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Physics

Complete Course at a Glance for Class XII

[Prepared strictly according to the latest syllabus issued by the Central Board of

Secondary Education, New Delhi for 2020 Examination of Class XII]

By

Marksadda.com

(A Unit of Ultra Creations )

ISBN 978-81-943778-6-3

e-Crash Course

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Preface to the First Edition

This book is an effort to provide basic concepts and explanations in a concise way.

The topics have been explained through the examples.

Some main features of this book are:

1. The language used in this particular book is simple, lucid and easily

understandable by the students.

2. Essential graphs and diagrams have been correctly drawn and labeled well.

3. The concepts and explanations are provided in a concise manner.

Improvement is a consistent process to make the things better. Ultra Creations will

add more values to this particular work regarding betterment and upgradation of

content and quality in further editions. Suggestions and feedbacks are always

welcomed from teachers and students on [email protected]





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CONTENTS

CHAPTER 1 – ELECTROSTATICS………………………………..……………….....…5

CHAPTER 2 – CURRENT ELECTRICITY…………………………….……...…….…25

CHAPTER 3 – MAGNETIC EFFECTS OF CURRENT & MAGNETISM…....43

CHAPTER 4 – ELECTROMAGNETIC INDUCTION &. A.C…...................60

CHAPTER 5 – ELECTROMAGNETIC WAVES…………………………...……….73

CHAPTER 6 – RAY OPTICS…………………………………….……………...……….80

CHAPTER 7 – DUAL NATURE OF MATTER & RADIATION…………….….96

CHAPTER 8 – ATOMS & NUCLEI…………………………..………….……….….106

CHAPTER 9 – ELECTRONIC DEVICE……………………………………..…..…..113

CHAPTER 10 – COMMUNICATION SYSTEM…………………….….…..……144





A. ELECTROMAGNETIC INDUCTION:-

1. Magnetic Flux:-

Qualitatively:- No. of magnetic field lines crossing any surface normally is called

magnetic flux(∅) through that surface

Quantitatively:-

Where B is magnetic field, A is area of the surface, 𝜃 is the angle between the magnetic field

vector and area vector.

SI unit of magnetic flux is weber (Wb).

1 weber = 108 maxwell =1T𝑚2

2. Electromagnetic Induction:- A production of a e.m.f in a conductor due to a

change in magnetic flux linked with it, is called electromagnetic induction.

The e.m.f so produced is called induced e.m.f. and the current is called induced

current.

3. Faraday’s Laws of Electromagnetic Induction.

Faraday’s law

(i) Whenever there is a change in the magnetic flux linked with a circuit an induced

e.m.f is set up in it and lasts as long as the magnetic flux linked with it is

changing.

(ii) The magnitude of the induced e.m.f. 𝜀 is directly proportional to the rate of

change of magnetic flux.

i.e., |𝑒|α 𝑑∅

𝑑𝑡

4 ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT

∅=�⃗� 𝐴⃗⃗ ⃗=BAcos 𝜃





Note:-

a) A current (Called induced current ) can flow as a result of an induced

e.m.f. only if the circuit is complete.

b) It is the magnetic field due to the induced current or the force acting on

the conductor due to the induced current in it, which opposes the cause of

production of induced current.

c) Lenz’s law complies with the principle of conservation of energy. For

example, when the N-pole of a bar magnet is pushed into a coil is shown,

the direction of induced current in the coil will be such that the end 2 of

the coil will act as N-pole. Thus, work has to be done against the magnetic

repulsive force to push the magnet into the coil. The electrical energy

produced in the coil is at the expense of this work done.

d) The induced e.m.f. has no direction of its own.

4. Lenz’s Law.

This current induced in a circuit always flows in such a direction that it opposes

the change or the cause that produces it.

Mathematically,

5. Difference Methods of Production of Induced e.m.f.

Since e= 𝑑∅

𝑑𝑡 and ∅ = 𝐵𝐴 cos𝜃, e.m.f. 𝜀 can be induced in a circuit (a coil or a

conductor) by either changing B or by A or by changing 𝜃 alone

a) By changing B alone :- If the magnetic flux density, i.e., B in a close loop

of conductor changes, then the flux inked with the loop will change

thereby producing an induced e.m.f. in it .

E=−𝑑∅

𝑑𝑡

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Mathematically,

𝜀 = −𝑑∅

𝑑𝑡 = −

𝑑(𝐵𝐴 cos𝜃)

𝑑𝑡

𝜀=−𝐴 cos 𝜃𝑑𝐵

𝑑𝑡

𝒃) By changing A alone.

