Electromagnetic Induction

Electromagnetic Induction17

COMPREHENSIVE REVIEW

1. Magnetic flux

i) The dot product of magnetic field B

& the

area element dA

is called magnetic flux.

ii) The magnetic flux is denoted by . If B

be

the magnetic field through the area element

dA

. Then, the flux through the area is given

by :

d B dA

a) Unit for magnetic flux

The unit of magnetic flux is called weber.

It is abbreviated as Wb.

If B

is parallel to dA

. Then

0d B dA B(dA)cos0

This gives d B(dA)

If B = 1 tesla, dA = 1 square metre,

then d = 1 weber.

Thus, magnetic flux is said to be 1 weber if

a magnetic field of 1 tesla crosses through

1 square metre area, held perpendicular to

the magnetic field.

Mathematically : Wb = Tm2

Note. The area vector is taken perpendicular to

the surface. Therefore, area vector parallel to

the magnetic field vector means that the magnetic

field is perpendicular to the surface on which the

area lies.

b) Magnetic flux density

Magnetic flux is given by : d B(dA)

For B

parallel to dA

, we have

0d B(dA)cos0 B(dA)

Therefore, d

BdA

ELECTROMAGNETIC INDUCTION ( 196 )

That is, magnetic induction is equal to the

magnetic flux density. In other words,

magnetic field may be measured in terms

of the magnetic flux density.

From equation (i), we find :

Unit of Unit of d

BUnit of dA

Or2

WbT

m

That is tesla = weber per square metre.

2. Electromagnetic induction

When the magnetic flux linked with a circuit

changes, an emf is set up in the circuit. The

phenomenon is called electromagnetic induction.

a) Induced emf and current

When the magnetic flux linked with a circuit

changes, emf set up in the circuit is called

induced emf.

The current due to induced emf is called

induced current.

b) Faraday's laws of electromagnetic

induction

i) Whenever, the magnetic flux linked with a

circuit changes, induced emf is produced.

ii) The induced emf lasts as long as the change

in magnetic flux continues.

iii) The magnitude of induced emf (E) is directly

proportional to the rate of change in

magnetic flux.

Thus, if d be the change in magnetic

flux during the time dt, then :

dE

dt

Ord

E kdt

where k is the constant of proportionality.

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In SI, k = – 1, hence : d

Edt

It is called Faraday's flux rule.

Remarks. The negative sign indicates that the

induced emf opposes the change in magnetic

flux. In SI, the change in flux d is measured in

weber, dt in second and E in volt.

Hence volt = weber/second. Or Wb

Vs

3. Lenz's law

The Lenz'slaw explains the –VE sign in the

Faraday's flux rule d

E .dt

It states that the induced emf is such as to

oppose the cause that produces it.

4. Lenz's law is in accordance with the conser-

vation of' energy.

As the induced emf opposes the cause that

produces it. Therefore mechanical work need to

be done to continue the process. It is this

mechanical energy which is converted into

electrical energy, in accordance with the law of

conservation of energy.

5. Mutual Induction

The production of induced emf in a circuit, when

the current in the neighbouring circuit changes is

called mutual induction.

The figure below shows a primary coil P

and a secondary coil S. When the circuit of the

primary coil is closed or opened, deflection is

produced in the galvanometer of the secondary

coil. This is due to mutual induction.

Fig. 5.1

i) Factors on which mutual induction

depends

The mutual induction between two

coils depends on the the following factors :

a) The number of turns of P and S coils.

b) The shape and size or geometry of the

two coils. That is, the area of cross-

section and the length of the coils affect

the mutual induction between the coils.

ii) Coefficient of mutual induction

a) Suppose, the instantaneous current in the

primary coil is I. Let the magnetic flux linked

with the secondary coil be . It is found that

the magnetic flux is proportional to the

current. That is,

I Or MI ... (i)

where M is the constant of proportionality.

It is called coefficient of mutual induction.

The induced emf E in the secondary is given

by :

d dIE M

dt dt

... (ii)

b) The negative sign is in accordance with the

Lenz's law. That is, the induced emf in the

secondary coil opposes the variation of

current in the primary coil.

c) From the equation (ii), we find

EM

(dI / dt) ... (iii)

Thus, coefficient of mutual induction is

the ratio of induced emf in the secondary

coil to the rate of change of current in the

primary coil.

d) Unit of M. The unit of coefficient of mutual

inductor is called henry (H).

If E = 1 V and 1dI

1As ,dt

then M = 1 H.

That is, the coefficient of mutual

induction of two coils is said to be 1 henry if

the induced emf equal to 1 volt is produced

in the secondary coil, when the current in

the primary coil changes at the rate of 1

ampere per second.

e) Now E

MdI / dt

Therefore, 1

1

VH VA s

As





6. Self induction

The production of induced emf in a circuit, when

the current in the same circuit changes is called

self induction.

i) Factors on which self induction depends

The self induction in a circuit mainly

depends upon its geometry. For a solenoid it

is determined by the number of turns, area

of cross-section and the length of the

solenoid.

ii) Coefficient of self induction

a) Suppose, the instantaneous current in the

circuit is I. If the magnetic flux linked with

the solenoid is , then it is found that :

I Or LI ... (i)

where L is the constant of proportionality. It

is called coefficient of self induction.

The induced emf in the coil is given by :

d dIE L

dt dt

... (ii)

b) The negative sign is in accordance with the

Lenz's law. That is, the induced emf opposes

the variation of current in the coil.

c) From the equation (ii), we find :

EL

(dI / dt) ... (iii)

Then, coefficient of self induction is the

ratio of induced emf in the circuit to tlie rate

of change of the current in the circuit.

d) Unit of L. The unit of self induction is also

called henry (symbol H).

From equation (ii),

we find that if

1dI1 As ,

dt

E = 1 V, then L = 1 H.

That is, the coefficient of self induction of a

coil is said to be one henry if induced emf

equal to 1 volt is produced in the coil, when

the current in it changes at the rate of 1

ampere per second.

e) Also, as explained early,

H = VA–1 s.

7. Motional emf

If a rod of length moves perpendicular to

a magnetic field B with a velocity , then the

induced emf produced across it is given by,

E B

In general, we have :

E B

i) If a metallic rod of length rotates about

Fig. 7.1

one of its ends in a plane perpendicular to

the magnetic field, then the induced emf

produced across its ends is given by,

2BE BAf

2

Here, = angular frequency of rotation,

A = 2 = area of circle and f = frequency

of rotation.

ii) If a metallic disc rotates about its own

centre in a plane perpendicular to the

magnetic field B, then the induced emf is

produced between the centre and the edge.

