Define duality property.
Duality property states that every algebraic expression deducible from the
postulatesof Booleanalgebraremainsvalidiftheoperatorsandidentityelementsare
interchanged.Ifthedualofanalgebraicexpressionisdesired,wesimply interchangeOR and
AND operatorsand replace1’s by0’s and 0’s by1’s.
5. StateDe Morgan’s theorem.
DeMorgan suggested two theorems that form important part ofBooleanalgebra.
Theyare,
1)The complement ofaproduct is equal to thesum ofthe complements. (AB)’=A’+B’
2)The complement ofasum term is equal to theproduct ofthe complements. (A
+B)’= A’B’
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6.ReduceA (A + B) A(A +B)= AA +AB
=A (1 +B)[1 +B=1]
=A.
7. Reduce A’B’C’+ A’BC’+ A’BC
A’B’C’+ A’BC’+ A’BC= A’C’(B’+B)+ A’B’C
=A’C’+A’BC[A + A’=1]
=A’ (C’+BC)= A’(C’+B)[A + A’B=A +B]
8. Reduce AB+ (AC)’+ AB’C(AB+ C) AB+(AC)’+AB’C(AB+C)=AB+(AC)’+AAB’BC+AB’CC
=AB+ (AC)’+AB’CC[A.A’=0]
=AB+ (AC)’+AB’C[A.A =1]
=AB+ A’+C’ =AB’C[(AB)’=A’+B’]
=A’+B+C’+AB’C[A +AB’=A+B]
=A’+B’C+B+C’[A + A’B=A+B]
=A’+B+C’+B’C
=A’+B+C’+B’
=A’+C’+1
=1 [A +1 =1]
9. Simplify thefollowing expressionY = (A + B)(A + C’)(B’+ C’) Y= (A+B)(A +C’ )(B’+C’)
=(AA’+ AC+A’B +BC)(B’+C’)[A.A’=0]
=(AC+A’B+BC)(B’+ C’)
=AB’C+ ACC’+A’BB’+ A’BC’+ BB’C+BCC’
=AB’C+ A’BC’
10. Simplify thefollowing using De Morgan’s theorem [((AB)’C)’’ D]’[((AB)’C)’’D]’
=((AB)’C)’’+ D’[(AB)’= A’+B’]
=(AB)’C+D’
=(A’+B’)C+D’
11.Showthat (X + Y’+ XY)(X + Y’)(X’Y)= 0 (X + Y’+ XY)(X+Y’)(X’Y)= (X+ Y’+X)(X + Y’)(X’+Y)[A + A’B=A +B]
=(X +Y’) (X +Y’)(X’Y)[A +A =1]
=(X +Y’ )(X’Y)[A.A =1]
=X.X’+ Y’.X’.Y
=0 [A.A’=0]
12.Prove thatABC + ABC’+ AB’C + A’BC =AB+ AC + BC
ABC+ABC’+AB’C+A’BC =AB(C+C’)+AB’C+A’BC
=AB+AB’C+A’BC
=A(B+B’C)+A’BC
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=A(B+C)+A’BC
=AB + AC + A’BC
=B(A + C) + AC
=AB+BC+ AC
=AB+ AC +BC...Proved
13. Convertthegivenexpression incanonical SOPformY = AC + AB+ BC
Y= AC+AB+BC
=AC(B+B’)+AB(C+ C’)+ (A+ A’)BC
=ABC+ABC’+AB’C+ AB’C’+ABC+ABC’+ ABC
=ABC+ABC’+AB’C+AB’C’[A +A=1]
14. Convertthegivenexpression incanonical POSformY = (A + B)(B+ C)(A + C)
Y=(A+B)(B+C)(A+C)
=(A +B+C.C’)(B+C+ A.A’ )(A +B.B’+C)
=(A +B+C)(A +B+ C’ )(A +B+C)(A’+B +C)(A +B+C)(A +B’ + C)[A +
=(A +B)(A +C) Distributivelaw]
=(A +B+C)(A +B+C’)(A’+B+C)(A’+B+ C)(A +B’+C)
15.Findthemintermsofthelogical expressionY = A’B’C’+ A’B’C +A’BC + ABC’ Y= A’B’C’+ A’B’C+A’BC+ABC’
=m0 +m1 +m3 +m6
16.Write themaxtermscorresponding to thelogical expressionY = (A+ B+ C’) (A + B’+
C’)(A’+ B’+ C)
Y= (A+B+C’ )(A + B’+C’)(A’+B’+C)
=M1.M3.M6
17.Whatare called don’t care conditions? In some logic circuits certain input conditions never occur, therefore the
correspondingoutputneverappears.Insuchcasestheoutputlevelisnotdefined,itcan
beeitherhighorlow.Theseoutputlevelsareindicatedby‘X’or‘d’inthetruthtables and arecalled
don’t careconditions orincompletelyspecified functions.
18.Whatare thebasicdigital logicgates? Thethreebasiclogicgates are
ANDgate
ORgate
NOTgate
19.Whatis a Logicgate?
Logicgatesarethebasicelementsthatmakeupadigitalsystem.Theelectronic
gateisacircuitthatisabletooperateonanumberofbinaryinputsinordertoperforma
Particularlogical function.
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20.Whichgates arecalledas theuniversal gates? Whatareits advantages? TheNANDandNORgatesarecalledastheuniversalgates.Thesegatesareused to perform
anytypeoflogicapplication.
21.Implement theBoolean ExpressionforEX– OR gateusing NANDGates.
22. Definehalfadderandfull adder Thelogiccircuitthatperformstheadditionoftwobitsisahalfadder.Thecircuit that
performs theaddition ofthreebits is a full adder.
23. DrawthelogicSymbolandconstructthetruthtableforthetwoinputEX–
.
24.Define Decoder? Adecoderisamultiple-inputmultipleoutputlogiccircuitthatconvertscoded inputs into
coded outputswheretheinput and output codes aredifferent.
25. Whatis binary decoder? Adecoderisacombinationalcircuitthatconvertsbinaryinformationfromninput lines to
amaximum of2noutputs lines.
26. DefineEncoder?
Anencoderhas2n
inputlinesandnoutputlines.Inencodertheoutputlines
generatethebinarycodecorrespondingto theinput value.
27.Whatis priority Encoder?
Apriorityencoderisanencodercircuitthatincludesthepriorityfunction.In
priorityencoder,if2ormoreinputsareequalto1atthesametime,theinputhavingthe highest
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prioritywill takeprecedence.
28.Definemultiplexer?
Multiplexerisadigitalswitch.Ifallowsdigitalinformationfromseveralsources to be
routed onto asingleoutput line.
29.Whatdo youmeanby comparator?
Acomparatorisaspecialcombinationalcircuitdesignedprimarilytocomparethe
relativemagnitudeoftwo binarynumbers.
30.State thelimitations ofkarnaughmap.
Generallyitislimitedtosixvariablemap(i.e)morethensixvariableinvolving
expression arenot reduced.
Themapmethodisrestrictedinitscapabilitysincethey areusefulforsimplifying only
Boolean expressionrepresented in standard form.
31.Whatis a karnaughmap?
Akarnaughmaporkmapisapictorialformoftruthtable,inwhichthemap diagramis made
upofsquares,witheachsquaresrepresentingonemintermofthe function.
32.Findthemintermsofthelogical expressionY = A'B'C' + A'B'C +A'BC + ABC'
Y=A'B'C' +A'B'C+A'BC+ABC'
=m0 +m1 +m3 +m6=∑m(0, 1, 3, 6)
33.Write themaxtermscorresponding to thelogical expression
Y= (A+B+C' )(A+B' +C')(A'+ B' +C)
=(A +B+C')(A + B' +C')(A'+ B' +C)
=M1.M3.M6
=πM(1,3,6)
34. Whatare theapplications ofDecoders?
Decoders areused in countersystems.
Decoders areused in Analog to Digital converters.
Decoderoutput can beused to driveadisplay system.
35. Whatis thedifferencebetween decoderand demultiplexer?
A Decoder is a multiple input; multiple output logic circuits which convert coded
inputs coded inputs into coded outputs.
A Demultiplexer is a circuit that receives information on a single line and
transmits this information on oneof2n possibleoutput lines.
36.Mentionthedifferences between demultiplexerandmultiplexer.
Demultiplexer is the process of taking information from one input and
transmitting thesameoveroneofseveral outputs.
Multiplexer is the process of selecting one information from several sources and
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transmit on singleoutput line. It has several datainput lines and singleoutput line
37.Whatis a primeimplicant?
Aprime implicant is a product term obtained by combining the maximum
possiblenumberof adjacent squares in themap.
UNIT III
SYNCHRONOUSSEQUENTIALCIRCUITS
1.Whatare the classifications ofsequential circuits? Thesequentialcircuitsareclassifiedonthebasisoftimingoftheirsignalsinto two types.
Theyare,
Synchronous sequential circuit.
Asynchronous sequential circuit.
2.DefineFlipflop. Thebasicunitforstorageisflipflop.Aflip-flopmaintainsitsoutputstateeither at 1 or0
until directed byan input signal to changeits state.
3.Whatare thedifferent types of flip-flop? Therearevarious types of flip flops. Someofthem arementioned below theyare,
RSflip-flop, SRflip-flop, D flip-flop, K flip-flop, T flip-flop
4.Define racearoundcondition. In JK flip-flop output is fed back to theinput. Therefore changein theoutput results
changein theinput. Dueto this in thepositivehalfoftheclock pulseifboth Jand K arehigh then
output toggles continuously. Thiscondition is called ‘racearound condition’.
5.Whatis edge-triggeredflip-flop?
Theproblemof race aroundconditioncansolvedby edgetriggeringflipflop.The
termedgetriggeringmeansthattheflip-flopchangesstateeitheratthepositiveedgeor
negativeedgeoftheclockpulseanditissensitivetoitsinputsonlyatthistransitionof the clock.
6.Whatis a master-slaveflip-flop? Amaster-slaveflip-flopconsistsoftwoflip-flopswhereonecircuitservesasa master and
theother as aslave.
7.Define rise time.
The timerequiredtochangethevoltagelevelfrom10%to90%isknownasrise time (tr).
8.Definefall time.
Thetimerequiredtochangethevoltagelevelfrom90%to10%isknownasfall time (tf).
9.Definepropagationdelay.
Apropagationdelayisthetimerequiredtochangetheoutputaftertheapplication
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oftheinput.
10.Define registers. A registerisagroupofflip-flopsflip-flopcanstoreonebitinformation.Soann- bit register
has a group of n flip-flops and is capable of storing any binary information/number
containingn-bits.
11.Defineshift registers. Thebinaryinformationinaregistercanbemovedfromstagetostagewithinthe
registerorintooroutoftheregisteruponapplicationofclockpulses.Thistypeofbit
movementorshiftingis essentialforcertainarithmeticandlogicoperationsusedin
microprocessors. This gives risetogroup ofregisters called shift registers.
12.Whatare thedifferent types ofshift type? Therearefivetypes. Theyare,
Serial In Serial Out Shift Register
Serial In Parallel Out Shift Register
Parallel In Serial Out Shift Register
Parallel In Parallel Out Shift Register
Bidirectional Shift Register
13.Definesequential circuit? Insequentialcircuitstheoutputvariablesdependentnotonlyonthepresentinput variables
but theyalso depend up on thepast historyoftheseinput variables.
14.Give thecomparison betweencombinational circuits andsequential circuits.
Combinational circuits Sequential circuits
Memoryunit is not required Memoryunityis required
Parallel adderis a combinational circuit Serial adderis asequential circuit
15.Whatdo youmeanby presentstate? Theinformationstoredinthememoryelementsatanygiventimedefinesthe present
stateofthesequential circuit.
16.Whatdo youmeanby nextstate? Thepresentstateandtheexternalinputsdeterminetheoutputsandthenextstate
ofthesequential circuit.
17.State the types ofsequential circuits? 1.Synchronous sequential circuits
2.Asynchronous sequential circuits
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18.Definesynchronoussequential circuit Insynchronoussequentialcircuits,signalscanaffectthememoryelementsonlyat
discreteinstant oftime.
19.Define Asynchronous sequential circuit? Inasynchronoussequentialcircuitschangeininputsignalscanaffectmemory element at
anyinstant oftime.
20.Give thecomparison betweensynchronous& Asynchronous sequentialcircuits?
Synchronous sequentialcircuits Asynchronous sequential circuits
Memoryelements are clocked flip-flops Memoryelementsareeitherunlockedflip-
flops ortimedelayelements.
Easierto design Moredifficult to design
21.DrawthelogicdiagramforSR latch usingtwo NOR gates.