𝜺 = −𝒅∅

𝒅𝒕 = −

𝒅(𝑩𝑨 𝐜𝐨𝐬𝜽)

𝒅𝒕

𝜺 = −𝐵 cos 𝜃𝑑𝐴

𝑑𝑡

When a straight conductor of length l moves with speed v perpendicular

to its own length in a uniform magnetic field �⃗� as shown such that the

normal to the area swept by the conductor makes an angle 𝜃 with the

direction of �⃗� . The induced e.m.f. set up across the ends of the conductor

is given by 𝜀 = 𝐵𝑙𝑣 cos 𝜃

The induced e.m.f. produced across the ends of conductor will be

max(= 𝐵𝑙𝑣) when 𝜃 = 𝑜0, e.g., when a conductor moves at a constant

speed v perpendicular to its own length in a horizontal plane where there

is a uniform magnetic field �⃗� in vertical plane.

Due to the motion of the conductor, the free charge carriers i.e., electrons

in it experience a force whose direction is given by Fleming’s Left Hand

Rule. As a result, electrons accumulate at one end of the conductor

thereby setting up an e.m.f., across the ends of the conductor.

c)By changing 𝜃 alone:- Consider a loop of N turns of area of cross-

section A each placed in a magnetic field �⃗� in a such a way that is able to

rotate about an axis perpendicular to �⃗� when the loop is rotated at

constant angular velocity 𝜔, the induced e.m.f. set up in given by











𝜀 = −𝑑∅

𝑑𝑡

Where, ∅ = 𝐵(𝑁𝐴) cos 𝜃 and 𝜃 = 𝜔𝑡.

So 𝜀 = −𝑑(𝐵𝑁𝐴cos𝜔𝑡)

𝑑𝑡

𝜀 = BNA𝜔 sin𝜔𝑡

𝜀 = 𝜀0 sin 𝜔𝑡

𝜀0=BNA𝜔

Here,

𝜀 = instantaneous value of induced e.m.f. and depends on the instantaneous position of the

coil given in terms of 𝜃 or t.

𝜀0= maximum value of the called peak e.m.f.

𝜔= angular velocity (or frequency) of rotation of the coil and is generally given in

rpm (𝑖. 𝑒 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛 𝑝𝑒𝑟 𝑚𝑖𝑛𝑢𝑡𝑒)

NOTE:- 1 rpm = 𝜋

30 𝑆−1

6. Determination of the Direction of induced current :

a) Use of Lenz’s law:- When N-pole of a ba

b)

1.Alternating Current and Alternating Voltage:-

Alternating Current. It is the current whose magnitude changes with time and direction

reverses periodically.


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Instantaneous Value of AC is given by

I=𝐼0 sin 𝜔𝑡

Or I=𝐼0 cos𝜔𝑡

Here, 𝐼0 is the peak value of current.

𝜔= 2𝜋v

Similarly alternating e.m.f. changes in magnitude continuously with time and reverses its

direction periodically.

Instantaneous value of alternating e.m.f is given by

E=𝐸0 sin 𝜔𝑡

E=𝐸0 cos𝜔𝑡

Here, 𝐸0 is the peak value of current.

𝜔= 2𝜋v

2.Root mean square (R.M.S):-The r.m.s value of an alternating current is given by that

steady (D.C) current which when flowing through a given circuit for a given time produces

the same heat as produced by the alternating current when flowing through the same

circuit for the same time.

R.M.S. value is the value which is taken for power purposes of any description.

𝐸𝑟.𝑚.𝑠 = 𝐸𝑚𝑎𝑥 × 1

√2 = 0.707 𝐸𝑚𝑎𝑥


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3.Average or mean value:- The average value of an alternating current is expressed by

that steady current which transfers across any circuit the same change as is transferred by

that alternating current during the same time.

𝐸𝑎𝑣 = 0.636 × 𝐸𝑚𝑎𝑥

Average value = 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑡ℎ𝑒 𝑐𝑢𝑟𝑣𝑒

𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑎𝑠𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑢𝑟𝑣𝑒

4. Form factor:-Form factor for a particular waveform is defined as the ratio of the r.m.s

value to the average value. It is denoted by 𝑘𝑓.

𝑘𝑓 = 𝑟.𝑚.𝑠.𝑣𝑎𝑙𝑢𝑒

𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑣𝑎𝑙𝑢𝑒

For a sine wave

𝑘𝑓 =0.707 ×𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒

0.637 ×𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒 =

0.707

0.637

𝑘𝑓 = 1.11

5. Peak factor :- The peak factor for a given waveform is defined as the ratio of the peak(or

maximum) value and the r.m.s. value. It is denoted by 𝑘𝑝.