The induced emf is given by :

2B rE BAf

2

Fig. 7.2

Here, = angular velocity of rotation

f = frequency of rotation

A = area of disc = r2





8. Eddy currents

In the year 1895, A.D., Focault discovered that if

a metallic plate is moved in a magnetic field,

induced current is set up in the plate. It flows in

closed loops within the plate. Such a current is

called eddy current. In accordance with the

Lenz's law, the induced current opposes the cause

that produces it.

If a current I is set up in a coil of inductance

L, then the magnetic field energy stored in it is

given by,

2

p

1U LI

2

9. Finding the direction of induced emf

The direction of induced emf can be found be

using the Lenz's law. That is, the induced emf is

such as to oppose the cause that produces it.

Below we discuss a number of such cases.

i) A copper ring is held horizontally and a

magnet with its N-pole downwards is

dropped into it. The direction of induced

current will be anticlockwise. Because, the

induced current makes the ring a magnetic

dipole, with its N-pole upwards. This

opposes the motion (cause of induced emf)

of the bar magnet.

Fig. 9.1

If in the above case, the magnet is

moved upwards, the induced current will be

clockwise, so that the upper side of the ring

behaves as S-pole.

ii) A circular coil is placed near a straight

conductor as shown below.

Fig. 9.2

When the current in the straight conductor

increases the current in the coil is clockwise

so as to oppose the increasing magnetic field

of the straight conductor, which is passing

through the coil. Similarly, if the current in

the straight conductor decreases, then the

current will be anticlockwise.

iii) Figure below shows an irregular shaped coil

turning into a circular coil.

Fig. 9.3

The magnetic field is directed into the

paper. The area of the coil is increasing and

hence the flux through the coil is also

increasing. To oppose the increase of flux,

the current through the coil is anticlockwise.

Because the anticlockwise current produces

magnetic field which is directed upwards.

iv) Figure below shows a coil in a magnetic field

coming out of the paper. If the coil is taken

out of the fields the upwards flux decreases

and to oppose it the induced current through

the coil is anticlockwise.

Fig. 9.4

10. Transformer

The transformer is a device for converting a

low alternating voltage to a high alternating voltage

or vice versa. In the former case we call it step

up transformer and in the latter case we call it

step down transformer.

a) Principle of transformer

The transformer works on the principle

of mutual induction. That is a varying current

is set up in a circuit, induced emf is produced

in the neighbouring circuits. The varying

current in a circuit produces varying magnetic

flux which induces emf in the neighbouring

circuit.





b) Construction of transformer

The transformer consists of two coils.

They are insulated from each other and

wound on a common core. For operation at

low frequency, we may have a soft iron core.

But for operating at high frequency air core

is used.

Fig. 10.1

The soft iron core is made by joining

thin iron strips coated with varnish to insulate

them from each other. It is called laminated

iron core. This is done to reduce energy

losses due to eddy currents.

The input circuit is called primary. And

the output circuit is called secondary.

c) Transformer ratio

i) Suppose, the number of turns in the primary

coil is Np. And that in the secondary coil is

Ns.

The resistance of the coils is assumed

to be zero.

Let d

dt

be the rate of change of flux

in each turn of the primary coil. If Ep be the

emf in the primary circuit, then

p p

dE N

dt

... (i)

If there is no loss of flux between the

primary and secondary coils. Then, the

induced emf in the secondary coil will be :

s p

dE N

dt

... (ii)

From equations (i) and (ii), we find,

s s

p p

E Nk (say)

E N ... (iii)

ii) s

p

Nk

N is called transformer ratio or turn

ratio.

iii) For step up transformer k > 1 and for the

step down transformer k < 1.

iv) For step up transformer Ns > N

p, therefore

Es > E

p. And for the step down transformer

Ns < N

p, therefore E

s < E

p.

d) Efficiency of transformer

The efficiency of the transformer is given

by :

Output power

Input power

If Ip and I

s be the currents in the primary

and secondary circuits.

Then : s s

p p

E I

E I

For ideal transformer = 1 = 100%.

Therefore EsI

s = E

pI

p.

Orps

p s

NI 1

I N k

Therefore, for step up transformer

current in the secondary is less than that in

the primary (Is< I

p). And in a step down

transformer we have Is > I

p.

e) Energy Losses in Transformers

In practice, the output energy of a

transformer is always less than the input

energy, because energy losses occur due to

a number of reasons as explained below.

i) Loss of magnetic flux. The coupling

between the coils is seldom perfect. So,

whole of the magnetic flux produced by the

primary coil is not linked up with the

secondary coil.

ii) Iron loss. In actual iron cores, inspite of

lamination, eddy current, are produced. The

magnitude of eddy current may, however,

be small. And a part of energy is lost as the

heat produced in the iron core.

iii) Copper loss. In practice, the coils of the

transformer possess resistance. So, a part

of the energy is lost due to the heat produced

in the resistance of the coil.





iv) Hysteresis loss. The alternating current

in the coil takes the iron core through

complete cycle of magnetisation. So, energy

is lost due to hysteresis.

v) Humming losses. The alternating current

in the transformer may set its parts into

vibrations and sound may be produced. It is

called humming. Thus, a part of the energy

may be lost due to humming.

11. D.C. Motor

It is device to convert electrical energy into

mechanical energy.

Fig. 11.1

It consists of armature abed, permanent

magnet NS, brushes B1 and B

2, split rings R

1 and

R2 and a source of direct current. When the

current is passed through the coil, the armature

rotates due to the magnetic torque.

mp B

where, pm = nIA is the magnetic dipole

moment of the armature coil and B is the magnetic

field of the permanent. magnet.

12. Back emf in d.c. motor

i) As the coil moves in a magnetic field an

induced emf is developed in the coil that

opposes the emf of the source from which

the current is supplied to the motor. The back

emf is given by :

b

dE n BAsin t

dt

where n = number of turns, = angular

frequency, B = magnetic field, A = area of coil.

ii) The back emf opposes the applied emf. Let

the applied emf be E. The net emf in the

circuit will be E0 = E – E

b. Therefore current

in the circuit will be :

bE EI

R

... (i)

Or Eb = E – IR ... (ii)

a) Efficiency of the d.c, motor

i) The efficiency of d.c. motor is defined as

the ratio of output mechanical power to the

input electric power.

ii) Let the output mechanical power be P0 and

the input electric power be Pi.

Then : Pi = E I

And P0 = Power supplied power dissipated

as heat

2 2

iP I R EI I R (E IR)I

But E – IR = Eb. Therefore P

0 = E

b I

Also P0 = P

i – I2 R ... (iii)

Hence efficiency

0 b b

i

P E I E Back emf

P EI E Applied emf ... (iv)

b) Maximum efficiency

i) The efficiency of d.c. motor is given by :

b bE E I

E EI

ii) Here EI is the input power. It is fixed.

Therefore is maximum, when EbI is

maximum.