22.The following wave formsareappliedtotheinputsofSRlatch.DeterminetheQ
waveformAssumeinitially Q = 1
Herethelatchinputhastobepulsedmomentarilytocauseachangeinthelatch outputstate,
andtheoutputwillremaininthatnewstateevenaftertheinputpulseis over.
23.Whatare the typesofshift register?
Serial in serial out shift register?
Serial in parallel out shift register
Parallel in serial out shift register
Parallel in parallel out shift register
Bidirectional shift registershift register
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24.State the types ofcounter?
Synchronous counter
Asynchronous Counter
25.Thetpdfor eachflip-flop is 50 ns. Determine themaximumoperating frequency for
MOD -32 ripple counter fmax(ripple)=5 x50 ns =4 MHz
26.Whatis racearoundcondition?
In theJK latch, theoutput is feedback to theinput,and thereforechanges inthe output
results changein theinput. Dueto this in thepositivehalfofthe clock pulseifJ and K areboth
high thenoutput toggles continuously. This condition is known as race around condition.
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UNITIV
ASYNCHRONOUS SEQUENTIAL CIRCUITS AND PROGRAMMABLE
LOGIC DEVICES
1.Defineasynchronoussequential circuit?
Inasynchronoussequentialcircuits,changeininputsignalscanaffectmemory element at
anyinstant oftime.
2.Givethe comparisonbetweensynchronous andasynchronous sequential circuits?
Synchronous sequentialcircuits Asynchronous sequential circuits
Memoryelements are clocked flip-flops Memoryelementsareeitherunlockedflip
-flops ortimedelayelements.
Easierto design Moredifficult to design
3.Whatare thesteps for thedesignofasynchronous sequential circuit?
Construction ofprimitive flow table
Reduction of flow table
State assignment is made
Realization ofprimitive flow table
4.Whatis fundamentalmodesequential circuit?
Input variables changes if the circuit is stable
Inputs are levels, not pulses
Only one input can change at a given time
5.Whatarepulsemodecircuits?
Inputs are pulses
Width of pulses is long for circuit to respond to the input
Pulse width must not be so long that it is still present after the new state is
reached
6.Whatis thesignificanceofstateassignment?
In synchronous circuits-state assignments are made with the objective of circuit
reduction
Asynchronous circuits-its objective is to avoid critical races
7.When does race conditionoccur?
Two ormorebinarystatevariables changetheirvalueinresponseto thechangein i/p
variable
8.Whatare thedifferent techniques used instateassignment?
Shared row state assignment
One hot state assignment
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9.Whatare thesteps for thedesignofasynchronous sequential circuit?
Construction of primitive flow table
Reduction of flow table
State assignment is made
Realization of primitive flow table
10.Whatis hazard?
Unwanted switchingtransients arecalled hazards.
11.Whatis static1 hazard?
Output goes momentarily0 when it should remainat 1
12. Whatarestatic0 hazards?
Output goes momentarily1 when it should remainat 0
13.Whatis dynamichazard? Output changes 3 ormoretimes when it changesfrom 1 to 0 or0 to 1
14. Whatis the causefor essential hazards?
Unequal delaysalong2 ormorepath from sameinput
15.Whatis SM chart?
Describes thebehavior of a state machine
Used in hardware design of digital systems
16.Whatare theadvantages ofSMchart?
Easy to understand the operation
Easy to convert to several equivalent forms
17.Whatis primitiveflowchart? Onestablestateper row
18.Whatis combinational circuit?
Output depends on thegiven input.It has no storageelement.
19. Whatis state equivalence theorem? TwostatesSAandSBareequivalentifandonlyifforeverypossibleinputX
sequence, theoutputs arethesame and thenext states are equivalent i.e., ifSA (t +1)=SB(t+1)
andZA=ZBthen SA =SB.
20. Whatdo youmeanby distinguishing sequences?
Twostates,SAandSBofsequentialmachinearedistinguishableifandonlyif
theirexistsatleastonefiniteinputsequence.Which,whenappliedtosequentialmachine causes
different output sequences dependingon whetherSA orSBis theinitial state.
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21.Prove thatthe equivalencepartition is unique Considerthattherearetwoequivalencepartitionsexist:PAandPB,andPA)PB.
Thisstatesthat,thereexist2statesSi&Sjwhichareinthesameblockofonepartition
andnotinthesameblockoftheother.IfSi&SjareindifferentblocksofsayPB,there
existsatleastoninputsequencewhichdistinguishesSi&Sjandtherefore,theycannot bein
thesameblock ofPA.
22. Define compatibility
StatesSiandSjsaidtobecompatiblestates, ifandonlyifforeveryinput sequencethat
affectsthetwostates,thesameoutputsequence,occurswheneverboth outputs arespecified
andregardless of whetherSi on Sj is theinitial state.
23. Define mergergraph. Themergergraph is defined asfollows.It contains thesamenumberofvertices as
thestatetablecontainsstates.Alinedrawnbetweenthetwostateverticesindicateseach
compatiblestatepair.It two states areincompatibleno connectinglineis drawn.
24.Defineincompatibility
Thestatesaresaidtobeincompatibleifnolineisdrawninbetweenthem.If implied states
areincompatible, theyarecrossed&the correspondinglineis ignored.
25.Explaintheprocedureforstateminimization.
Partition the states into subsets such that all states in the same subsets are 1 -
equivalent.
Partition the states into subsets such that all states in the same subsets are 2 -
equivalent.
Partition the states into subsets such that all states in the same subsets are 3 -
equivalent.
26.Definestate table. Forthedesignofsequentialcounterswehavetorelatepresentstatesandnext
states.Thetable,whichrepresentstherelationshipbetweenpresentstatesandnextstates, is called
statetable.
27.Whatare thesteps for thedesignofasynchronous sequential circuit?
Construction of a primitive flow table from theproblem statement.
Primitive flow table is reduced by eliminating redundant states using the state
reduction
State assignment is made
The primitive flow table is realized using appropriate logic elements.
28.Defineprimitiveflowtable
Itisdefinedasaflowtablewhichhasexactlyonestablestateforeachrowinthe table.
Thedesign processbegins with the construction ofprimitive flowtable.
102
29.Whatare the typesofasynchronous circuits?
Fundamental mode circuits
Pulse mode circuits
30.GivethecomparisonbetweenstateAssignmentSynchronouscircuitandstate
assignmentasynchronous circuit.
In synchronous circuit, thestateassignments aremadewith theobjectiveof
circuitreduction.Inasynchronouscircuits,theobjectiveofstateassignmentistoavoid critical
races.
31.Whatare races? When2ormorebinarystatevariableschangetheirvalueinresponsetoachange
inaninputvariable,raceconditionoccursinanasynchronoussequentialcircuit.Incase of unequal
delays, a race condition may cause the state variables to change in an unpredictablemanner.
32.Definenoncritical race.
Ifthefinalstablestatethatthecircuitreachesdoesnotdependontheorderin
whichthestatevariablechanges,theraceconditionisnotharmfulanditiscalledanon critical race.
33.Define critical race?
Ifthefinalstablestatedependsontheorderinwhichthestatevariablechanges, the race
condition is harmful and it is called a critical race.
34.Whatis a cycle?
Acycleoccurswhenanasynchronouscircuitmakesatransitionthroughaseries
ofunstablestates.Ifacycledoesnotcontainastablestate,thecircuitwillgofromone unstableto
stableto another, until theinputs arechanged.
35.Writea shortnoteonfundamentalmodeasynchronous circuit. Fundamentalmodecircuitassumesthat.Theinputvariableschangeonlywhen
thecircuitisstable.Onlyoneinputvariablecanchangeatagiventimeandinputsare levels and not
pulses.
36.Writea shortnoteon pulsemode circuit.
Pulsemodecircuitassumesthattheinputvariablesarepulsesinsteadoflevel. The width
ofthepulses is longenoughforthecircuit to respond to theinput and thepulse width must not
beso longthat it is still present afterthenew stateis reached.
37.Definesecondary variables
Thedelayelementsprovideashorttermmemoryforthesequentialcircuit.The present
state and next state variables in asynchronous sequential circuits are called
secondaryvariables.
38.Defineflowtableinasynchronous sequential circuit.
103
Inasynchronoussequentialcircuitstatetableisknownasflowtablebecauseof the
behaviouro ftheasynchronoussequent ia lc ircuit . The
stagechangesoccur inindependentofaclock,based
onthelogicpropagationdelay,andcausethestatestoflowfrom onetoanother.
39.Apulsemodeasynchronousmachinehastwoinputs.Ifproducesanoutput
whenevertwoconsecutivepulsesoccurononeinputlineonly.Theoutputremains at1until
apulsehas occurredontheotherinputline.Writedownthestatetable for themachine.
40.Whatis fundamental mode?
Atransitionfromonestablestatetoanotheroccursonlyinresponsetoachange
intheinputstate.Afterachangeinoneinputhasoccurred,nootherchangeinanyinput
occursuntilthecircuitentersastablestate.Suchamodeofoperationisreferredtoasa fundamental
mode.
41.Writeshortnoteonsharedrowstateassignment. Racescanbeavoidedbymaking aproperbinaryassignmenttothestatevariables. Here,
thestatevariablesare assignedwith binarynumbers in such awaythat onlyone
statevariablecanchangeatanyonestatevariablecanchangeatanyonetimewhena
statetransitionoccurs.Toaccomplishthis,itis necessarythatstatesbetweenwhich
transitionsoccurbegivenadjacentassignments.Twobinaryare saidtobeadjacentif theydifferin
onlyonevariable.
41.Whatis programmablelogicarray? Howitdiffers fromROM?
In some cases the number of don’t care conditions is excessive, it is more
economicaltouseasecondtypeofLSIcomponentcalledaPLA.APLAissimilartoa
ROMinconcept;howeveritdoesnotprovidefulldecoding ofthevariablesanddoesnot generates
all theminterms as in theROM.
42.Whatis mask-programmable?
WithamaskprogrammablePLA,theusermustsubmitaPLAprogramtableto
themanufacturer.
43.DefinePLD.
ProgrammableLogicDevicesconsistofalargearray ofANDgatesandORgates that can
beprogrammed to achievespecificlogic functions.
44.Give theclassificationofPLDs. PLDs are classified as
PROM (ProgrammableRead OnlyMemory)
104
ProgrammableLogicArray(PLA)
Programmable ArrayLogic (PAL)and
GenericArrayLogic(GAL)
45.DefinePLA
PLAisProgrammableLogicArray(PLA).ThePLAisaPLDthatconsistsofa
programmableAND arrayandaprogrammableORarray.
46.DefinePAL
PALisProgrammableArrayLogic.PALconsistsofaprogrammableANDarray and a
fixed ORarraywith output logic.
47.Why theinputvariables to a PALarebuffered
TheinputvariablestoaPALarebufferedtopreventloadingbythelargenumber of
ANDgateinputs to which availableorits complement can beconnected.
48.Whatis programmablelogicarray? Howitdiffers fromROM?
In some cases the number of don’t care conditions is excessive, it is more
economicaltouseasecondtypeofLSIcomponentcalledaPLA.APLAissimilartoa
ROMinconcept;howeveritdoesnotprovidefulldecoding ofthevariablesanddoesnot generates
all theminterms as in theROM.
49.Give thecomparison betweenPROMandPLA.
PROM PLA
1. AndarrayisfixedandORarray
is programmable.
2.Cheaperand simpleto use.
Both AND and OR arrays are
Programmable.
Costliest and complexthan PROMS.
105
UNITV
VHDL
1.Write theacronymfor VHDL?
VHDLisanacronymforVHSICHardwareDescriptionLanguage(VHSICisan acronym
forVeryHigh SpeedIntegrated Circuits).
2. Whatare thedifferent types ofmodeling VHDL?
Structural modeling
Data flow modeling
Behavioral modeling
Mixed typeofmodeling
3. Whatis a packageandwhatis theuseofthesepackages Apackagedeclarationisusedtostoreasetofcommondeclarationsuchas
componentstypesproceduresandfunctionsthesedeclarationcanthenbeimportedinto others
design units using ause clause.
4.Whatis variable class give exampleforvariable?
Anobjectofvariableclasscanalsoholdasinglevalueofagiventype,However in this
casedifferent values can beassigned to avariable at different time.
Ex: variabless: integer;
5.Nametwo subprograms andgive thedifferencebetweenthese two.
Function: Only one output is possible in function
Procedure: Many outputs possible using procedure
6.Whatis subprogramoverloading? Iftwoormoresubprogramtobeexecutedin asamename. Overloadingof subprogram
should beperformed.
