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Transcript of @ McGraw-Hill Education 1 Kulshreshtha, D. C. Basic Electrical Engineering McGraw-Hill Education ©...
@ McGraw-Hill Education
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Kulshreshtha, D. C. Basic Electrical Engineering McGraw-Hill Education © 2010
PROPRIETARY MATERIAL. © 2010 The McGraw-Hill Companies, Inc. All rights reserved. No part of this PowerPoint slide may be displayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this PowerPoint slide, you are using it without permission.
BASIC ELECTRICAL ENGINEERING
PowerPoint Slides
D. C. KULSHRESHTHA,
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@ McGraw-Hill Education
2
Kulshreshtha, D. C. Basic Electrical Engineering McGraw-Hill Education © 2010
Chapter 3Network Analysis–
Part I D.C. Kulshreshtha
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 3
Thought of The DAY
Whatever
THE MIND OF MAN
can CONCIEVE and BELIEVE,
it can
ACHIEVE.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 4
Topics to be Discussed Electric Circuit, The Resistance
Parameter, The Capacitance
Parameter, The Inductance
Parameter, Energy Sources--Energy Sources--
ClassificationClassification Ideal Voltage Source.Ideal Voltage Source. Ideal Current Source.Ideal Current Source.
Series and Parallel Series and Parallel Combinations.Combinations.
Practical Voltage Practical Voltage Source.Source.
Practical Current Practical Current Source.Source.
Source Transformation.Source Transformation. Kirchhoff’s Laws.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 5
Electric Circuit It is a closed path, composed of active and
passive elements. Active Element : It supplies energy to the
circuit. Passive Element : It receives energy and then
1) either converts it to heat, as in a Resistance (R).
2) or stores it in (a) Electric Field, as in a Capacitor (C).(b) Magnetic Field, as in an Inductor (L).
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 6
Energy SourcesEnergy Sources
ClassificationIndependent Source Or Dependent Source
Voltage Source Or Current Source
DC Source Or AC Source
Ideal Source Or Practical Source
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 7
Independent Ideal Voltage Source
The source has zero internal resistance.
Note that the source determines the voltage, but the current is determined by the load.
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LoadSource
Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 8
The voltage source is said to be idle if the output terminals are open such that i = 0.
When turned off (killed or made inactive), so that v = 0, it is equivalent to a short circuit.
Reference Marks : One terminal is marked plus and the other minus. (Oversimplification; one mark can be omitted.)
When actual polarity is opposite to the reference marks, the voltage is a negative number.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 9
Independent Ideal Current Source
The Source has infinite internal resistance (Ri). Next
Source
Load
Note that the source determines the current, but the voltage is determined by the load.
Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 10
The current source is said to be idle if the output terminals are shorted together, such that v = 0.
When turned off (killed or made inactive), so that i = 0, it is equivalent to an open circuit.
Reference Marks : An arrow is put. When actual direction of current is opposite to the
reference (arrow) direction, the current is a negative number.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 11
Do you observe duality ?
The roles for the current and voltage are interchanged in the two sources.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 12
PracticalPractical Voltage Source Voltage Source
It is represented by an ideal voltage source in series with an internal resistance (RSV).
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 13
Practical Practical Current SourceCurrent Source
It is modelled as an ideal current source in parallel with an internal resistance (RSI).
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 14
Source Transformation A practical current source can be converted
into its equivalent practical voltage source, and vice versa.
This conversion is valid only for the external load connected across the terminals of the source.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 15 Next
Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 16
Equivalence betweenVoltage Source and Current Source Two sources would be equivalent if they produce
identical values of VL and IL, when they are connected across the same load.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 17
Series and Parallel Combinations What would be the net emf of the combination if two ideal voltage sources of 2 V and 4 V are connected in series so as to aid each other?
Ans. 6 V What would be the net emf of the combination
if two ideal voltage sources of 4 V and 4 V are connected in parallel ? 4 V or 8 V ?
Ans. Obviously, it should be 4 V
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Click
Click
Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 18
What would be the net emf of the combination if two ideal voltage sources of 2 V and 4 V are connected in parallel ? 2 V or 4 V or 3 V ?
The question seems to be quite tricky! Ans. The question is wrong. The question contradicts
itself. Ideal Voltage Sources in parallel are permissible
only when each has the same terminal voltage at every instant of time.
What is its dual ?