That is : b

b

d[E I] 0

dE

Orb b

b

E (E E )d0

dE R

This gives

2

b b b

b

E E E E 2Ed0

dE R R

Since R and E are constants. Therefore,

bE 2E 0

That is, b

EE

2 ... (v)

iii) Thus, the efficiency is maximum, when the

back emf is half the applied emf.





13. A.C. Generator

The electric generator is a device for converting

mechanical energy into electric energy. If the

electric current produced varies in direction

alternatively, it is called alternating current or a.c.

generator.

a) Principle of a.c. generator

It is based on the principle of electromagnetic

induction. When the magnetic flux linked

with a circuit varies, induced e.m.f, is set up

in the circuit.

b) Construction of a.c. generator

The a.c. generator consists of following

parts.

(a) Armature abcd

(b) Magnet X1S

(c) Brushes B1 and B

2

(d) Rings R1 and R

2

Fig. 13.1

c) Working of a.c. generator

The armature coil is rotated mechanically

about its axis YY'. As the coil rotates, the

magnetic flux linked with the coil changes

continuously. So, induced current is set up

in the coil.

For one half of the rotation, the current

is along abcd R1B

1RB

2R

2a. And in the other

half it will be along aR2B

2RB

1R

1dcba. Thus,

the current changes direction alternatively.

14. Expression for emf

The emf of a.c. generator is given by :

0E nBA sin t E sin t

Here 0E nBA is the peak value of a.c.

For the expression we find that the value of E at

time t = 0, T

4,

T

2,

3T

4 and T will be as follows.

Here T = time period = 2

0 0

T T 3TTime t 0 T

4 2 4

emf E 0 E 0 E 0

The variation of E with time is shown in the figure

below :

Note.

The electric generator is also called dynamo.

Fig. 14.1

15. Three phase generator

It consists of three armature coils, inclined to each

other at 1200. See fig. below. The emf produced

by them differ in phase by 1200.

Fig. 15.1

a) Neutral and phase lines

In the polyphase generator, one end of each

coil is connected to a common ring. The

other end is connected to different rings.

Thus, in the three phase, a.c. generator we

have four slip rings and four brushes. The

output from the brush in contact with

common slip ring is called neutral line. The

output from the other brushes in contact with

the separate ringfor each coil is called phase

line or live line.

Thus, in three phase generator we have

one neutral line and three live lines or phase

lines. The single phase power supply can

be taken across one phase line and the

neutral line.





b) Potential of neutral line of three phase

generator

In the neutral line, three alternating

emfs differing in phase by 1200 are mixed

up. Fig. below shows the vector diagram. It

is assumed that the amplitude of each emf

is same say E0. The X-component of the

resultant is given by :

Fig. 15.2

0 0

x 0 0 0E E E sin30 E sin 30

0 0E E

The Y-component of the resultant is given

by : 0 0

y 0 0E E cos30 E cos30 0

Thus, the resultant potential of the

neutral line is zero. That is why we call it

NEUTRAL.

Analogous quantities in mechanics and

electromagnetism

Mechanics Electromagnetism

Displacement (x) Charge (q)

dx dqVelocity = Current I=

dt dt

Mass (m) Inductance (L)

Momentum p mv Magnetic flux LI

Emf/potential diffdv

Force F mdt

22k

m

erence

dIL

dt

Magnetic energy1

1Kinetic energy U mvU LI2

2

1Spring constant (k) Inverse of capacitance

C

16. Alternating Current

i) Alternating current. The current that

reverses direction periodically is called

alternating current. The alternating current

is abbreviated as a.c.

ii) Alternating emf. The emf that reverses

direction periodically is called alternating

emf. The symbol for the sources of ac is as

follows

iii) Direct current. The current that does not

change direction with time is called direct

current. The direct current is abbreviated

as d.c.

iv) Direct emf. The emf that does not change

direction with time is called direct emf.

v) Steady d.c. It is that direct current which

does not change in magnitude with time.

Symbol for the source of direct current

or emf is as follows.

a) Mathematical expressions for alternating

current and emf

Simplest form of alternating current and emf

is that which changes harmonically. Such

alternating current I and emf E may be

expressed as follows :

0I I cos t

0E E cos( t )

Meaning of the symbols

I = Instantaneous value of alternating

current.

10 = Maximum or peak value of alternating

current.

E = Instantaneous value of alternating emf.

E0 = Maximum or peak value of alternating

emf.

= Angular frequency = 2

2 fT

where f is the frequency and T is the time

period.

And = the phase at t = 0.

b) Phase difference

Suppose, the emf and current in a circuit

are E = E0 cos t and I = I

0 cos (t + ).

Then is called the phase difference

between E and I.





If the sign with is +VB, then we

say that the current leads the emf by phase

angle .

If the sign with is –VE, then we say

that the current lags behind the emf by phase

angle .

c) Average value of alternating current is

that steady direct current which sends the

same charge through the circuit in halftime

T

2

period as is sent by the a.c. during the

same time.

It is given by : 0a 0

2II 63.66% of I

d) Average value of alternating emf is that

steady emf which sends same charge

through the circuit during half time period

T

2

as is sent by the alternating emf during

the same time.

It is given by :

0a 0

2EE 63.66% of E

e) The root mean square value of the

alternating current is defined as the steady

direct current that produces same heat in a

resistance, as is done by the alternating

current during one time period (T).

It may be denoted by Irms

. It is also

called effective value or virtual value of

the alternating current. The ammeter, when

connected in the circuit measures rms value

of a.c. Its value is given by,

0rms 0 0

II 0.7071 I 71.71% of I

2

f) The root mean square value of the

alternating emf is defined as that steady

direct emf which produces same heat in a

resistance as the alternating emf does in one

time period (T).

It may be denoted by Erms

. It is also

called effective value or virtual value of

alternating emf. The voltmeter connected

in an a.c. circuit measures Erms

.

Its value is given by :

0rms 0

EE 70.71% of E

2

g) In the pure resistance, the alternating

current and the corresponding alternating

emf are in phase.

That is if0I I cos t

Then0E E cos t

h) In pure inductance the alternating emf

leads the alternating current by /2.

That is if 0I I cos t

Then 0 0E E cos t E sin t

2

i) In the pure capacitance, the alternating

emf lags behind the alternating current

by /2.

That is if : 0I I cos t

Then 0 0E E cos t E sin t2

j) In the pure inductance (L), we have

0 0E I ( L)

Here L= XL is called inductive reactance.

Its unit is same as that of resistance (ohm).

k) In the pure capacitance (C), we have

00

iE

C

Here, C

1X

C

is called capacitive reactance.

Its unit is same as that of resistance (ohm).

17. Phase Diagram

Fig. 17.1





The graphical representation of the phase

relationship between two or more quantities is

called phase diagram.