7.Write theVHDLcoding fora sequentialstatement (d-flipflop) entitydffis port(clk,d:in std_logic; q:out std_logic);
end;
architecturedffofdffis begin
process(clk,d)
begin
if clk’ eventand clk=’1’then q<=d;
end process;
end;
8.Whatare thedifferentkinds ofthe testbench?
Stimulus only
Full test bench
Simulator specific
Hybrid test bench
Fast test bench
106
9.Whatis MooreFSM The output of a Moore finite state machine (FSM) depends only on the state and not
on itsinputs.Thistypeofbehaviourcanbemodeledusingasingleprocesswiththe casestatement that
switches on thestatevalue.
10.Write thetestbenchforandgate
entitytestand2 is end entity
architectureio oftestand2 is signal a,b,c:std_logic;
begin
g1:entitywork.and2(ex2)port map(a,b,c)
a<=’0’,’1’after100 ns;
b<=’0’,‘1’after150 ns;
end;
11.Givethedifferentarithmeticoperators? Operatorsymbol Operation performedNumberofoperands
*MultiplyTwo
/DivideTwo
+Add Two
-Subtract Two
%Modulus Two
**Power (exponent)Two
12.Givethedifferentbitwiseoperators.
Operatorsymbol Operation performedNumberofoperands
~Bitwisenegation One
&Bitwiseand Two
|BitwiseorTwo
^BitwisexorTwo
^~or~^ BitwisexnorTwo
~&Bitwisenand Two
~| BitwisenorTwo
13.Differentiatea signal andvariable?
Signal Variable
Represents circuit in interconnects(wires) Represents local information
Can beglobal(seen byentire code) Local(visible only inside the
correspondingprocess,function,or
procedure)
Update is not immediate in sequential
code(newvaluegenerally only availableatthe
conclusionof the process,function,or procedure
Updatedimmediately(newvaluecanbe
used in thenext lineof code)
14.Explain‘case’statementinVHDLwithanExample. Thecasestatementselectsoneofthebranchesforexecutionbasedonthevalueof
expression.Theexpressionvaluemustbeofdiscretetypeorofaone-dimensionalarray
type.Caseisthestatementintendedexclusivelyforsequentialcode(alongwithIF,LOOP and
107
WAIT).
Thesyntaxis
CASE identifierIS
WHEN value=>assignments; WHEN value=>assignments;
ENDCASE;
Example
entitydffis
port(clk,rst,d:in std_logic;q:out std_logic);
end dff;
architecturebehaviourofdffis begin
process(clk,d)
begin
case rst is
WHEN ‘1’=>q<=’0’; WHEN ‘0’=>
if (clk’event and clk=’1’)then q<=d;
end if;
WHEN OTHERS=>NULL; End case;
end process;
end behaviour
15.Explain‘Generate’statementinVHDLwithan Example. GENERATEisaconcurrentstatement(alongwithoperatorsandWHEN).Itis
equivalenttothesequentialstatementLOOPinthesensethatitallowsasectionofcode to be repeated
anumberoftimes, thus creatingseveral instances ofthesame assignments.
Thesyntaxis
Label:FOR identifierIN rangeGENERATE (concurrentassignments)
EndGENERATE;
Example:
SIGNALx: bit_vector(7 downto 0); SIGNALy: bit_vector(15 downto 0); SIGNALz:
bit_vector(7downto 0);
G1:FORIIN x’RANGEGENERATE Z(i)<=x(i)andy(i+8);
EndGENERATE;
16.Give thebehavioralmodel forJKflipflop.
entityJKFFis
port(SR, RN, J, K,clk:in std_logic;q:out std_logic);
end JKFF;
architecturebehaviourofJKFFis begin
process(clk, SN, Rn)
begin
ifRN=’0’then q<=’0’;
elsifSN=’0’then q<=’1’;
elsifclk=’0’and clk ‘event then q<=(Jand NOT q)or (NOTk and q); end if;
end process;
end JKFF;
17.Give thebehavioralmodel forTflip-flop. entitytffis
port (clk,t:in std_logic;q:out std_logic);
108
end tff;
architecturebehaviouroftffis begin
process(clk,t)
18.Give thedataflowmodel for full subtractor. Entityfulladderis
port(a,b, c:in std_logic;diff, borrow:out std_logic);
end fullsubtractor;
architecturebehaviourof fullsubtractoris diff<=(a XORb) XORc;
borrow<=(NOT a ANDb)OR(b ANDc) OR(cANDNOT a);
end behaviour
19.Whatis componentinstantiation? Acomponentinstantiationstatementdefinesasubcomponentoftheentityin which it
appears.Itassociates thesignal in theentitywith theportsofthat subcomponent. A format
ofacomponentinstantiation statement is
Component-label:component-name[port map(association-list)]; Example:
-- Component declaration:
Component NAND2 port (A, B: in std-logic;
Z: out std_logic); End component;
-- Componentinstantiation: N1:NAND2 port map (s1, s2, s3);
20.Differentiatesequential fromconcurrentsignal assignmentstatements.
Sequential signal assignmentstatements concurrentsignal assignmentstatements
Signal assignment statements can also
appear within the body of process
statement called sequential signal
assignment statements
Signal assignment statements that appear
outside of process are called concurrent
signal assignment statements.
Notevent triggered and are executed in
sequence in relation to other sequential
statement that appear within theprocess.
Event triggered i.e., they are executed
wheneverthereisaneventonasignalthat appears
in its expression.
109
DIGITAL LOGICCIRCUITS-16 MARKS QUESTIONS
UNIT - I
REVIEW OF NUMBER SYSTEM AND DIGITAL LOGIC FAMILIES
1. Convert the following into decimal
a. 4021.2)5
b. (1101.101)2
c. (634)8
2. Convert the following into
a. (9 B 2.1A) H to its decimal equivalent.
b. 0.640625 to its octal equivalent.
c. 0.1289062 decimal number to its hex equivalent.
d. Decimal number 22.64 to hexadecimal number.
e. Gray code 101011 into its binary equivalent.
f. 10111011 is binary into its equivalent gray code.
3. DrawthecircuitofaCMOStwoinputNANDgateandexplainitsoperation.
4. Design an odd Parity hamming code generates and detector for 4 bit data and explain the
logic. 5. The hamming code 101101101 is received. Correct it if any errors. There are four parity
bits and even parity is used.
6. Given that a frame with bit sequence 1101011011 is transmitted, it has been received as
1101011010. Determine the method of detecting the error using any one error method.
7. DrawthecircuitofTTLNANDgateandexplainitsoperation.
8. Draw thecircuit ofNMOSNANDgate andexplain its operation.
9. A 12 bit hamming code word containing 8 bit of data and 4 parity bit is read from
memory. What was the original 8 bit word that was written in to the memory of 12 bit word is
as (1) 101110010100 (2) 111111110100.
10. Explain thetotem pole, open collector and Tri-state logic ofTTLlogic family.
UNIT - II
COMBINATIONAL CIRCUITS
1. Designa4-bit binaryadder/ subtractorcircuit.
2. ExplainhowafulladdercanbebuiltusingtwohalfaddersandanORgate.
3. DesignahalfadderusingatmostthreeNORgates.
4. Using8to1 multiplexer, realizetheBoolean function T= f(w, x,y,
z)=Σ(0,1,2,4,5,7,8,9,12,13).
5. Designa8421 tograycode converter.
6. Draw thelogicdiagram of full subtractor and explain its operation.
7. Designa full adder circuit usingonlyNORgates.
8.What is Decoder? Implement the following Boolean function with 4*16 decoder.
9. What is Demultiplexer? Explain the concept of 1 to 8 Demultiplexer
10. Design and implement 16:1 multiplexer by using two 8:1 multiplexer.
11.Minimize the following boolean function by using K-map T= f(w, x,y, z)=
Σ(0,1,2,4,5,7,8,9,12,13)
12. Using4 : 1 6 d e c o d e r , realizetheBoolean function T= f(w, x,y,
z)=Σ(0,1,2,4,5,7,8,9,12,13).
14. Parity Encoder.
110
UNIT - III
SYNCHRONOUSSEQUENTIALCIRCUITS
1. RealizeaJK flip flop usingSRflip flop.
2. RealizeaSRflip flop usingNANDgates and explain its operation.
3. Explain various steps in the analysis ofsynchronous sequential circuits with suitable
example.
4. Distinguish betweenacombinational logic circuit and asequential logiccircuit.
5. Derivethecharacteristic equation ofSRflip flop T1PG 257
6. UsingaJK flip flop, explain how aD flip flop can beobtained.
7. Designa fourstatedowncounterusingT flip flop.
8. Designa4-bit synchronous 8421 decade counterwith ripple carry.
9. Designasynchronous 3-bit graycodeup counterwith thehelp of excitation table.
10. Describetheinput and output action ofJK master/slave flip flops.
11. DesignaMOD-10 synchronous counterusingJK flip flops. Write excitation table and
statetable.
12. RealizeSRflip flop usingNORgates and explain its operation.
13. Designa3-bit binaryup-down counter.
14. Designa4-bit UP/DOWN synchronous binarycounter.
15. Designadivideby6 (MOD 6) counterusingTflip flop.
16. RealizeaD flip flop usingSRand T flip flops.
17. Explain the workingofBCD RippleCounter with thehelp ofstatediagram and logic
diagram.
18. Designasequential detector which produces an output 1 everytimetheinput sequence
1011 is detected.
19. Explain in detail about serial in serial out shift register.
UNIT - IV
ASYNCHRONOUSSEQUENTIALCIRCUITS AND
PROGRAMMABLELOGICDEVICES
1. A combinational circuit is defined bythe followingfunction. f1(a,b,c)=Σ(0,1,6,7)
f2(a,b,c)=Σ(2,3,5,7)ImplementthecircuitwiththePLAhaving3inputs,3product
termandtwo outputs.
2. UsingROM,designacombinationalcircuitwhichaccepts3bitnumberand
generates an output binary number equivalent to square of input number.
3. Explain theoperation ofbipolarRam cell with suitablediagram.
4. Explain thedifferent types ofROM.
5. What is Ram?Explain thedifferent types ofRAMin detail.
6. Explainwithneatdiagramthedifferenthazardsandthewaytoeliminatethem.
7.State with aneat examplethemethod fortheminimization ofprimitive flow table.
8.Designa asynchronous sequential circuit with2 inputs T and C. Theoutput attains
valueof1 when T =1&cmovesfrom 1 to 0. Otherwisetheoutput is 0.
9.Explain in detail aboutRaces.
10.Explain thedifferentmethods ofstate assignment
11.Explain the fundamental mode asynchronous sequential circuit.
12.Brieflyexplain thepulsemode asynchronous sequential circuit.
13.What arethesteps in the analysis and design ofasynchronous sequential circuits?
111
Explain with an example.
14.Find a circuit that has no statichazards and implements theBoolean function
F(A,B,C,D)=Σ(0,2,6,7,8,,10,12)
15.Develop thestatediagram and primitive row flow table foralogicsystem that has two
inputs Sand Rand asingleoutput Q. Thedeviceis to bean edgetriggered SR flip flop
but withouta clock. Thedevicechanges stateon the risingedgesofthetwo inputs. Static
inputvalues arenot to have anyeffect in changingtheQ output.
16.Designan asynchronous sequential circuit that has two inputs X2 and X1and one
output Z. Theoutput is to remain a0 as long as X1 is a0. The first changein X2 that
occurs while X1 is a1 will causeZto bea1.zis to remain a1 until X1returns to 0.
Construct astatediagram and flow table. Determinetheoutput equations.