𝑘𝑝= 𝑝𝑒𝑎𝑘 𝑣𝑎𝑙𝑢𝑒

𝑟.𝑚.𝑠 𝑣𝑎𝑙𝑢𝑒

Peak factor is also called the crest factor or yhe amplitude factor. For a sine wave

𝑘𝑝= 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒

0.707 ×𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒

𝑘𝑝 = 1.414

The form factor and peak factor give an indication of the shape of a waveform. The more

pointed the peak of the wave, the higher are the values of these factors.





S.N Wave form Form factor 𝑘𝑓 Peak factor 𝑘𝑝

1. Sine wave

:-

R.M.S Value = 𝐼𝑚𝑎𝑥

√2 =

0.707𝐼𝑚𝑎𝑥

Average Value = 2

𝜋𝐼𝑚𝑎𝑥

= 0.636 𝐼𝑚𝑎𝑥

𝑘𝑓 =0.707 × 𝐼𝑚𝑎𝑥

0.637 × 𝐼𝑚𝑎𝑥

=1.11

𝑘𝑝= 𝐼𝑚𝑎𝑥

0.707×𝐼𝑚𝑎𝑥

= 1.41

2. Half wave rectified sine wave:-

R.M.S Value =

𝐼𝑚𝑎𝑥

2 =

0.5𝐼𝑚𝑎𝑥

Average Value = 1


= 0.318𝐼𝑚𝑎𝑥

𝑘𝑓 =0.5 × 𝐼𝑚𝑎𝑥

0.318 × 𝐼𝑚𝑎𝑥

= 1.57



= 2.0

3. Full wave rectified sine wave :-

R.M.S Value =

𝐼𝑚𝑎𝑥

√2 =

0.707𝐼𝑚𝑎𝑥

Average Value = 2


= 0.636 𝐼𝑚𝑎𝑥

𝑘𝑓 =0.707 × 𝐼𝑚𝑎𝑥

0.637 × 𝐼𝑚𝑎𝑥

= 1.11



=1.41

4. Rectangular wave:-

R.M.S Value = 𝐼𝑚𝑎𝑥 Average value =

𝐼𝑚𝑎𝑥

𝐾𝑓 = 1

𝑘𝑝 = 1





5. Triangular wave :-

R.M.S. Value=

𝑰𝒎𝒂𝒙

√𝟑 =

0.578 𝐼𝑚𝑎𝑥

Average value= 𝑰𝒎𝒂𝒙

𝟐 = 0.5

𝐼𝑚𝑎𝑥

𝑘𝑓 =0.578 × 𝐼𝑚𝑎𝑥

0.5 × 𝐼𝑚𝑎𝑥

= 1.16



= 1.73

6. AC Through Resistor:- Here alternating current and alternating e.m.f. are in phase.

V= IR

This relation is true for instantaneous , peak and r.m.s values of V and I.

7. AC Through Inductor :- Here alternating current lags behind the alternating e.m.f . by a

phase angle of 𝜋 2⁄ .

𝑉𝑟𝑚𝑠

𝐼𝑟𝑚𝑠 = 𝑋𝐿

And 𝑋𝐿= 𝜔𝐿= 2𝜋𝑣L

Here, 𝑋𝐿 is called inductive reactance and is measured in ohm.

8. Ac Through Capacitor:- Here alternating current leads the alternating e.m.f by a phase

angle of 𝜋

2.

𝑉𝑟.𝑚.𝑠

𝐼𝑟.𝑚.𝑠 =𝑋𝑐

V= L𝑑𝑙

𝑑𝑡

I=c𝑑𝑣

𝑑𝑡

Note: In inductor voltage lead current by

𝟗𝟎𝟎











Here, 𝑋𝑐 = 1

𝜔𝐶 =

1

2𝜋𝐶

Where 𝑋𝑐 is called capacitive reactance and is measured in ohm.

9. Phasor Diagram: A diagram representing alternating voltage and alternating currents

(of same frequency) as vectors along with the phase angle between them is called a phasor

diagram.

Phasors:- Phasors are rotating vectors which are used to represent peak values of

alternating currents and voltages. Peak value of each alternating quantity is represented

by an arrow rotating anticlockwise about the origin at the angular frequency 𝜔.The

projection of this vector on the vertical axis gives the instantaneous value. Phasors are very

useful in:

a) Showing graphically the variation of instantaneous values of alternating

voltages and currents.

b) Showing the phase difference between instantaneous values of alternating

voltages and currents.

c) Analyzing AC circuits geometrically for the purpose of finding Z and ∅.