Suppose, we wish to draw the phase diagram

for alternating current and alternating emf. Let :

0E E cos t & 0I I cos( t )

Then we draw two vectors OP and OQ as

shown in fig. 49.1. where OP = E0 and OQ = I

0

and POQ= .

The instantaneous values of current and emf

will be given by the projections of OQ and OP on

the X-axis. That is E = OA = E0 cos t and

I = OB = I0 cos (t + ), where t = XOP. It is

the phase angle for the emf.

Note. As the time passes, the vectors OP and

OQ rotate about O. Because the phase angle t

changes with time. Therefore they are also called

phasors.

Vector diagram. Since E0 and I

0 are represented

as vectors in the phase diagram. Therefore, the

phase diagram is also called vector diagram.

18. Phase diagrams for A.C.

Through pure resistance, pure inductance and

pure capacitances are shown below in the figures

50.1 (a), (b) and (c) respectively.

Fig. 18.1

19. Alternating current through RCL series

circuit

i) Let an emf E = E0 cos t be applied across

a series RCL circuit. The current through

the circuit is I. The currents through R, C

and L are respectively denoted by IR, I

C and

IL. Then in this case :

R C LI I I I

Fig. 19.1

That is the same current flows through all

parts of the circuit.

ii) Let the potential difference across R, C

and L respectively be : ER, E

C, E

L. And the

total emf across the circuit be E.

iii) The phase diagram for the circuit is as shown

in fig. 19.2.

Fig. 19.2

Note that EL is ahead of I by

2

and E

C is

lagging behind I by 2

.

iv) From the voltage triangle OMP, we find

2 2 2OP OM MP

or 2 2 2

R L CE E (E E )

Since ER

= IR, EL = LI and C

IE .

C

Therefore, we find :

2

2 2 2 1E I R L

C





or

1/ 22

2 1E I R L

C

Here

1/ 22

2E 1R L Z

I C

is called impedance of the circuit. It consists

of two parts, the resistance R and the

reactance

2

L C

1X (X X ) L

C

.

v) Impedance triangle. The expression

2

2 2 1Z R L

C

can be depicted as

impedance triangle as shown in fig. 51.3.

Hence

1L

CtanR

Fig. 19.3

This gives the phase difference between I

and E. Here E leads I by .

Thus if0E E cos t

Then0I I cos( t )

20. Variation of XL, X

C, X, Z & with frequency

.

We know that :

LX L and C

1X

C

L C

1X X X L

C

1/ 22

2 1Z R L

C

And L C

1L

X X CtanR R

i) As increases, XL increases. The graph

between and XL is a straight line. See fig.

21.1.

Fig. 20.1

The slope of the graph is, L

tan L

.

ii) As increases, XC decreases. The graph

between XC and is a rectangular

hyperbola. See fig. 21.2.

Fig. 20.2

iii) As increases X = XL – X

C varies as

shown in fig. 52.3.

Fig. 20.3

At = 0, we find X = . As > 0,

X decreases in magnitude and becomes zero

at a certain frequency = 0. It is called

resonant frequency. At = 0, we find

L CX X X 0 or 0

0

1L 0

C

That is : 0

1

LC

iv) As increases, the Z first decreases and

then becomes equal to R for = 0. This is

the minimum value of Z. For > 0, the Z

again increases. The variation of Z with is shown in fig. 20.4.





Fig. 20.4

v) The current in the circuit is given by,

EI

Z

Hence, the variation of current with is as

shown in fig. 20.5.

Fig. 20.5

The maximum value of current is E

IR

at

the resonant frequency = 0.

vi) The variation of with is shown in fig.

20.6.

The is 2

for = 0, = 0 for =

0 and

it is equal to 2

for tending to infinity..

Fig. 20.6

21. The alternating emf across parallel RCL

circuit.

Fig. 21.1

i) Let an emf E = E0 cos t be applied across

a parallel RCL circuit. The current through

the circuit is I. The currents through R, C

and L respectively are IR, I

C and I

L.

ii) Let the potentials across the resistance R,

capacitance C and inductance L be respec-

tively : ER, E

C and E

L. Then

Fig. 21.2

R C LE E E E

iii) The phase diagram for the circuit is as shown

in fig. 21.2.

Note that IC leads Ee by

2

and I

L lags

behind EL by

2

. Also E = E

R = E

C = E

R.

iv) From the triangle OMP, we find that

OP2 = OM2 + MP2

or 2 2 2

R C LI I (I I )

Since R C

EI , I E C

R

And L

EI ,

L

therefore





222

2

E EI E C

R L

or

2

2 2

2

1 1I E C

R L

or

1/ 22

2

1 1I E C

R L

Here

1/ 22

2

I 1 1 1C

E R L Z

where Z is the impedance of the circuit.

1Y,

Z where Y is called admittance of the

circuit.

v) Admittance triangle. The expression

2

2

2 2

1 1 1Y C

Z R L

can be depicted as admittance triangle as

shown in fig. 21.3.

Fig. 21.3

Hence

1C

Ltan1/ R

This gives the phase difference I and E.

Here I leads E by .

Thus, if0E E cos t

Then0I I cos( t )

22. Parallel resonance

i) The circuit is said to be in resonance when,

1C 0

L

or

0

1

LC

Thus, the resonance frequency is same both

for the series and parallel resonance.

ii) As increases, the Z first increases,

becomes maximum and then decreases. The

maximum value of Z is at resonance. That

is for = 0, we find :

1/ 22

02

max 0

1 1 1C

Z R L

1/ 2

2

10

R

Ormax

1 1

Z R or

maxZ R

Fig. 22.1

The variation of Z with is shown in fig.

22.1.

iii) The current in the circuit is given by :

EI

Z

At = 0, we find Z = Z

max = R

Hence I = Imin

= E

R

The variation of I with is shown in fig.

22.2.

Fig. 22.2





23. Parallel LC circuit

The LC circuit can be of two types ;

a) Ideal or pure LC circuit, in which the inductance

possesses no resistance.

b) Real LC circuit in which the inductance has

finite but small resistance.

(a) Ideal or pure LC circuit

i) The circuit is shown below (fig. 23.1)

Fig. 23.1

ii) For such a circuit, we have

C LI I I

Because IC & I

L are out of phase with each

other.

iii) The impedance of the circuit is given by,

C L

1 1 1 1C

Z X X L

iv) At resonance XL = X

C

Hence 1

0Z and Z .

That is no current flows through the circuit

at resonance. That is why it is called rejector

circuit.

v) In such a circuit, the phase difference between

the current and emf is 2

. The current leads

the emf when XC

> XL and the current lags

behind the emf when XC < X

L.

vi) At resonance, when XC = X

L, the phase

difference between the current and emf is

arbitrary.