UNIT - V
VHDL
1. Explain thevarious modelingmethods used in VHDLwith an example.
2. Explain in detail about theprincipal ofoperation of VHDLSimulator.
3. Writethe VHDLprogram for4 bit counter.
4. Writethe VHDLprogram for full adderinall threetypes ofmodeling?
5. Write VHDLprogramfor4:1 MUX and 1:4 DEMUX usingbehavioral modeling.
6. Write VHDLprogramfor encoder and decoderusingstructural modeling.
7. With an example explainin detail thetest bench creation.
8. Writeaverilogprogramfor1)Full Adder2)ShiftRegister
112
UNIT-I PARTIAL DIFFERENTIAL EQUATIONS
PART A 1. Form a PDE by eliminating the arbitrary constants ‘a’ and ‘b’ from z = ax2+by2. (AU-A/M- 2017) Given z = ax2+by2
p = 2ax 2
p = ax----------------------------- (1)
q = 2by2
q = by------------------------------- (2)
From (1) and (2) , eliminate a and b
z =22
qypx
2z = px+qy 2. Form the partial differential equation from (x-a)2+(y-b)2+z2 = 1,by eliminating a and b. Partial differentiation w.r.to x and y gives (AU-M/J-2013)-2 2(x-a)+2zp=0 ; (x-a)= - pz 2(y-b)+2zq=0 ; (y-b)= - qz Using these in the given equation we get , p2z2+q2z2+z2=1 3. Form the p.d.e from z=ax3+by3(AU-M/J-2014)-2 z=ax3+by3
………(1)
; ie) p= 3ax2 q= 3ay2
ie)
(1) z= ie) 3z=px+qy
4. Form a PDE by eliminating the arbitrary function f from z = eayf(x+by) (AU-
A/M-2017)
PDE required theis
)(
..)( q
.)(.)().(
1).(
)(
'
'
apbq
e
zbyxf
ae
pbq
aebyxfpb
aebyxfbe
peaebyxfbbyxfe
y
zq
byxfex
zp
byxfez
ayay
ay
ay
ay
ayayay
ay
ay
5. Find the PDE of all spheres whose centre lie on x=y=z. (AU-N/D-2016)-3
23axx
z
23ayy
z
ax
p
23b
y
q
23
b
qypx
3
113
General equation of the sphere is
Here centre is (a,b,c) and radius r. Centre lies on x =y = z . i.e a = b = c.
Equation of the sphere is --------------(1)
Diff. w.r.to x partially 2(x-a) +2(z-a) = 0 ; (x-a) + (z-a) p= 0 ----(2)
Diff. w.r.to y partially 2(y-a) +2(z-a) = 0 ; (y-a) + (z-a) q= 0 ----(3)
(2) x – a+zp –ap = 0 ; x + zp = a+ap ; x+zp = a(1+p) ------------- (4) (3) y –a+ zq - aq = 0 ; y + zq = a + aq; y + zq = a(1+q) ------------(5) (4) / (5) x+xq+zp+zpq = y+yp+zq+zpq x+xq+zp-y-yp-zq = 0 ; x-y+(x-z)q+(z-y)p = 0 x-y = (z-x)q+(y-z)p ; (z-x)q+(y-z)p = x-y. 6. Form the partial differential equation by eliminating the arbitrary constants a and b from log(az-1) = x+ay+b (AU-A/M-2015) Given log(az-1) = x+ay+b -------------------------------(1)
Differentiating w.r.t x : 11
1
ap
az --------------------(2)
Differentiating w.r.t y : aaqaz
1
1 ---------------------(3)
From (2) : pz
a
1
--------------------------------------(4)
From (3) : q= az-1 -----------------------------------------(5) Solving (4) and (5) and eliminate ‘a’. p(q+1) = zq This is the required PDE. 7. Form the p.d.e by eliminating the arbitrary function f from z = f(y/x).(AU- N/D- 2012)-2
Given:
x
yfz . -------------- (1)
Diff. (1) p.w.r.to x we get
2
'
x
y
x
yfp
x
z -------- (2)
Diff. (1) p.w.r.to x we get
xx
yfq
y
z 1' -------- (3)
x
y
xx
y
q
p 12
; xp + yq = 0 is the required p.d.e.
8. Form the p.d.e by eliminating the function f from z = f(x2-y2) (AU-N/D- 2017)
Given z =f(x2-y2) Differentiation w.r.to x : p = f’(x2-y2).2x----------------(1) Differentiation w.r.to y : q = f’(x2-y2).-2y ----------------(2) Eliminating f from (1) and (2)
2222 )()()( rczbyax
2222 )()()( rczbyax
x
z
y
z
114
y
x
q
p
2
1
Px – qy = 0. This is the required p.d.e. 9. Form the p.d.e by eliminating the arbitrary function f(x2-y2, z) = 0. (AU -N/D-2014) Given x2-y2 = f(z) Partially differentiating w.r.to x , 2x = f’(z)p------(1) Partially differentiating w.r.to y , -2y = f’(z)q------(2) (1)/(2)implies that p/q = -x/y py = -qx qx+py = 0.This is the required p.d.e. 10. Form the p.d.e by eliminating the arbitrary function from f(x2+y2, z-xy) = 0. (AU-M/J-2016) Given x2+y2 = f(z-xy) Partially differentiating w.r.to x, 2x = f’(z-xy)(p-y)-------(1) Partially differentiating w.r.to y, 2y = f’(z-xy)(q-x)-------(2) (1)/(2)implies that x/y = (p-y)/(q-x) qx-x2 = py-y2 This implies that x2+y2 = qx- py. This is the required p.d.e. 11.Find the complete integral of p+q = 1.(AU- N/D- 2014) Given p+q = 1--------------------------(1) Let z = ax+by+c-----------------------(2)
apx
z
and bq
y
z
-----(3)
Substitute equation (3) in equation (1) , we get a+b = 1 That is b = 1- a--------------------(4) Substitute equation (4) in equation (2),we get Z = ax + (1-a) y+ c is the complete integral. 12. Find the complete solution of the partial differential equation p3-q3 = 0. (AU-A/M-2016) This equation is of the form F(p,q) = 0 Hence the trial solution is z = ax+by+c p= a and q = b Therefore a3 – b3 = 0
13. Find the complete integral of 1 qp (AU-N/D-
2017)
1 qp --- (1)
This is of the type F(p,q)=0
The trial solution is z=ax+by+c
Sub. p=a and q=b in (1)
Therefore (1) implies 21 ab
115
Then, cyaaxz 2
1 which is Complete Integral
14. Find the complete integral of pqp
y
q
x
pq
z
(AU-N/D-2016) This is of the form z = px + qy + f(p,q) Given z = px+qy+(pq)3/2
Hence the complete integral is z = ax+by+(ab)3/2
15. Find the complete integral of p+q=x+y (AU-N/D-2013)-2 Let p+q=x+y=k p-x=k, y-q=k p=k+x, q=y-k
z=
=
= ckyyx
kx 22
22
16. Find the complete solution of q = 2px. (AU-A/M-2015) q=2px=a (say) q=a; p=a/2x dz = (a/2x) dx + ady Integrating, Z = (a/2) logx + ay +b This is the complete solution. 17.Find the general solution of the Lagrange linear equation given by pyz+qzx = xy.
(AU-N/D-2013) This is of the form : Pp+Qq= R
Auxiliary equation is : R
dz
Q
dy
P
dx
xy
dz
zx
dy
yz
dx
Group 1: zx
dy
yz
dx
xdx = ydy Integrating , x2/2 = y2/2+c1
2/2 x2-y2 = u
Group 2: xy
dz
yz
dx
xdx = zdz Integrating, x2-z2 = v Therefore the solution is φ(u,v) = 0 Φ(x2-y2, x2-z2) =0 18. What is the C.F of (D2-DD’)z=x+y
The A.E is m2-m=0 implies m=2(twice)
qdypdx
dykydxxk )()(
116
Therefore C.F = f1(y+2x)+xf2(y+2x)
19. Solve (D4-D’4)z = 0. (AU- M/J -2014) A.E is m4-14 = 0 (m2)2-(12)2 = 0 implies that (m2+1)(m2-1) = 0 m= 1,-1 and m = i,-i z = f1(y+x)+f2(y-x)+f3(y+ix)+f4(y-ix). 20. Solve (D3-3DD’2+2D’3)z = 0.(AU A/M 2018)-3 A.E is m3-3m+2 = 0 m= 1,1,-2 The solution is z = f1(y-2x)+f2(y+x)+xf3(y+x) 21. Solve (D3-D2D’-8DD’2+12D’3)z=0
The A.E is m3-m2-8m+12=0
m=2,2,-3
The Solution is , z= )3()2()2( 321 xyfxyxfxyf
22. Find the particular integral of (D2-D’2+DD’)z = cos(x+y).(AU-N/D- 2012)
P.I =
yxDDDD
cos1
2''2[Replace D2,DD’,D’2 by -1,-1,-1]
= yx cos0
1= yx
DD
cos
2
1'
= yxDD
DD
cos
4
22'2
'
= yxDD
cos
3
2 '
=3
sinsin2
yx
23. Solve x
z
yx
z
x
z
2
2
2
= 0
(AU-N/D- 2013) (D2-DD’+D)=0 D(D-D’+1) = 0 that implies (D-m1D’-0)(D-D’+1) = 0 m1 = 0 , c1 = 0, m2 = 1 ,c2 = -1 The solution is z = e0xf1(y)+e-xf2(y+x)
24. Solve 02
yx
z (AU-A/M-
2017)
002
y
z
y
z
xyx
z
0
y
z
yyfzyyfzyf
y
z)()()(
z=F(y)+g(x)
117
25. Solve (D+D’-1)(D-2D’+3)z = 0 (AU-N/D- 2015) Here c1 = 1 c2 = -3 m1= -1 m2 = 2 C.F = exf1(y-x)+e-3xf2(y+2x)
PART – B 1. a. Form the PDE by eliminating the arbitrary function φ from the relation Φ(x2+y2+z2, xyz) = 0. (AU-M/J-2016)-2-(8) b. Find the partial differential equations of all planes which are at a constant distance ‘k’ units from the origin. (AU-A/M-2016)(8) 2. a. Form the PDE by eliminating the arbitrary function ‘f’ and ‘g’ from z = x2f(y) +y2g(x) (AU-N/D-2013)(8) b. Form the PDE by eliminating the arbitrary functions ‘f’ and ‘ф’ from the relation z = x f(y/x) +y ф(x). (AU-A/M-2016)(8) 3. a. Form the partial differential equation by eliminating arbitrary functions from z = y2+2f(1/x+log y)(AU-M/J-2014)(8) b.Find the complete solution of 9 (p2z + q2) = 4. (AU-N/D-2014)-2(8)
4. a. Find the singular solution of the p.d.e. z = px+qy+ 221 qp
(AU-N/D-2015)-4(8) b. Solve: z = px + qy +p2+p-q2. (AU-M/J-2014)-2(8) 5. a. Find the general solution of z=px+qy+p2+pq+q2 (AU A/M 2018)-3(8) b. Find the singular solution of z = px+qy+p2-q2(AU A/M 2017)-4 (8) 6. a. Solve p2x2+q2y2 = z2 . (AU-N/D-2014)-2-(8) b. Solve z = px+qy+p2q2 and obtain its singular solution.(AU-A/M-2015)- (8) 7. a. Find the complete solution of z2 (p2+q2) = x2 +y2. (AU-A/M-2015)- (8) b. Obtain the complete solution of p2+x2y2q2 = x2z2(AU –M/J-2015)-(8) 8. a. Find the general solution of (z2-2yz-y2)p+(xy+zx)q=xy-zx (AU A/M 2017)(8) b. Find the general solution of (z2-y2-2yz) p+(xy+zx)q = (xy-zx)(AU-A/M-2015)- (8) 9. a. Solve (x2-yz)p + (y2-zx)q = (z2-xy) (AU-A/M-2016)-3(8) b. Solve (x-2z)p + (2z - y)q = y-x (AU-A/M-2017)(8)
10. a. Solve x(y-z)p+y(z-x)q = z(x-y)(AU-M/J-2014)-2(8) b. Solve x(z2-y2)p + y(x2-z2)q =z(y2-x2) (AU-M/J-2016)-3(8) 11. a. Solve (D3-2D2D’)z = 2e2x+3x2y.(AU-A/M-2016)(8) b. Solve (D2-5DD’+6D’2)z = ysinx (AU N/D 2017)(8) 12. a. Solve (D2+DD’-6D’2)z = ycosx (OR) (r+s-6t)=y cosx. (AU-A/M-2018)-3(8) b.Find the general solution of (D2+2DD’+D’2)z=xy+ex-y(AU N/D 2017)(8) 13. a. Solve (D3-7DD’2-6D’3)z = sin(2x+y) (AU-M/J- 2013)(8) b. Find the general solution of (D2+2DD’+D’2)z=x2y+ex-y (AU-A/M-2017)(8) 14. a.Solve: (D2-3DD’+2D’2)z = (2+4x)ex+2y (AU-N/D-2015)-2(8) b.Find the general solution of (D2-3DD’+2D’2+2D-2D’)z=sin(2x+y)
(AU A/M 2017)(8) 15. a. Solve (D2+2DD’+D’2-2D-2D’)z = sin(x+2y)(AU-N/D-2015)(8) b. Solve : (D2+4DD’-5D’2)z=sin(x-2y)+e2x-y (AU-N/D-2017)(8)
UNIT - II FOURIER SERIES
PART A
118
1. State Dirichlet’s conditions for a given function to expand in Fourier series. (AU -N/D- 2017)-8
Let f(x) be defined in the interval c<x<c+2 π with period 2 π and satisfy the following conditions: (1) f(x) is single valued (2) It has a finite number of discontinuities in a period of 2 π. (3) It has a finite number of maxima and minima in a given period.