1- Resistor in AC

2- Pure Inductor in AC

Note- In Capacitor voltage lag current by 𝟗𝟎𝟎





3- Pure Capacitor in AC

4- Series LCR Curcuit

10. AC Through a series LCR Circuit.

Series LCR circuit. If the applied voltage is V=𝑉0 sin 𝜔𝑡 then with the help of phasor

diagram it can be shown that the current in the circuit will be I=𝐼0 sin(𝜔𝑡 − ∅) where we

assume circuit to be inductive by nature, i.e., 𝑋𝐿 > 𝑋𝐶

𝑉0

𝐼0=

𝑉𝑟𝑚𝑠

𝐼𝑟𝑚𝑠= Z= √𝑅2 + (𝑋𝐿 − 𝑋𝑐)

2

And ∅ = tan−1 (𝑋𝐿−𝑋𝐶

𝑅)

Here, e.m.f is leading the current by phase angle ∅.

Here, Z is called the impedance of the circuit and is measured in ohm.











i.e., 𝑉𝑟𝑚𝑠 ≠ 𝑉𝐿+𝑉𝐶+𝑉𝑅

Rather 𝑉𝑟𝑚𝑠=√𝑉𝑅2 + (𝑋𝐿 − 𝑋𝐶)

2

11. Resonance Condition for series LCR Circuit:- A series LCR circuit is said to be in

resonance at a frequency 𝑓𝑟 called resonant frequency at which 𝑋𝐿=𝑋𝐶 . Hence,

𝑓𝑟= 1

2𝜋√𝐿𝐶

Also f=𝑓𝑟 current is maximum and for f< 𝑓𝑟 and f > 𝑓𝑟 the current is less than its maximum

value.

A given series LCR circuit is

i. Inductive at a frequency f >𝑓𝑟 .

ii. Capacitive at a frequency f< 𝑓𝑟 .

iii. Resistive at a frequency f=𝑓𝑟 .

(It is important to note that at resonance when 𝑋𝐿=𝑋𝐶)

a) The impedance of the circuit is minimum and is equal to R(i.e., Z=R)

b) The current (rms) in the circuit is maximum and is equal to 𝑉𝑟𝑚𝑠 𝑅⁄ .

c) The applied voltage and the current in the circuit are in phase.

d) The power dissipation in the circuit is maximum and therefore, the Sharpness of

resonance decreases as shown in figure.











12. Quality factor:- The quality factor Q of a series LCR circuit is measure of sharpness of

resonance. It is given by

If R is low or L is high, the quality factor is large which implies that such a circuit will have

shaper resonance. Figure shoes that while the current is always maximum at 𝜔 = 𝜔𝑟 (or at

f=𝑓𝑟) the sharpness of this maximum decreases with increasing R.

It is also the ratio of p.d. across resistance in RLC circuit at resonance.

13. Power Dissipation in an AC circuit:-In an AC circuit the average power dissipation

𝑃𝑎𝑣 over a cycle can be calculated from the relation

𝑃𝑎𝑣= ∫ 𝑉𝐼 𝑑𝑡

𝑇

0

∫ 𝑑𝑡𝑇

0

Taking V=𝑉0 sin 𝜔𝑡 and I=𝐼0 sin(𝜔𝑡 − ∅) it can be shown that in a series LCR circuit in

general

𝑃𝑎𝑣 = 𝑉𝑟𝑚𝑠𝐼𝑟𝑚𝑠 cos∅

Where 𝑉𝑟𝑚𝑠 𝐼𝑟𝑚𝑠 is called apparent power

IF ∅ = 0 then

𝑃𝑎𝑣 = 𝐼𝑟𝑚𝑠2 R

This shows that in an AC circuit, power dissipation takes place only in the resistor.

For a purely resistive circuit and even for a series LCR circuit at resonance:

∅ = 0𝑜 and therefore, 𝑃𝑎𝑣= 𝑉𝑟𝑚𝑠 . 𝐼𝑟𝑚𝑠

Q=𝜔𝑟𝐿

𝑅=1

𝑅√

𝐿

𝐶


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For a purely inductive or purely capacitive circuit.

∅ = 90𝑜 and therefore, 𝑃𝑎𝑣=0

Power Factor: Power factor, cos∅, of an AC circuit is the ratio of true power dissipation to

the apparent power dissipation in the circuit.

Also

The value of power factor of an AC circuit lies between 0 and 1, being 0 for a purely

inductive or a purely capacitive circuit and 1 for a purely resistive circuit.

14. Wattless current:- we know that

𝑃𝑎𝑣= 𝐸𝑣𝐼𝑣 cos∅

Suppose 𝐸𝑣 leads 𝐼𝑣 by phase angle ∅ in a given circuit. Its phasor diagram is given as Here

we consider 𝐼𝑣 as a vector sum of two perpendicular components 𝐼𝑣 cos∅ and 𝐼𝑣 sin ∅.

As the component of current 𝐼𝑣 sin ∅ does not contribute to the power, it is called wattles

current.

cos∅=𝑅

𝑍





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Physics - Marks Adda.com · 2019-12-03 · Instantaneous value of alternating e.m.f is given by...

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