(b) Real LC circuit.

i) Figure (23.2) below shows the real LC

circuit. Here, the inductance has resistance

R, which is depicted in series with L in the

inductance arm.

Fig. 23.2

ii) For this circuit we have :

CI E C

L2 2 2

EI cos( t )

R L

where L

tan .R

iii) The impedance of such a circuit is given

by :

1/ 22 2

2 2 2 2 2 2

1 R LC

Z R L R L

iv) At resonance, we have

2 2 2

LC

R L

This gives the resonant angular frequency

as :

1/ 22

2

1 R

LC L

*Note, that in earlier circuits, the resonant

frequency was 1

.LC

v) The impedance at resonance is given by :

2 2 2

1 R

Z R L

Or2 2 2R L

ZR

... (i)

Substituting the values of angular frequency.

1/ 22

2

1 R

LC L

We find, L

ZRC





It is called dynamic resistance of the circuit

At resonance, the impedance is maximum.

That is,

max

LZ Z

RC

vi) The variation of impedance with is shown

below (Fig. 23.3).

Fig. 23.3

vii) The peak current at resonance is given by,

0 0E E RCI

L / RC L

And the peak current through the capacitor

is given by,

C 0I E C

viii)Peak value of oscillator current

Peak value of make up current fromthe power supply

0

0

E C L= Q factor

E RC R

L

Thus, the Q-factor is the measure of current

amplification.

24. Power in a.c.

i) The average power in a.c. circuit is given

by,

0 0av rms rms

E IP cos E I cos

2

Here cos is called power factor.

ii) For series RCL circuit

2

2

R Rcos

Z 1R L

C

iii) For parallel RCL circuit

2

2

1 1C

R L1/ R Zcos

1/ Z R R

iv) At series resonance, the power factor is

given by :

Rcos 1

R

v) At parallel resonance, the power factor is

given by :

Rcos 1

R

a) AC through RL circuit.

Proceed as for RCL circuit but donot write

the terms involving C.

No resonance can occur in this case.

b) AC through RC circuit

Proceed as for RCL circuit but donot write

the terms involving L.

c) Wattless current

Average power is given by :

a rms rmsP E I cos

The phase difference between Erms

& Irms

is

. See fig. 24.1. We can resolve Irms

into

two components.

OM = Irms

cos ... (1)

& MP = Irms

sin ... (2)

Here, the component Irms

cos contributes

for power dissipation as clear from equation

(1). And the component Irms

sin does not

dissipate power. Therefore, it is called

Wattless current.

Fig. 24.1

Thus wattless current is the component

of the rms current that does not dissipate

power.





25. Quality factor

The ratio of voltage across the inductor or

capacitor at resonance to that across the resistor

is called quality factor of the circuit. It is denoted

by Q.

It is also called Q-factor.

Thus, CL

R R

VVQ

V V

Since L 0 0V I L

0C R 0

0

IV & V I R

C

Therefore 0 0 0 0

0 0

I L I / CQ

I R I R

or0

0

L 1Q

R CR

Also, 0

1

LC

Therefore

1/ 21 L 1 L

QR R CLC

26. Importance of Q-factor

i) It is found that Q-factor determines the

sharpness of resonance of the a.c. circuit.

Greater the value of Q, higher is the

sharpness of resonance.

ii) Since CL

R R

VVQ .

V V

Therefore Q-factor may be called as the

voltage amplification factor.

27. Choke coil

Inductance coil having very low resistance

and used to control the current in a.c. circuit

is called choke coil.

It is so named because it is used to choke or

reduce the current in the circuit.

The choke coils used at low frequency a.c.

are made of thick copper wires on soft iron core.

For high frequency a.c., they have air core. The

resistance of the coils is very very small.

The choke coil in inductance L & resistance

r possesses impedance.

2 2 2 1/ 2Z (r L )

The current in the circuit is

EI

Z .

The energy dissipated as heat is I2r.

The main advantage of the use of choke

coil is that it can vary the current in the a.c. circuit

without much loss of energy as heat. This is

possible because the inductance offers impedance

but the current in it is wattless, which causes no

dissipation of energy as heat.

The power factor of the choke coil is given

by 2 2 2 1/ 2

rcos

(r L )

which is small because

r is small.

28. Transmission of electric power

Suppose, a certain amount of electric power

is to be transmitted to another place separated

by a large distance. The power generated will be

given by P = VI, where V is the voltage and I is

the current generated. If R be the resistance of

the transmission wire, then the rate of loss of

power will be given by :

Q = I2R

This power is lost as heat to the atmosphere

which we donot want. Since, the resistance (R)

of the transmission wire is fixed, therefore, the

only way to reduce the loss of power and potential

drop is that we should decrease the current in

the circuit. This is achieved by stepping up the

power supply at the generating station so that the

current is reduced and then stepping it down to

the required voltage at the station where power

is to be consumed.

i) The extent of stepping up of power supply

for the purpose of transmission is determined

by the economy considerations.

ii) Higher voltage transmission line requires

less conductor but the cost of insulation is

also higher. Lower voltage transmission on

the other hand requires more conductor but

the cost of insulation is low.





iii) At the generating station (GS) the power

obtained from the generator (G), may be

stepped up to 132 kV and near the consumer

region (CR) it may be stepped down to

33 kV and supplied to power stations (PS)

located in the consumer area. At the power

station it is stepped down to 11 kV and then

supplied to the sub power station (SS) in the

consumer locality, where it is stepped down

to 230 V and then supplied to the consumer

premises. (See fig. 28.1).

Fig. 28.1

29. Relative merits and demerits of a.c. power

supply over d.c. power supply.

Merits :

i) The generation cost of a.c. is less than that

of d.c.

ii) It can be made available in wide range of

voltages using transformers.

iii) The a.c. devices such as motors are

mechanically more robust and stout than the

d.c. devices.

iv) The power loss in a.c. transmission is

negligible as compared to that in d.c.

transmission.

v) The a.c. can be easily converted to d.c. The

reverse is not true.

vi) For reducing alternating current we can use

choke coils in which the loss of energy is

much less than that in the rheostate used

for reducing d.c.

Demerits :

i) The a.c. is more dangerous and fatal than

d.c.

ii) The 220 V a.c. supply has the peak value

of about 311 V, which can cause more

severe shock to the persons coming in

contact with it.

iii) The a.c. is transmitted mostly at the outer

surface of the wire, and so the conductor

need to be in the form of several stranded

wires.

iv) The a.c. contains higher harmonics in

addition to the fundamental frequency.

v) The a.c. cannot be used for electrolysis,

electroplating, electrorefining, electrotyping

etc.