(4) is convergent
These conditions are Dirichlet’s conditions. 2. State the sufficient conditions for existence of Fourier series. (AU A/M 2017)-2 The sufficient conditions for existence of Fourier series is given by (i) f(x) is defined and single valued except possibly at a finite number of points in (-π, π). (ii) f(x) is periodic with period 2π. (iii) f(x) and f ’(x) are piecewise continuous in (-π, π), then the Fourier series of f(x) converges to
(a) f(x) if x is a point of continuity
(b)
2
00 xfxf if x is a point of discontinuity.
3. Find the value of the Fourier series of f(x) = 0 in (-c,0) = 1 in (0,c) , at the point of discontinuity x = 0. (AU-M/J-2016)
The value of the Fourier series is f(x) =
2
00 ff =
2
1
2
10
4. If f(x) is discontinuous at a point x=a, then what does its Fourier series represent at that point. (AU-N/D-2017) If f(x) is discontinuous at a point x=a, then at that point f(x) cannot be expanded as Fourier series. 5. Find the constant term in the Fourier series corresponding to f(x) = cos2x expressed in the interval (-π, π).(AU-M/J-2012)
Given f(x) = cos2x = 2
2cos1 x
We know that f(x) = nxbnxaa
n
n
n
n sincos2 11
0
a 0 = xdxxdx
0
22 cos2
cos1
= dxxdxx
00
2cos11
2
2cos12 = 1
Therefore the Constant term = 2
1
2
0 a
6.Write down the form of the Fourier series of an odd function in (-l,l) and associated Euler’s formulas for Fourier coefficients.(AU-N/D-2013)
f(x) = l
xnb
n
n
sin
1
dxxf
c
c
)(
2
119
bn = dxl
xnxf
l
l
l
sin
1
7. Find the co-efficient bn of the Fourier series for the function f(x)=xsinx in (-2,2). (AU-N/D-2012) f(x) = xsinx f(-x) = -xsin(-x) = xsinx = f(x) Therefore f(x) is an even function. Therefore bn = 0.
8. Find a0 in the expansion of f(x)=ex as a Fourier series in ; 0<x<2π
(AU-N/D-2013)
1111)(
1 2
2
0
2
0
2
0
0
eedxedxxfa xx
9. Determine the Fourier series for the function f(x) = x in x . (AU-N/D-2015)
f(x) = x f(-x) = -x = -f(x) Therefore f(x) is an odd function .Therefore a0 = an = 0
bn =
nxdxxnxdxxf sin1
sin1
u = x v = sin nx u’ = 1 v1 = -cosnx/n u’’ = 0 v2 = -sinnx/n2
bn =
nnn
nx
n
nxxnn
12121sincos12
f(x) =
nxnn
n
sin12
1
10. Find the value of bn in the Fourier series expansion of f(x) = x+ π in (-π, 0) = -x + π in (0, π) (AU-M/J-2016)
Let f(x)= ф1(x) , (-π, 0) = ф2(x) , (0, π) ф1(x) = x+ π , ф2(x) =-x + π ф1(-x) = - x+ π = ф2(x) f(x) is an even function. Therefore bn=0. 11. Find bn in the expansion of f(x)=x2 as a Fourier series in ; -π<x<π
(AU-N/D-2017)
f(-x)=(-x)2=x2=f(x)
Therefore f(x) is an even function.
0 nb
12. Find the sum of the Fourier series for f(x) = x+x2 in – π<x< π at x = π. (AU-A/M-2017)
120
x= π is an end point. Sum of Fourier series =
2
ff =
2222
2
2
2
13. If
1
2
22 cos
43 n n
nxx
in 0<x<2π, then deduce that the value of
12
1
n n
(AU-N/D-2014)
Put x = 0,
1
2
2
12
2
12
22 1
6
1
12
214
3 nnn nnn
14. Expand f(x) = 1 as a half range sine series in the interval (0, π) (or) Find the sine series of function f(x) = 1 , 0 ≤ x ≤ π (AU-A/M-2015)-3
The half range sine series formula is f(x) = nxbn
n sin1
Where
nnn
nxnxdxnxdxxfb
n
n
112cos2sin
2sin
2
000
= oddisnif
nn
n
411
2
, 𝑓(𝑥) = ∑4
𝑛𝜋𝑠𝑖𝑛𝑛𝑥𝑛isodd
15. Expand f(x)=x in (0,1) as a Fourier sine series
1
sin)(n
n xnbxf
0 0
sin2
sin)(2
nxdxnxdxxfbn
odd isn ,n
4
even isn ,0
112cos2
0
when
when
b
nn
nxb
n
n
n
f(x)=
1
sin44
n
nxn
16. If f(x) is expanded as a half range cosine series, express dxxf
l 2
0
)( in terms of
a0 and an.(AU-N/D-2011)
dxxf
l 2
0
)( =
1
2
2
0
24 n
nalla
17. Write the complex form of the Fourier series of f(x).(AU N/D 2017)-3 The series for f(x) defined in the interval (C,C+2π) satisfying the Dirichlet’s Conditions can be put in the complex term as
121
f(x) = where
18.Find the complex form of Fourier series for f(x) = ex ; -π<x<π and f(x+2π) = f(x)
(AU-N/D-2017)
We know that f(x) = inx
n
neC
Where Cn =
sinh1
11
12
1
2
1
2
122
11
n
in
in
edxedxee
nxinxininxx
19. Write the complex form of the Fourier series of f(x) defined in –l<x<l
(AU-N/D-2017)-3
The series for f(x) defined in the interval (-l,l) satisfying the Dirichlet’s Conditions can be put in the complex term as
n
l
xin
necxf
)( where dxexfl
c
l
l
l
xin
n
)(2
1
20. State Parseval’s Theorem on Fourier series.(AU-A/M- 2017)-3 If f(x) is expressed as a Fourier series in the interval (a,b) then
Where a0 , an , bn are the Fourier constants and is the
R.M.S. value. 21. Define root mean square value of a function f(x) in a<x<b. (AU A/M 2018)-4 Let f(x) be a function defined in an interval (a,b) then ,
R.M.S = is called the root mean square.
22. Find the root mean square value of f(x) = x2 in the interval (0, π). (AU-A/M-2017)
RMS value 5
20
4
dxx
x
23. Find the root mean square value of the function f(x) = x in the interval (0,l) (AU –N/D-2017)-3
R.M.S = in the interval (a,b) = Here a = 0 ; b = implies that
24. Find the R.M.S value of f(x) = x(l-x) in 0≤x≤l. (AU-N/D-2015)
RMS value in (0,l) is
inx
neC
dxexfC
C
C
inx
n
2
)(2
1
1
222
02
2
1
4nn ba
ay y
ab
dxxf
b
a
2
)(
ab
dxxf
b
a
2
)(
0
0
2
l
dxx
l
33
2 ll
122
dxxfl
yl 2
0
2 2 Here l = 1
30
17
453
2
4
2
53
22 45551
0
453221
0
22 llll
l
lxxxl
ldxxlx
ly
25 . What do you mean by Harmonic Analysis?(AU –M/J-2013)-2 When a function f(x) is given by its numerical values at q equally spaced points, the Process of determining the co-efficient of Fourier series representing f(x) using numerical integration is known as Harmonic Analysis.
PART-B
1. a. Determine the Fourier series for the function f(x) = xcosx in (0,2π) (AU-A/M 2017)(8) b. Find a Fourier series with period 3 to represent f(x) = 2x-x2 in (0,3). (AU-N/D-2014)(8) 2. a. Find the Fourier series expansion of f(x) = 1 for 0<x< π = 2 for π<x<2π (AU-N/D-2013)(8) b.Find the Fourier series expansion the following periodic function of period 4 f(x) = 2+x , -2≤x≤0
= 2-x , 0<x≤2. Hence deduce that 222 5
1
3
1
1
1 ---- =
8
2
(AU-A/M-2015)(8) 3. a. Find the Fourier series of f(x) = x in - π <x<π. (AU-N/D-2016)(8)
b. Find the Fourier series for the function f(x) = xcos in - π <x<π. (AU-A/M-
2016)(8) 4. a. Determine the Fourier series for the function f(x) = x2 of period 2π in - π <x<π. Hence
deduce the value of
12
1
n n
(AU A/M 2018)-2-(8) b. Expand f(x) = x2 as a Fourier series in the interval (-π,π) and hence deduce that
90..............
4
1
3
1
2
11
4
444
(AU-N/D-2015)(8)5. a. Find the Fourier series
expansion of the periodic function f(x) of the period 2 defined by f(x) = l-x , 0<x≤l = 0 , l<x≤2l . in (o.2l) (AU- N/D 2017)(8)
b. Find the Fourier series for the function f(x) = xsin over the interval (-π,π).
(AU-A/M-2015)(8)
123
6. a. Obtain the Fourier series for the function given by f(x) =
lxinl
x
xlinl
x
02
1
02
1
Hence deduce that 8
................5
1
3
1
1
1 2
222
(AU-N/D-2014)-2(8)
b. Expand f(x) = x+x2 as a Fourier series in (-π,π) and hence deduce the value of (AU- N/D 2017)(8) 7. a. Find the half range sine series of f(x) = x cosπx in (0,1). (AU-N/D-2016)(8) b. Find the half range sine series of f(x) = 4x-x2 in the interval (0,4).Hence deduce the value of
the series ...........7
1
5
1
3
1
1
13333
(AU-N/D-2014)(8)
8. a. Find the half range sine series of f(x) = x , 0<x< π/2 = π –x , π /2 < x < π.
Hence deduce the sum of the series
12
12
1
n n
(AU-A/M-2017)(8) b.Find the half range cosine series for f(x)=x( -x) in (0, )
(AU-A/M-2018)(8)
9. a. Find the half range cosine series of f(x) = x in 0<x< . Hence deduce the value of
...............5
1
3
1
1
1222
to (AU- N/D 2017)-2-(8)
b. Find the half range cosine series expansion of (x-1)2 in 0<x< l. (AU-N/D-2014)(8)
10. a. Find the Half range cosine series of f(x) = sinx in (0,π) (AU-N/D-2015)(8)
b. Expand f(x) = x, 0< x <1 = 2-x, 1 < x <2 as a series of cosine in the interval (0, 2).
(AU A/M 2017)(8) 11. a. Find the complex form of the Fourier series f(x)=e-ax in the interval;–π<x<π.(AU A/M 2017)-2(8) b. Find the complex form of Fourier series of the function f(x) = ex in -π<x<π
(AU-M/J-2016)-(8) 12. a. Find the complex form of Fourier series of the function f(x) =sinx in -π<x<π
(AU-A/M-2014)-2-(8)
b. Find the complex form of Fourier series of the function f(x) =e-x in (-l,l) (AU-M/J-2016)-2-(8) 13. a. Find the complex form of the Fourier series f(x)=eax in the interval – π<x<π
where ‘a’ is a eeal constant. Hence deduce that
aanan
n
sinh
122
(AU-N/D-2015)(8) b. Calculate the first three harmonic of Fourierseries from the following data
124
x 0
2
y 1.0 1.4 1.9 1.7 1.5 1.2 1.0 (AU A/M 2018)-7(8) 14. a. Obtain the constant term and the coefficient of the first sine and cosine terms in the Fourier expansion of y as given in the following table: (AU A/M 2017)-5(8)
b.Compute first two harmonic of the Fourier series for f(x) from the table below:
(AU-A/M-2010)(8)
x : 0 600 1200 1800 2400 3000 y: 1.98 1.30 1.05 1.30 -0.88 -0.25 15. a. Determine the first two harmonics of Fourier series for the following data (AU-A/M-2015)(8)
x 0
3
3
2
3
4
3
5
2
y 1.98 1.30 1.05 1.30 -0.88 -0.25 1.98 b. Find the Fourier cosine series up to third harmonic to represent the function given by the following table (AU-N/D-2015)-2(8)
UNIT – III APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS
PART-A
1. Classify the differential equation 026432
22
2
2
u
y
u
y
u
yx
u
x
u
(AU-N/D- 2013) A = 3, B = 4, C = 6 B2-4AC = 16-72 <0 Therefore, elliptic equation. 2. Classify the partial differential equation uxx+uyy = f(x,y) (AU-M/J- 2016) A = 1,B = 0,C = 1 B2-4AC = -4 < 0 Elliptic equation 3. Classify the PDE of uxy=uxuy+xy (AU-N/D-2017)
Here B=1,A=0,C=0
B2-4AC=1>0
Given PDE is Hyperbolic equation.