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Click
Click
Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 19
Ideal Voltage Sources Connected in Series
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 20
Ideal Current Sources Connected in Parallel
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 21
Practical Current Sources Connected in Series
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 22
Practical Voltage SourcesConnected in Parallel
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 23
Example 1 : Reduce the network shown in figure to its simplest possible form by using source transformation.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 24
Solution
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 25 Next
Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 26
Example 2
In the given figure, (a) If RL = 80 Ω, find current iL.(b) Transform the practical current source into a practical voltage source and find iL if RL = 80 Ω again.(c) Find the power drawn from the ideal source in each case.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 27
Solution :
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mA20
8020
20)100()( Lia
mA20
2080
2)( Lib
V6.1)80)(mA20()( LLL Rivc
mW160 )mA100)(V6.1(IvP L
mW40 V)2)(mA20(
case, second In the
ViP L
Click
Click
Click
Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 28
Benchmark Example 3 Take the benchmark example of the circuit
given in figure. Using source transformation, determine the voltage v across 3-Ω resistor.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 29
Solution :Transforming the 4-A current source into a
voltage source,
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 30
Combining the two voltage sources,
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 31
Again transforming the voltage source into current source,
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 32
Combining the two current sources we get Fig. (e). Transforming this current source into voltage source (Fig. f )
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 33
Combining the two resistances, we get Fig. (g).
V2.5
33
35v
Finally, using voltage divider, we get
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 34
Kirchhoff’s Laws
(1) KCL : Algebraic sum of currents meeting at a junction of conductors in a circuit is zero. It is simply a restatement of the principle
of conservation of charge.
b
jjI
1
0
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 35
(2) KVL :The algebraic sum of voltages around a closed circuit or a loop is zero. It is simply a restatement of the principle of
conservation of energy.
k
jjv
1
0
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 36
Polarity of Voltages
NoteNote that polarity of the voltage (emf) across a battery does not depend upon the assumed direction of current.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 37
Applying KVL
1. Select a closed loop.
2. Mark the voltage polarity (+ and -) across each element in the closed loop.
3. Go round the selected loop, and add up all the voltages with + or – signs.
4. Any one of the following two rules can be followed :
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 38
(i) Rule 1 : While travelling, if you meet a voltage rise, write the voltage with positive sign ; if you meet a voltage drop, write the voltage with negative sign. (ii) Rule 2 : While travelling, write the voltage with positive sign if + is encountered first; write the voltage with negative sign if – is encountered first.
We shall be following Rule 1, as it has a strong analogy with the physical height (altitude) of a place.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 39
Example 5 : Use KVL to find vR2 and vx.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 40
For finding vR2, we write KVL eqn. going around loop abgha clockwise :
If you choose to go around the loop anticlockwise, you get
Giving the same result.
V320436 22 RR vv
V320364 22 RR vv
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Click
Click
Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 41
There are two ways to determine vx
1) We can consider this voltage as the voltage across the gap from d to f. Writing KVL (habcdfgh) :
2) Knowing vR2 , apply a short-cut (bcdfgb) :
V6
x
x
v
v 01412364
V6
x
x
v
v 0321412
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Click
Click
Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 42
Important Note about KVL
The assumed direction of current through a resistor and the polarity of voltage across it are always in conformity.
The end into which the current enters is marked positive.
Passive-element sign convention.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 43
Example 6 : Find the current supplied by the 60-V source in the network.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 44
Solution : We need not find the currents I1, I2 and I3. Instead, we reduce the network.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 45
Example 7 : Determine the value of current I.
2 – 3 – 2 – 3 – I I – 4 = 0 – 4 = 0 or I = -5 A
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 46
Example 8
Using KCL and KVL, determine the currents ix
and iy in the network shown.
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 47
Solution : Using KCL, the currents in other branches are marked as shown. Writing KVL equations for the loops 1, 2 and 3,
50353
0)(3502
50227
02)(2505
1001005
0510100
1
1
1
1
1
1
III
IIII
III
IIII
III
II
yx
yxy
yx
yxx
yx
x
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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 48
;
50
50
100
353
227
1005
1
I
I
I
y
x
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Writing the above equations in matrix form,Click
Using Calculator, we solve for Ix and Iy, Click
; and x yI I 3.87 A 0.51 A
Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 49
Review Electric Circuit, The Resistance
Parameter, The Capacitance
Parameter, The Inductance
Parameter, Energy Sources--Energy Sources--
ClassificationClassification Ideal Voltage Source.Ideal Voltage Source. Ideal Current Source.Ideal Current Source.
Series and Parallel Series and Parallel Combinations.Combinations.
Practical Voltage Practical Voltage Source.Source.
Practical Current Practical Current Source.Source.
Source Transformation.Source Transformation. Dependent Sources. Kirchhoff’s Laws.
Next