Magnetic Flux

1. The unit of magnetic flux in SI is :

a) weber b) gauss

c) oersted d) tesla

2. The unit of magnetic induction B in SI is :

a) weber b) gauss

c) oersted d) tesla

3. The magnetic flux through a coil is inversely

proportional to :

a) number of turns

b) area

c) magnetic field

d) none of the above

4. If the magnetic field is parallel to a surface, then

the magnetic flux through the surface is :

a) zero

b) small but not zero

c) infinite

d) large but not infinite

5. The magnetic flux () linked with a coil is related

to the number (n) of turns of the coil as :

a) 2n b) 2n

c) 1n d) n

6. The magnetic flux () linked with a coil is related

to the area (A) of the coil as :

a) 1/ 2A b) 1/ 2A

c) A d) 1A

7. A square loop of side b is rotating with angular

speed about one of the diagonals as axis. At

t = 0, the plane of the loop is perpendicular to the

magnetic field B. If the number of turns of the

loop be N, then what is the instantaneous flux

through the coil ?

a) BAN b) BAN sin t

c) BAN cos t d) BAN t

8. The length of a solenoid of radius 2.5 cm having

500 turns/cm is 0.5 m. A current of 1 ampere is

set up in the solenoid. What is the magnetic flux

through the coil ?

a) 1.5 Wb b) 2.0 Wb

c) 3 Wb d) 4 Wb

MULTIPLE CHOICE QUESTIONS

Electromagnetic Induction

9. Which one of the following scientists is NOT

connected with the electromagnetic induction ?

a) Faraday b) Lenz

c) Henry d) Ohm

10. Which of the following gives the direction of the

induction emf ?

a) Faraday's laws b) Lenz's law

c) Ampere's theorem

d) Biot Savart law

11. The expression for the induced emf contains a

negative sign d

dt

. What is the significance

of the negative sign ?

a) The induced emf is produced only when the

magnetic flux decreases

b) The induced emf opposes the changes in the

magnetic flux

c) The induced emf is opposite to the direction

of the flux


12. Which of the following phenomena makes use of

electromagnetic induction ?

a) Charging a storage battery

b) Magnetising an iron piece with a bar magnet

c) Generation of hydroelectricity

d) Magnetising a soft iron piece by placing inside

a current carrying solenoid

13. A varying electric field generates :

a) emf b) electric current

c) magnetic field d) none of the above

14. Which of the following is based on the law of

conservation of energy ?

a) Lenz's law b) Faraday's law

c) Ampere's law d) Biot Savart law

15. The induced emf cannot be produced by :

a) moving a magnet near a circuit

b) moving a circuit near a magnet

c) changing the current in one circuit placed near

the other

d) maintaining large but constant current in a

circuit





16. Two coils are placed close to each other as shown

in the figure. When the key K is pressed a current

flows in the secondary coil abed. What happens

on breaking the circuit ?

a) No current flows in the coil S

b) A current greater in magnitude but same in

direction flows through the coil

c) The magnitude of the current is greater but

direction is reversed

d) The magnitude of the current is lower and

direction is reversed

17. Dynamo is designed on the principle of :

a) electromagnetic induction

b) self induction

c) mutual induction d) none of the above

18. What does a dynamo generate ?

a) Electrons b) Charge

c) emf d) None of the above

19. What is motional emf ? It is the induced emf :

a) across the ends of a wire moving in a magnetic

field

b) in a coil due to the motion of the magnet near

it

c) in a circuit due to variation in its own current

d) in a circuit due to the variation of current in

the neighbouring circuit

20. The force between two current carrying parallel

wires is due to :

a) electrostatic interaction

b) magnetic effect of electric current

c) electric effect of magnetic field

d) electromagnetic induction

21. The frequency (in Hz) of the commercial alter-

nating current generated in India is :

a) 50 b) 60

c) 110 d) 220

22. Which of the following is used to determine the

direction of induced current in a generator ?

a) Fleming's left hand rule

b) Fleming's right hand rule

c) Maxwell's cork screw rule

d) Ampere's swimming rule

23. The current from which of the following devices

does not vary in magnitude ?

a) Transformers b) Dynamo

c) Cell d) Induction coil

24. What should be the rate of variation of current in

a circuit of self inductance one henry to generate

induced emf equal to one volt ?

a) Less than one ampere per second

b) One ampere per second

c) Two ampere per second

d) More than two ampere per second

25. The motional emf produced across a wire moving

through a magnetic field does not depend on its :

a) velocity b) length

c) diameter d) orientation

26. Which of the following is independent of the

direction of the current in a circuit ?

a) Mutual induction

b) Joule's heating

c) Electrolysis

d) None of the above

27. The north pole of a bar magnet is rapidly

introduced into a solenoid at the end A. Which of

the following statements correctly depicts the

phenomenon taking place ?

a) No induced emf is developed

b) The end A of the solenoid behaves like a south

pole

c) The end A of the solenoid behaves like a north

pole

d) The end A of the solenoid acquires positive

potential

28. In which of the following cases with a bar magnet

and the solenoid no induced emf is produced ?

a) When magnet is inserted

b) When magnet is withdrawn

c) When coil is moved towards or away from

the magnet

d) When the relative velocity of the coil w.r.t the

magnet is zero





29. A copper rod moves parallel to the horizontal

direction. The induced emf developed across its

ends due to earths magnetic field will be maximum

at the :

a) equator b) latitude 300

c) latitude 600 d) poles

30. A copper rod is moved in a magnetic field. The

charge developed across its ends will be

proportional to :

a) magnetic flux

b) total change of magnetic flux

c)1

velocity of the rod

d)1

magnitude of the magnetic field

31. What determines the charge that flows through

a circuit due to the induced emf ?

a) The rate of change of magnetic flux

b) The total change in magnetic flux

c) The initial magnetic flux

d) The final magnetic flux

32. Which of the following is NOT the name of the

part of the a.c. generator ?

a) Armature b) Field magnet

c) Split ring commutator

d) Brushes

33. In the circuit shown below, what will be the

reading of the ammeter long time after closing

the key ?

a) 1 A b) 2 A

c) 4

A3

d) 3

A4

34. A long straight wire lies along the axis of long

straight solenoid. The wire carries a current

I = 10 sin t. The induced emf may be expressed

as :

a) E = E0 sin t b) E = E

0 cos t

c) E = constant d) E = zero

35. The Lenz's law is the consequence of the

conservation of :

a) charge b) momentum

c) energy d) none of the above

36. The induced emf in a coil is independent of :

a) resistance of the coil

b) number of turns

c) rate of change of flux


37. The induced current in a coil is independent of :

a) resistances of the coil

b) number of turns

c) rate of change of flux


38. The current in the armature of de motor is the

maximum when the motor is :

a) switched off

b) switched on

c) running at full speed

d) running at intermediate speed

39. The induced emf LdI

dt is analogous in mechanics

to :

a) force b) work

c) power d) impulse

40. Which of the following in electrodynamics is

analogous to the momentum in mechanical

dynamics ?