4. Classify the partial differential equation (1-x2) zxx – 2xy zxy + (1-y2) zyy + x zx
3
3
2
3
4
3
5
x 0 1 2 3 4 5 y 9 18 24 28 26 20
x 0 1 2 3 4 5 y 4 8 15 7 6 2
125
+3x2y zy -2z = 0 (AU-A/M-2015)-2
A = (1-x2) ,B = -2xy , C = (1-y2) B2-4AC = 4x2y2 – 4(1-x2)(1-y2) = 4x2y2-4+4x2+4y2-4x2y2 = 4x2+4y2-4 x = y = 0, B2-4AC = -4 < 0 , Elliptic equation x = y = positive, B2-4AC = 4 > 0, Hyperbolic equation x = y = negative, B2-4AC = 4 > 0, Hyperbolic equation 5. Find the nature of the p.d.e 4uxx+4uxy+uyy+2ux-uy = 0 A = 4, B = 4, C = 1 B2-4AC = 0 Therefore, Parabolic equation
6. Use method of separation of variables, Solve ut
u
x
u
2 , where u(x,0)=6e-3x
(AU A/M 2017)
)23(
3
2
1
6
3,6
6)0,(
)0,(
tx
x
kx
lkkx
eu
kab
exu
abexu
eabeu
7. Write down the three mathematically possible solutions of one dimensional wave equation.(AU-A/M-2015)-5 y(x,t) = (c1epx+c2e-px)(c3epat+c4e-pat) y(x,t) = (c1coskpx+c2sinpx)(c3cospat+c4sinpat) y(x,t) = (c1x+c2)(c3t+c4)
8. In the wave equation 2
22
2
2
x
yc
t
y
, what does c2 stand for?
stringtheoflengthunitmass
Tension
m
Tc
/
2
9. What is the basic difference between the solutions of one dimensional wave equation and one dimensional heat equation with respect to the time?(AU- N/D- 2017)-2 Solution of the one dimensional wave equation is of periodic in nature. But solution of the One dimensional heat equation is not of periodic in nature. 10. State the assumptions in deriving one-dimensional wave equation.
(AU- N/D- 2017)-3 (i) The motion takes place entirely in one place i.e., xy plane. (ii) Only transverse vibrations are considered. The horizontal displacement of the particles of the string is negligible. (iii) The tension T is constant at all times and at all points of the deflected string. (iv) T is considered to be so large compared with the weight of the string and hence the force of gravity is negligible.
126
(v) The effect of friction is negligible. (vi) The string is perfectly flexible,i.e., it can transmit tension but not bending or sheering forces. (vii) The slope of the deflection curve at all points and at all instants is so small that sin α can be replaced by α, where α is the inclination of the tangent to the deflection curve. 11. Write down the diffusion problem in one-dimensional as a boundary value problem
in two different forms. (AU-M/J-2013)
one dimensional heat flow
Where s
Ka 2 is known as diffusivity of the material of the bar.
In the steady state 02
2
dx
ud
12. Write down one-dimensional heat equation and all possible solution for the same. (AU-A/M-2018)-10 ut=α2uxx
.
13. How many conditions are needed to solve the one dimensional heat equation? (AU-M/J- 2009)
Totally three conditions needed.
14. State the suitable solution of the one dimensionalheat equation
(AU-A/M-2017)
The suitable solution of the given equation is u(x,t) = (Acospx+Bsinpx) 15. State the governing equation for one dimensional heat equation and necessary conditions to solve the problem.
The one dimensional heat equation is where u(x,t) is the temperature
at time t at a point distant x from the left end of the rod. The boundary conditions are
a)u(0,t) = k10C for all t≥0
b)u(l,t) = k20C for all t≥0
c)u(x,0) = f(x) , 0<x<l 16. A rod of 30cm long has its ends A and B kept at 200C and 800C respectively until steady state conditions prevail. Find the steady state temperature in the rod.
(AU-A/M-2015)-2
2
22
x
ua
t
u
txx eCeBeAtxu22
111,
teCxBxAtxu22
222 sincos,
333, CBxAtxu
2
22
x
ua
t
u
tpce22
2
22
x
ua
t
u
127
The steady state equation of the one dimensional heat flow is =0 ..........(1)
The general Solution of (1) is u(x) =ax+b ......(2) The boundary conditions are u(0) = 30, and u(30)=80
Put x=0 in (2) , u(0)=b=20 Put x=30in (2) , u(30)=30a+b =80 30a+b=80 that implies 30a=60 implies that a=2 and equation (2) implies
u(x)=2x+20 17. A rod of length 20cm whose one end is kept at 300C and the other end is kept at 700C is maintained so until steady state prevails. Find the steady state temperature. (AU-N/D-2014)-2
The steady state equation of one dimensional heat flow is =0 ......(1)
The general Solution of (1) is u(x) =ax+b ......(2) The boundary conditions are u(0) = 30, and u(l)=70 Put x=0 in (2) , u(0)=b=30 Put x=l in (2) , u(l)=al+b =70 al=40 that implies a=40/l
(2) implies u(x)= Here l=20.Therefore u(x)=2x+30
18. An insulated rod of length l cm has its ends A and B maintained at 00C and 800C
respectively. Find the steady state solution of the rod. (AU-N/D-2013)
The steady state equation of the one dimensional heat flow is =0 .......(1)
The general Solution of (1) is u(x) =ax+b ......(2) The boundary conditions are u(0) = 0, and u(l)=80
Put x=0 in (2) , u(0)=b=0 Put x=l in (2) , u(l)=la+b =80 la+b=80 that implies la=80 implies that a=80/l and equation (2) implies
u(x)=(80/l)x 19. A bar of length 50cm has its ends kept at 200C and 1000C until steady state conditions prevail. Find the temperature at any point of the bar. (AU-A/M-2014)
The steady state equation of one dimensional heat flow is =0 .......(1)
The general solution of (1) is u(x)=ax+b .........(2) Put x=0 in (2) , u(0) = b = 20 Put x=l in (2), u(l) = al+b=100 al=80 a=80/l
a=80/50 that is a=8/5. Equation (2) implies u(x) =
20. A rod of 60cm long has its ends A and B kept at 200C and 800C respectively until
steady state conditions prevail. Find the steady state temperature in the rod.
(AU-N/D-2012)
2
2
dx
ud
2
2
dx
ud
3040
xl
2
2
dx
ud
2
2
dx
ud
205
8x
128
The steady state equation of the one dimensional heat flow is =0 ..........(1)
The general Solution of (1) is u(x) =ax+b ......(2) The boundary conditions are u(0) = 20, and u(60)=80
Put x=0 in (2) , u(0)=b=20 Put x=60in (2) , u(60)=20a+b =80 20a+20=80 that implies 20a=60 implies that a=3 and equation (2) implies
u(x)=3x+20
21. In 2D heat equation or Laplace equation, what is the basic assumption. When the heat flow is along the curves instead of straight lines, the curves lying in parallel planes the flow is called two dimensional.
22. Write all possible solutions of two dimensional heat equations 02
2
2
2
y
u
x
u
(AU-N/D-2017)-6 u(x,y)= (A1epx+ A2e-px)(A3 cospy+A4sinpy) u(x,y)=(A5cospx+A6sinpx)(A7 epy+A8 e-py) u(x,y)=(A9x+A10)(A11y+A12) 23. State two-dimensional Laplace equation.
The two-dimensional Laplace equation is given by =0 i.e.,
24. An infinitely long rectangular plate with insulated surface is 10 cm wide. The two long edges and one short edge are kept at zero temperature while the other short edge x=0 is kept at temperature given by u = 20y , 0≤y≤5 = 20(10-y), 5≤y≤10. Give the boundary conditions.
The equation to be solved is =0.The boundary conditions are
(i) u(x,0) = 0 for all x (ii) u(x,10) = 0 for all x (iii) u(∞,y) = 0 (ie) when x→∞, u→0 (iv) u(0,y) = 20y , 0≤y≤5
= 20(10-y), 5≤y≤10 25. A square plate has its faces and the edge y=0 insulated. It’s edges x=0 and x=π are kept at zero temperature and its fourth edge y =π is kept at temperature πx-x2
.Write the boundary conditions alone.
The equation to be solved is =0. The boundary conditions are
a) u(0,y) = 0 0≤ y≤π b)u(π,y) = 0 0≤ y≤π
c) 0≤ x≤π
d)u(x, π) = πx-x2 0<x< π PART-B
2
2
dx
ud
2
2
2
2
y
u
x
u
,02 u
2
2
2
2
y
u
x
u
2
2
2
2
y
u
x
u
0)( 0
y
y
u
129
1. A string is stretched and fastened to 2 points x=0 and x=l . Motion is started by displacing the string into the form y=kx(l-x) or y=l(lx-x2) from which it is released at time t=0. Find the displacement at any point on the string at a distance of x from one end at time t. (AU-A/M-2018)-7(16) 2. A string of length 2l is fastened at both ends. The midpoint of the string is taken to a height b and then released from rest in that position. Find the displacement. (AU-A/M- 2017)-3(16) 3. A string is stretched and fastened to points at a distance l apart. Motion is started by displacing the string in the form y=a sin(πx/l),0<x<l, from which it is released at time t=0. Find the displacement at any time t.(AU-M/J- 2014)(16) 4. A tightly stretched string of length ‘l’ with fixed end points is initially at rest in its equilibrium position.If it is set vibrating by giving each point a velocity
l
x
l
xvxy t
cos
3sin0, 0 ,where 0<x<l.Find the displacement of the string at a point,
at a distance x from one end at any instant‘t’.(AU –N/D-2012)(16) 5. A tightly stretched string with fixed end points x=0 and x=l is initially at rest in its equilibrium position. if it is set vibrating giving each point a velocity λx(l-x), show that
l
atn
l
xn
na
ltxy
n
12sin
12sin
12
18,
144
3
(AU –N/D-2014)(16) 6. Find the displacement of a string stretched between two fixed points at a distance of 2l apart when the string is initially at rest in equilibrium position and points of the
string are given initial velocities v = l
xin (0, l )=
l
xl 2 in (l, 2l), x being the distance
measured from one end. (AU –M/J-2016)16) 7. If a string of length l is initially at rest in its equilibrium position and each of its points is given a velocity v such that V=2 kx/l for 0<x<l/2 =2k(l - x)/l for l/2 <x <l (AU –N/D-2015)(16)
8. A bar, 10cm long with insulated sides, has its ends A and B kept at 200C and 400C
respectively until steady state conditions prevail. The temperature at A is then suddenly raised
to 500C and at the same instant that at B is lowered to 100C. Find the subsequent temperature
at any point of the bar at any time. (AU-A/M-2018)(16) 9.A rod of length l has its end A and B kept at 00C and 1000C respectively until steady state conditions prevail. If the temperature at B is reduced suddenly to 750C and at the same time the temperature at A raised to 250C find the temperature u(x,t) at a distance x from A and at time t. (AU-N/D 2017) –2(16) 10. An insulated rod of length l its ends A and B are maintained at 00C and 1000C respectively untiL steady state conditions prevail. If B is suddenly reduced to 00C and maintained so, find the temperature at a distance x from A at time t. (AU N/D 2017) – 2-(16)
11. A square plate is bounded by the lines x=0,y=0,x=20,y=20. Its faces are insulated. The
130
temperature along the upper horizontal edge is given u(x,20)=x(20-x) while the other three edges are kept at 00C. Find the steady state temperature in the plate.
(AU-N/D- 2014)-2(16) 12. A square plate is bounded by the lines x=0,y=0,x=l and y=l, it faces are insulated. The temperature along the upper horizontal edge is given by u(x,l)=x(l-x) when 0<x<l while the other three edges are kept at 00C. Find the steady state temperature in the plate. (AU-N/D- 2013)(16)
13. A long rectangular plate with insulated surface is l cm wide.If the temperature along one short edge is u(x,0) = k(lx-x2) for 0 < x < l,while the other two long edges x = 0 and x= l as well as the other short edge are kept at 00 C, find the steady state temperature function u(x,y). (AU-N/D- 2016)(16) 14.A rectangular plate with insulated surface is 20cm wide and so long compared to its width that it may be considered infinite in the length without introducing an appreciable error. If the temperature along one short edge x=0 is given by u=
2010),20(10
5100,10
yy
yy and the two long edges as well as the other short edge are kept
at 00C, find the steady state temperature distribution u(x,y) in the plate. (AU-A/M -2017) (16) 15. An infinitely long rectangular plate with insulated surface is 10 cm wide. The two long edges and on short edge are kept at zero temperature, while the other short edge
y=0 is kept at temperature given by u=
105),10(20
50,20
Xx
Xx Find the steady state
temperature distribution in the plate. (AU –M/J-2014)-2-(16)
UNIT – IV FOURIER TRANSFORMS
PART-A 1. State Fourier integral theorem
(AU-A/M-2015)-6 If f(x) is piece-wise continuously differentiable and absolutely integrable in (-∞, ∞), then
f(x) = f(t)eis(x-t)dtds
or equivalently
This is known as Fourier integral theorem or Fourier integral formula. 2. Show that f(x)=1, 0<x< cannot be represented by a Fourier integral.