a) VI b) qV

c) LI d) Ld

dt

41. A straight line conductor of length 0.4 m is moved

with a speed of 7 m/s perpendicular to a magnetic

field of intensity 0.9 Wb/m2. The induced e.m.f.

across the conductor is :

a) 5.04 V b) 1.26 V

c) 2.52 V d) 25.2 V

42. The magnetic flux linked with a coil varies with

time as : = 3t2+ 4t + 9 weber. What is the

induced emf at t = 2 ?

a) 3 V b) 4 V

c) 9 V d) 16 V





43. What voltage is developed across the axle of the

wheels of a train, when it moves with a speed of

72 kmh–1 ? The horizontal component of the

earth's magnetic field is 0.40 10–4 T and the

angle of dip is 300. The length of the axle is 1.5 m :

a) 0.2 mV b) 0.4 mV

c) 0.6 mV d) 0.8 mV

44. The current passing through a choke coil of 15

henry is decreasing at the rate of 0.2 ampere per

second. The e.m.f. developed across the coil :

a) 3 volt b) 7.5 volt

c) 15 volt d) 30 volt

45. The equation of A.C. is represented by

e = e0 sin t

In what time the e.m.f. will be half of its maximum

value starting from zero ?

a) T

4b) T

c) T

12d)

T

8

46. The induced emf in a coil rotating in a magnetic

field is maximum when the angle between the

plane of the coil and the direction of field is :

a) zero b) 4

c) 2

d) Some angle other that those mentioned above

47. A horizontal telegraph wire 0.5 kilometer long

runing east and west is a part of a circuit whose

resistance is 2.5 ohm. The wire falls to the ground

from a height of 5 metres. If g = 10.0 m/s2 and

B = 2 10–5 weber per meter2, then the current

induced in the circuit is :

a) 0.7 ampere b) 0.02 ampere

c) 0.01 ampere d) 0.04 ampere

48. An electron moves on a straight line path XY as

shown in fig. The abcd is a coil adjacent to the

path of electron. What will be the direction of

current if any induced in the coil ?

a) no current is induced

b) abcd

c) adcb

d) the current will reverse direction as the electron

goes past the coil

49. Figure shows a straight wire placed between the

pole pieces of a magnet. Induced emf will be

developed across the ends of the wire, when it is

moved towards :

a) N b) S

c) P d) Q

50. A conducting square loop of side L and resistance

R moves in a plane with uniform velocity perpendicular to one of its sides. A magnetic

induction B, constant in time and space, pointing

perpendicular and into the plane of loop exists

everywhere. See fig. The current induced in the

loop is :

a) BLR

clockwise

b) BLR

anticlockwise

c) 2BLR

anticlockwise

d) zero

51. The electric current in a circuit varies from +2A

to –2A in a time interval of 10–2 s. Another coil of

resistance 20 and inductance 2 H is placed

near it. What will be the induced current in the

second coil ?

a) 4 A b) 8 A

c) 20 A d) 40 A





52. The magnetic flux through a surface varies with

time as follows :

= 12t2 + 7t + 3

Here is in milliweber and t is in seconds. What

will be the induced emf at t = 5s ?

a) 338 mV b) 127 mV

c) 105 mV d) none of the above

53. The current in a coil changes from +10A to –2A

in 3 ms. What is the induced emf in the coil ?

The self inductance of the coil is 2 mH :

a) 8 V b) 4 V

c) 0.8 V d) 0.4 V

54. The distance between the ends of the wings of an

aeroplane is 20 m. The aeroplane is descending with

a speed of 20 m/s. If the horizontal component

of the earth's magnetic field be 0.5 Gs, then what

will be the induced emf across the wings ?

a) 40 mV b) 20 mV

c) 10 mV d) 5 mV

55. There is a window 50 cm 100 cm in a wall which

is parallel to the magnetic meridian. The resistance

of the window is 0.07 . What is the induced

charge when the window is opened through 900 ?

Given that horizontal component of earth's

magnetic field is 0.35 Gs :

a) 2.5 C b) 25 C

c) 250 C d) 2500 C

56. A square loop of 10 turns has each side 10 cm. It

rotates in a magnetic field of 0.25 T and the

maximum induced emf is 20 mV. What is the

angular speed of rotation ?

a) 4 rad/s b) 0.4 rad/s

c) 8 rad/s d) 0.8 rad/s

57. The resistance of the armature of a dc motor is

50 . A power supply of 200 V is connected

across it and the current through the armature is

2 A. What is back emf ?

a) 10 V b) 50 V

c) 100 V d) 150 V

58. The magnetic flux passing normally through a coil

is = 20 sin 5 t + t2 + 50t + 25 milliweber,

where t is in seconds. What will be the induced

emf at t = 1 s ?

a) 52 V b) 72 V

c) 100 V d) (100 + 50) V

59. A 2 m long metallic conductor is rotated about

one end in a vertical plane with angular speed

of 2.5 rad/s. If the horizontal component of

earth's magnetic field be 0.5 10–4 T, then what

is the potential difference across the ends of

the conductor ?

a) 100 V b) 150 V

c) 200 V d) 250 V

60. The current through a coil of self inductance 5 mH

rises uniformly from 0 to 1 ampere in 0.1 s. What

is the induced emf ?

a) 2.5 V b) 2.5 mV

c) 0.5 V d) 0.5 mV

61. A coil of 1000 turns and area 20 cm2 is placed in

a magnetic field of 1000

ampere turn/m. The

magnetic field makes angle 300 with the plane of

the coil. If the field is reduced to zero in 0.2 s,

then what is the induced emf set up in the coil ?

a) 16 mV b) 8 mV

c) 4 mV d) 2 mV

62. A magnetic field of 20 T is normal to a coil of

100 turns and area 10–2 m2. If the coil is removed

from the magnetic field in 2 ms, what is the induced

emf set up in the coil ?

a) 2 kV b) 5 kV

c) 7 kV d) 10 kV

63. A current of 5000 A is flowing at 220 V in the

primary coil of a transformer. The voltage across

the secondary is 11000 V and 10% power is lost.