00
.1)( xdxdxxf
Therefore the given function cannot be represented as Fourier integral 3. Write the Fourier transforms pair.
2
1
dtdxttfxf )(cos)(1
)(0
131
(AU–M/J-2011)-2 If f(x) is a given function then F[f(x)] and F-1[f(x)] are called Fourier transform pair
F(s)=F[f(x)]=
dxexf isx)(
2
1
; The inverse f(x) =
dsesF isx)(
2
1
4.Prove that )()( sFxfF
(AU-N/D-2012)
dxexfsF
dxexfsF
isx
isx
)(2
1)(
)(2
1)(
Taking complex conjugate on both sides we get
)()(2
1)( xfFdxexfsF isx
5. Find the Fourier transform of f(x) if AU-N/D- 2014)-3
1 ; |x|<1
f(x) = 0 ; |x|>1>0
We know that F[f(x)] = = dxe isx
1
1
=
ssi
ee
sis
e
is
e
is
e isisisisisx
sin2
2
21
1
6. Find the (complex) Fourier transform of f(x)=
bxax
bxaeikx
,0
,
(AU-A/M- 2010)
F(s)=F[f(x)]= dxexf isx
)(2
1
= dxee isxikx
2
1= dxe xski
)(
2
1
=
b
a
xski
ski
e
)(2
1 )(
= ][
)(2
)()( askibski eesk
i
= ][
)(2
)()( bskiaski eesk
i
7. State Parseval’s identity in Fourier transforms. (AU-M/J- 2011)-2 Parseval’s identity in Fourier transforms is given by
If F(s) is the Fourier transform of f(x), then
8. State and prove modulation theorem on Fourier transform. (AU-A/M-2014)-2
Statement: If F(s) is the Fourier transform of f(x), then F[f(x)cosax] = 2
1[F(s+a)+F(s-a)].
dxexf isx)(
dssFdxxf
22
)()(
132
Proof:
dxeee
xfdxaxexfaxxfF
dxexfxfF
isxiaxiax
isx
isx
22
1cos
2
1cos
2
1
= dxeexf xasixasi
2
1
2
1=
2
1[F(s+a)+F(s-a)].
9. If F(s) is the Fourier transform of f(x) , then show that the Fourier transform of eiaxf(x) is F(s+a)(AU-A/M-2015)-4
F[eiaxf(x)] = = = F(s+a)
10. State and prove first shifting theorem. (AU -A/M -2017)-3 First shifting theoremis given by F[f(x-a)] = eiasF(s)
Proof : F[f(x-a)] =
Put x-a = y when x = - , y =- dx = dy when x = , y =
= = = = eias
F(s) 11. State change of scale property of Fourier transforms. (AU-N/D-2017)-3 Change of scale property of Fourier transforms is given by
If Ff(x) = F(s) then Ff(ax)= where a≠0
Proof :
dxaxfeaxfF isx )(2
1)((
Put t=ax , dt=adx =>dx=1/a dt
dttfea
axfF asit )(2
1)(( )/(
By definition,
dttfe
sFist )(
2
1)(
0)/(1
0)/(1
)((
aforasFa
aforasFa
axfF
Ff(ax)= where a ≠ 0
12. Find Fourier sine transform of (AU A/M 2017)-5
We know that
Fs[f(x)] = f(x)sin sx dx = sinsx dx = =
dxexfe isxiax )(2
1
dxxfe xasi )(2
1 )(
2
1
dxeaxf isx)(
2
1dyeyf ayis .).( )(
dyeyfe isy
ias
).(2
dxexfe isx
ias
).(2
a
sF
ac
1
a
sF
ac
1
x
1
2
0
2
0x
1
2
2
2
133
= , a>0
13. Find the Fourier sine transform of e-ax
We know that Fs[f(x)] = f(x)sinsxdx
Fs[e-ax] = e-axsinsxdx = 22 sa
s
14. If Fs(s) is the Fourier sine transform of f(x), show that (AU- N/D-2017)-3
Fs(f(s)sinax)=
Fs(f(x)sinax) = )()(2
1asFasF CC
=
0
)()(2
1)(
2dxxasCosxasCosxf
=
0 0
)()()()(2
2
1xdxasCosxfxdxasCosxf
= )()(2
1asFasF CC
15. Define Fourier cosine transform and its inversion formula The infinite Fourier cosine transform of f(x) is defined as
Fc[f(x)] = Fc(s) = f(x)cos sx dx
The inversion formula is f(x) = Fc(s) cos sx ds
16. Find the Fourier cosine transform of(AU-N/D-2011)-3 Cosx ;if 0<x<a
f(x) = 0 ; if x ≥a
Fc(s) = cos x cos sx dx = cos x cos sx dx
= =
= = provided
s≠1;s≠ -1
17. Find Fourier cosine transform of ,a>0. (AU-N/D- 2015)-3
We know that
dxx
axsin
0
2
2
0
2
0
2
)]()([2
1asFasF ss
2
0
2
0
2
0
2a
0
2a
sxdxx0
coscos2
1
2
a
dxxsxs0
])1cos()1[cos(2
1
a
s
xs
s
xs
01
)1sin(
1
)1sin(
2
1
1
)1sin(
1
)1sin(
2
1
s
as
s
as
axe
0
cos)(2
)]([ sxdxxfxfFc
134
= since
18. Find Fourier cosine transform of xe ,a>0. (AU-N/D- 2015)-3
We know that,
1
12cos
2cos)(
2))((
2
00s
sxdxesxdxxfxfF x
c
19. Prove that Fc[f(x)cosax ] = where Fc denotes the Fourier
cosine transform f(x). (AU-M/J- 2011)-3
Fc[f(x)cosax] = f(x) cosax cos(sx) dx = f(x)
= + =
20. If Fc(s) is the Fourier cosine transform of f(x). Prove that the Fourier cosine
transform of f(ax) is (AU-N/D- 2015)
To prove: Fc (f (ax)) is
We know that Fc[f(ax)] = f(at) cosst dt
Put at=u when , adt = du
= = =
21. Find the Fourier sine transform of e-3x (AU –M/J-2013)
We know that Fs[f(x)] = f(x)sinsxdx = e-3xsinsxdx = (s/s2+9)
22.Given that of 22xe is self reciprocal under Fourier cosine transform, find
Fourier sine transform of (AU-A/M- 2015)
WKT FC [ 22xe ]= 2
2s
e
, Fs [ ]=-d/ds Fc [ [ ] =-d/ds[ 2
2s
e
]=- 2
2s
e
(-
s)=s 2
2s
e
23.Define the Convolution of two function:
dttxgtfxgf )()(2
1)(*
24. State the convolution theorem for Fourier
transforms. (AU-A/M-2018)-3
0
cos2
][ sxdxeeF axax
c
22
2
as
a
0
22cos
ba
abxdxe ax
)()(2
1asFasF cc
2
0
2
0
dxxasxas
2
)cos()cos(
0
)cos()(2
2
1xdxasxf
0
)cos()(2
2
1xdxasxf
)]()([2
1asFasF cc
a
sF
ac
1
a
sF
ac
1
2
0
utut ,00
2
0
cos)(a
du
a
suuf
0
cos)(21
tdta
stf
a
a
sF
ac
1
2
0
2
0
2
2/2xxe
2/2xxe 2/2xxe
135
If F(s) and G(s) are the Fourier transform of f(x) and g(x) respectively, then the Fourier transform of the convolution of f(x) and g(x) is the product of their Fourier transform. F[f(x)g(x] = F(S)G(S) = F[f(x)]F[g(x)] and F-1[F(S)G(S)]= F-1[F(S)] * F-1[G(S)]
25. State Parseval’s identity of Fourier transform
Let F(s) be the Fourier transform of f(x) , then
dssFdxxf22
)()(
PART-B
1. a. Express the function
1,0
1,1)(
x
xxf as a Fourier Integral. Hence evaluate
d
x
0
cossin &
d
0
sin (AU-N/D-2015)-2- (8)
b. Solve for f(x) from the integral equation (AU-A/M-2014)-(8)
2. a. Solve for f(x) from the integral equation (AU-N/D-2015)(8)
2,0
21,2
10,1sin0
s
s
ssxdxxf
b. Find the Fourier transform of 1, f(x) = 1 for |x| < 1 0 otherwise. Hence prove that
0 0
2
2
2
sinsin dx
x
xdx
x
x(AU-M/J-2016 (8)
3. a. Find the Fourier transform of e-a|x|. Hence Deduce that
(i) )(
22][
22 as
asixeF
xa
(ii)
xae
adt
ta
xt
2
cos
0
22
(AU-N/D-2014)-4(8)
b. Show that the Fourier transform of 2
2x
e
is 2
2s
e
AU-A/M-2018)-3(8) 4. a. Find the Fourier transform of f(x) given by f(x) = 1-x2 for |x| ≤1
0 for |x| ≥1
Hence evaluate (AU A/M 2018)-6 (8)
b. Find the Fourier transform of f(x) given by f(x) = a2-x2 for |x| <a 0 for |x| >a>0
P.T =3𝜋
16 (AU-N/D-2015)-5(8)
5. a. Find the Fourier transform of f(x) if (AU N/D 2017)-3(8)
0
cos)( exdxxf
dxx
x
xxx
2cos
cossin
0
3
dxx
x
xxx
2cos
cossin
0
3
136
1-|x| for |x|<1 f(x) = 0 for |x|>1 . Hence deduce that
3
sin
2
sin4
0
2
0
dtt
tanddt
t
t
b. Find the Fourier transform of e-a|x| if a>0 .Deduce that
0,4)(
13
0
222
aifa
dxax
(8)
6. a. Find Fourier transform of ,a>0 and hence find is self reciprocal under
the Fourier transform. (AU-A/M-2016-3)(8)
b. Solve the integral equation 0cos)(0
whereexdxxf (AU-A/M-2016)(8)
7. a. Find the Fourier transform of ),()( 2
2
inexf
x
(AU-A/M-2018)-2-(8)
b. Find the Fourier Sine transform of (8) f(x) = sinx, 0<x<π = 0 π<x<∞ 8. a. Find the Fourier sine transform of e-ax, a>0 and hence deduce the inversion formula. (8)
b. Find the Fourier sine transform of (AU-A/M-2016)-3(8)
9. a. Find the Fourier Sine transform of the function f(x)=x
e ax
hence deduce the
infinite Fourier Sine transform of 1/x (AU-N/D-2016)-2(8) b. Find the Fourier sine transform of e-|x|. Hence show that
0,2)1(
sin
0
3
medxx
xx a(AU-A/M-2015)(8)
10. a. Find the Fourier cosine transform of f(x)= Hence show that
(AU-N/D-2015)(8)
b. Find the Fourier sine and cosine transform of ,0<n<1.Hence Show that is
self reciprocal under both the transformation (AU-A/M-2015)-2(8)
11. a. Solve the integral equation
0
cos)( exdxxf and also show that
0
2 21
cos edx
x
x (AU-M/J-2015)(8)
22 xae 2
2x
e
2/2xxe
otherwise
xx
,0
10,1
2
sinsin
0
2
2
0
dxx
xdx
x
x
1nxx
1
137
b. Prove that is self reciprocal under Fourier Cosine transform. (AU –A/M-2014)(8)
12. a. Find Fourier Cosine transform of and hence find Fourier sine transform of x
(AU-A/M- 2018)-5(8)
b.Use transform method to evaluate
0
22 41 xx
dx(AU-A/M- 2017)-2(8)
13. Find the Fourier cosine transform of f(x) = e-ax for x > 0 . a>0 Hence deduce that
∫𝑐𝑜𝑠𝑠𝑥
𝑎2+𝑠2∞
0𝑑𝑠 and
0
22
sinds
sa
sxs (AU-M/J-2016)(16)
14. Find the Fourier Sine transform and Cosine transforms of a function f(x)=e-x.
Using Parseval’s identity , evaluate (AU-A/M- 2017)-2(8)
(i)
0
22 1x
dx and (ii)
0
22
2
1x
dxx
15. a. Find the Fourier sine transform of e-|x|. Hence S.T 0,2)1(
sin
0
3
medxx
xx a
(AU-N/D-2014)(8)
b. Using Parseval’s identity evaluate the following integrals
(i)
0
222 xa
dx (ii)
0
222
2
xa
dxx, where a>0. (AU-N/D- 2017)-2(8)
16. a. Verify the convolution theorem for Fourier transform if f(x)=g(x)=2xe
(AU-M/J-2015)(8)
b. Evaluate
0
2222 )( bxax
dx using transforms. (AU-M/J- 2015)(8)
UNIT – V
Z- TRANSFORM PART-A
1.Define Z- Transforms Let x(n) be a sequence defined for all integers then its Z-transform is defined to be
Zx(n)=X(Z)= where z is an arbitrary complex number.
2.Find z[(n+1)(n+2)] z[(n+1)(n+2)] = z[n2+3n+2] = z[n2]+3z[n]+2z[1]
= +3 +2
3. Prove that Z = (AU A/M 2017)-5
2
2x
e
22 xae
22 xae
n
nznx )(
32
1
z
zz
21z
z
1z
z
naaz
z
138
We know that Zx(n)=X(Z)=
Z(an)= =
4. Find the Z (AU-N/D-2016)-3
put n=0 we get 1 = A put n=-1 we get 1=-B B=-1
(1) implies
we know that
= = (1-z)
5. Find niZ sincos (AU-M/J-2016)
Let a=eiθ
an=(eiθ )n=einθ=cosnθ+isinnθ
Z[an]=
Z[(eiθ )n]=
Z[einθ]=
n
nznx )(
0n
nn za
0n
n
z
a
azaz
z
z
a
z
a
z
a
,
1
.......1
1
2
)1(
1
nn
)()1(1
)1...(..........1)1(
1
nBnA
n
B
n
A
nn
1
11
)1(
1
nnnn
1log
1
z
z
nZ
1log
1
1
z
zz
nZ
1
11
)1(
1
nZ
nZ
nnZ
1log
1log
z
zz
z
z
1log
z
z
az
z
iez
z
)sin(cos iz
z
139
Z[cosnθ+isinnθ]=
Z[cosnθ]+iZ[sinnθ]=
= =
= =
6.Find
!
1
nZ (AU-M/J-2016)
0
)()(n
nznxnxZ
00
1
!
1
!
1
!
1
n
n
n
n
znz
nnZ
ze
zz
1
2
.......1
!2
11
!1
11
7.Prove that Z(n) = (AU-A/M-2018)-2
We know that Zx(n) =
Z[n] = = =
= = = =
8.Find Z(n2)(AU-M/J-2014)
We know that Z[nf(n)] = -z
Z(n2) = Z[nn] = -z = -z = -z
= -z = -z = z =
9.Find Z-transform of nC2 (AU-A/M- 2017)
23
22
2
2112
1)()(
2
1
22
)1(
z
z
z
zznZnZ
nnZ
nnZnCZ
)sin)cos( iz
z
)sin)cos(
)sin)cos(
)sin)cos(
iz
iz
iz
z
22
sincos
)sin)cos(
z
izzz
222 sincoscos2
)sin)cos(
ZZ
izzz
1cos2
)sin)cos(2
ZZ
izzz
1cos2
sin
1cos2
)cos(22
zz
zi
zz
zz
21z
z
n
n
znx
0
)(
n
n
zn
0
0nnz
n.....
3210
32
zzz
...
13
121
12
zzz
2
11
z
z
z
2
1
1
z
z
z 2)1( z
z
dz
zdF )(
)]([ nZdz
d
2)1(z
z
dz
d
4
2
)1(
)]1(2[)1()1(
z
zzz
3
1
21
z
zz
3
1
1
z
z3)1(
1
z
z
32
1
z
zz
140
10.Find (AU-N/D-2017)-2
We know that Zx(n) =
= =
= = =
11. Find Z[4.3n+2(-1)n]
Z[4.3n+2(-1)n]=4Z(3n)+2Z(-1)n=1
23
z
z
z
z
12.Find Z (AU-N/D-2015)
We know that Z[eatsin2t]=Z[f(t)]z->ze-aT
=[Z[sin2t]] z->ze-T (a=1)
= =
Z[sintat] =
13. Find Z(t)
We know that Zf(t) =
Z(t) = = = T z[n]=
14. Find Z[cos2t]
Z[cos2t]=
2
2cos1 tZ =
12cos2
)2cos(
12
12 Tzz
Tzz
z
z
15. Find the Z-transform of
Z[nCk]= = 1+nC1z-1+nC2z-2+. . . . . . +nCn z-n
This is expansion of binomial theorem = (1+z-1)
16. Evaluate (AU-M/J-2010)-2
= .............(1)
Here z= -2,-5 are simple poles.
)1
(n
Z
n
n
znx
0
)(
1
1]
1[
n
nznn
z
1
1
nnnz
.....1
3
11
2
1132
zzz
]1
1log[z
]1
log[z
z ]
1log[
z
z]loglog[ apa p
tet 2sin
TzezTzz
Tz
12cos2
2sin2
12cos2
2sin22 Tzeez
TzeTT
T
1cos2
sin
2 aTzz
aTz
0
)(n
nznTf
0n
nnTz
0n
nnzT 21z
Tz
kcn
k
n
k znC
0
1072
1
zz
zZ
)2)(5(
1)(
zzzX
11
)2)(5(
1)(
nn z
zzzzX nz
zz )2)(5(
1
) 5 )( 2 ( ) 2 ( ) ( lim Res
2
1
2
z z
z z z z X
n
z n
z
141
=
=
X(n)=sum of residues = + =
17.Evaluate (AU-N/D-2015)
=
z=a and z=b are simple poles
=
=
X(n) = Sum of the residues
= + =
18.Prove that Z(f(t+T))=[ )0()(_
fzf ],where )(_
zf =Z[f(t)]
Z[f(n+1)]= = = where m=n+1
= = zF(z)-zf(0) 19. Find the value of z[f(n)] when f(n) = nan (AU-N/D-2014)
z[nan] = -z [z(an)] = -z [ ] =
20.Prove that Z = -z (AU A/M 2018)-2
Given: F(Z)=Z[f(n)]
F(Z)=
=
= -Z[nf(n)]
3
)2( n
3
)5( n
3
)2( n
3
)5( n])5()2[(
3
1 nn
))((
21
bzaz
zZ
))(()(
2
bzaz
zZX
12
1
))(()(
nn z
bzaz
zzZX
))((
1
bzaz
z n
))(()()(Re
11
bzaz
zazLtzzXs
n
az
n
az
)(
1
bz
zLt
n
az
ba
a n
1
))(()()(Re
11
bzaz
zbzLtzzXs
n
bz
n
bz
)(
1
az
zLt
n
bz
ab
b n
1
ba
a n
1
ab
b n
1
][1 11
nn baba
0
)1(n
nznf
0
)1()1(n
nznfz
0
)(n
mzmfz
dz
d
dz
d
az
z
2az
az
)(nnfdz
zdF )(
0n
nn za
0
1)()()]([n
nznfnZFdz
d
0
)(n
n
z
znnf
0
)()]([n
nznnfZFdz
dz
) 5 )( 2 ( ) 5 ( ) ( lim Res
5
1
5
z z
z z z z X
n
z
n
z
142
Z[nf(n)] = -z
21.State and prove initial value theorem in Z-transforms. (AU-A/M-2017)-2 Initial value theorem in Z-transforms is given by
If Z[f(t)]=F(z),then f(0)=
Proof: F[z]=Z[f(t)]=
= =
= = f(0)
22. State final value theorem on Z-transform (AU-A/M-2017)
If Z[f(t)]-F(z) , then
)()1(lim)(lim1
zFztfzt
23. State convolution theorem on Z-transform. (AU-N/D- 2016) - 3 The convolution theorem on Z-transform is given by If )().(y(n)*x(n) then Z)(y(n) Zand )( ZYZXzYzXnxZ
24. Form the difference equation by eliminating arbitrary constants from
(AU-N/D-2017)-2
Given
..........(1)
........(2)
[Using (1)]
25. Solve yn+1-2yn=0, given that y(0)=2 (AU-N/D-2012)
Z[yn+1]-2Z[yn]=0
zY(z)-zy(0)-2Y(z)=0
Y(z)(z-2)-2z=0
Y(z)=2
2
z
z
y(n)=2(2)n=2n+1
PART-B
1. a. Find 2-t3 e Zand tnZ . (AU-N/D-2016)-(8)
b. Find Z-transform of
)2)(1(
32
nn
nby using method of partial fraction.
(AU-N/D-2017)-2-(8)
dz
zdF )(
)(lim zFz
0
)(n
nznTf
.....).2().1(
).0(2
z
Tf
z
TfTf .....
)2()()0(
2
z
Tf
z
Tff
)(lim zFz
....])2()(
)0([lim2
z
Tf
z
Tff
z
12 n
nU
12. n
n aU
2
1 2.
n
n aU
2.2. 1
1
n
n aU
nn UU 21
143
2. a. Find Z and Z . (AU-N/D-2015)-2-(8)
b. Find the Z transform of1)n(n
1 and
2cos
n(AU-A/M-2016)(8)
3. a. State and Prove initial value and Final value theorems. (AU-A/M-2010) (8)
b. Find Z
)1(
1
n and Z n (AU-A/M-2018)(8)
4. a. If U(Z)= 3
3
)1(
Z
ZZ, find the value of u0,u1 and u2. (8)
b. Find the Z transform of 1
1
n and .
2cos2
nn (8)
5.a. Find Z )sinh( Tt (8)
b. Find Z by using residue method. (AU-A/M-2015)(8)
6. a. Find Z)1()12(
42
3
zz
z by using method of partial fraction. (AU-A/M-2017)(8)
b. Find Z-1 by residue method. (AU-A/M-2018)(8)
7. a. Find Z-1 when 2<|z|<3 (AU-A/M-2015)(8)
b. Using the inversion integral method ,find the inverse Z-transform of
U(Z)= )4)(2( 2
2
zz
z (AU-A/M-2015)(8)
8. aFind Z)2()1( 2
3
zz
z by using method of partial fraction. (AU-A/M-2017)(8)
b. Find the inverse z-transform of 222 zz
zby residue method.
(AU-A/M-2015)(8) 9. a. Derive the difference equation from yn=(A+Bn)(-3)n
b. Using Convolution theorem evaluate Z 1
2
2
)( az
z(AU-M/J-2016)(8)
10. a. Find Z
4
1
2
1
2
ZZ
Z by using Convolution theorem. (AU-N/D-2017)(8)
b. Using Convolution theorem evaluate Z 1
)4)(3(
2
zz
z(AU-A/M-2015)(8)
11. a. Find Z by using Convolution theorem. (AU-M/J-2014)-3(8)
nra nn cos nra nn sin
1
)2()13(
92
3
zz
z
1
)5)(2(
32
zz
zz
)2()3(
131022
2
zz
zz
1
1
1
))((
2
bzaz
z
144
b. Using Convolution theorem evaluate Z (AU-A/M-2018)-3-(8)
12. a. Solve yn+2-4yn+1 +4 yn =0 given y0=1 and y1 =0. (AU- A/M-2018)-3(8) b. Using Z- Transform solve the equation u +3 u +2u = 0 given u(0) = 1 and
u(1) (AU- A/M-2015)-(8)
13. a. Using Z- Transform solve the equation u -5 u +6u = 4 given u(0) = 0 and
u(1) =1. (AU-M/J-2014)-2(8) b. Using Z- Transform solve the equation y +4 y -5y = 24n -8 given y(0) = 3
and y(1) = -5. (AU-M/J2010)(8) 14. a. Solve yn+2+yn=2 given y0=0 and y1=0 by using Z-transforms. (AU-M/J- 2016)(8) b. Solve using z-transform ,yn+2 -7yn+1+12yn=2n given y0= 1and y1=0 (AU-N/D-2017)-3-(8) 15.a. Solve yn+2+6yn+1 +9yn =2n, given y0= y1 =0. (AU-M/J- 2016)(8) b. Solve using z-transform, yn+2-3yn+1-10yn = 0 given y0=1 and y1=0.
(AU-M/J-2014)(8)
1
)14)(12(
8 2
zz
z
2n 1n n
2n 1n n
n
2n 1n n
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