What is the current through the secondary ?

a) 9 A b) 90 A

c) 900 A d) 9000 A

64. A cycle wheel with 64 spokes is rotatory at the

rate of 120 revolutions per second. A potential

difference of 10 V is produced between the axis

and the rim. What will be this potential difference,

it the number of spokes is reduced to 16 ?

a) 2.5 b) 5 V

c) 10 V d) 40 V

65. The varying electric field produces magnetic field.

This is known as :

a) Laplace's law b) Ampere's law

c) Maxwell's law d) Faraday's law





Self Induction & Mutual Induction

66. Which of the following is not equal to henry ?

a) volt second

ampereb)

2volt second

coulomb

c)

2volt second

coulombd)

2

2

joule second

coulomb

67. Which of the following is NOT a factor to determine

the mutual inductance of the two coils ?

a) The number of turns of each coil

b) The shape of each coil

c) Current through each coil

d) Separation between the coils

68. Which of the following is NOT the function of

transformer ?

a) Transform magnetic energy into electric energy

b) Transfer electrical energy from one part of

the circuit to another

c) Step up or step down the voltage

d) Decrease or increase the alternating current

69. Which of the following instruments do not make

use of eddy currents ?

a) Electrical brakes b) Induction motor

c) Transformer

d) Dead beat galvanometer

70. Induction furnace makes use of :

a) self induction b) mutual induction

c) eddy currents d) none of the above

71. The transformer is devised on the principle of :



72. The coil of the balistic galvanometer oscillates

due to :



73. For perfect coupling of two coils of inductance

L1 and L

2, their mutual inductance M should be

given by :

a) 1 2M L L b) 1

2

LM

L

c) 1 2M L L d)

1/ 2

1

2

LM

L

74. The coupling coefficient of the perfectly coupled

coils is :

a) zero

b) 1

c) slightly more than 1

d) infinite

75. What is the minimum value of inductance that

can be obtained with the help of three inductances

of 2 H, 3 H and 6 H ?

a) 1

H6

b) 1

H3

c) 1 H d) 11 H

76. If the magnetic flux linked with a coil through

which a current of xA is set up, is y Wb, then the

coefficient of self-inductance of the coil is :

a) (x y) henry b) x

henryy

c) y

henryx

d) xy henry

77. When the number of turns of a coil is doubled, its

self inductance :

a) is doubled b) is halved

c) becomes one quarter

d) becomes four times

78. Eddy currents donot cause :

a) damping b) heating

c) sparking d) loss of energy

79. The role of inductance is equivalent to :

a) momentum b) force

c) energy d) inertia

80. In the dead beat galvanometer, the coil is wound

on a frame made of :

a) magnetic material

b) non magnetic material

c) good conductor d) bad conductor

81. What happens when a magnet is dropped into a

solenoid, whose two ends are connected to each

other. While crossing the loop, it will fall with

acceleration.

a) equal to g b) less than g

c) more than g

d) less than g above the coil and more than g

below it





82. A coil is wound on a transformer of rectangular

cross-section. If all the linear dimensions of the

transformer are increased by a factor 2 and the

number of turns per unit length of the coil remains

unchanged, the self inductance of the coil will be

increased by a factor :

a) 16 b) 8

c) 4 d) 2

83. The induced emf of 2 V is generated when the

current in the circuit changes from 4 A to 5 A in

one millisecond. What is the self inductance of

the circuit ?

a) 8 H b) 10 H

c) 80 H d) none of the above

84. Two pure inductors each of inductance L are

connected in parallel but well separated from each

other. The equivalent inductance of the combination

is :

a) L

4b)

L

2

c) 2 L d) 4 L

85. What is the energy stored in a 50 mH inductor

carrying a current of 4 A ?

a) 0.4 J b) 0.2 J

c) 0.1 J d) 0.05 J

86. A transformer is used to light a 100 W and 110 V

lamp from a 220 V mains. If the main current is

0.5 A. The efficiency of the transformer is :

a) 11 % b) 50 %

c) 80 % d) 90 %

87. When the current changes from +2A to –2A in

0.05 second, an e.m.f. of 8 volt is induced in a

coil. The coefficient of self induction of the coil

is :

a) 0.1 H b) 0.2 H

c) 0.4 H d) 0.8 H

88. Two coils X and Y are placed in a circuit such

that a current changes by 3 ampere in coil X and

the magnetic flux changes of 1.2 weber occurs

in Y. The value of mutual inductance of the coils

is :

a) 0.2 henry b) 0.4 henry

c) 0.6 henry d) 3.6 henry

89. 1 henry =

a) weber + ampere b) weber + volt

c) weber ampere d) weber volt

90. The length of a solenoid is 20 cm, its area of cross-

section is 10 cm2, and the number of turns are

1000. Another coil of 500 turns is wound in the

middle. Their coefficient of mutual induction will

be nearest to :

a) / 2 b)

c) 2 d) 2

91. What is the energy stored in a coil of self inductance

2 H when a current of 10 A is set up through it ?

a) 10 J b) 50 J

c) 100 J d) 500 J

92. A step up transformer raises the voltage from

220 V to 11000 V. If the number of turns of the

secondary be 1000, what is the number of turns

of the primary ?

a) 2 b) 20

c) 200 d) 2000

93. What is the current through the primary coil of

the transformer shown below ?

a) 0.08 A b) 0.04 A

c) 0.02 A d) 0.01 A

94. What will be the self inductance of a coil of 100

turns if a current of 5 amperes produces a magnetic

flux of 5 10–5 Wb ?

a) 1 mH b) 10 mH

c) 1 H d) 10 H

95. The self inductance of two coils of a transformer

is 20 mH and 30 mH. What is the resistance

between them ?

a) zero b) 1.5

c) 600 d) infinite

96. The coefficients of self induction of two coils are

respectively 2 mH and 3 mH, They are coupled

so as to oppose each other. What will be their

self inductance if their mutual inductance is

1 mH ?

a) 7 mH b) 5 mH

c) 3 mH d) 1 mH

97. Two coils of self inductance 1 H and 3 H are

connected in series to support each other. Their

mutual inductance is 6 H. What is the self

inductance of the combination ?





a) 10 H b) 16 H

c) 26 H d) 40 H

98. What will be the self inductance of a coil of 200

turns in which a current of 2 A produces a

magnetic flux of 4 mWb ?

a) 0.1 H b) 0.2 H

c) 0.3 H d) 0.4 H

99. A circular coil of diameter 2 cm and 100 is placed

at the centre of a long solenoid redius 5 cm and

10 turns/cm. The mutual inductance of the two

coils will be nearest to :

a) 40 H b) 4 H

c) 40 mH d) 4 mH

100. The turn ratio of transformer is 5 and the

impedance of primary coil is 100 . What is the

impedance of the secondary coil ?

a) 500 b) 1000

c) 2500 d) 10000

101. Two coils each of self inductance L are connected

in parallel. If they are separated by a large

distance, then what will be the self inductance of

combination ?

a) L

4b)

L

2

c) L d) 2 L

102. The self inductance and resistance of a coil are

10 H and 40 respectively. Only applying a

potential difference of 200 V, what will be the

energy stored in it ?

a) 25 J b) 50 J

c) 75 J d) 125 J

103. Which of the following helps in the operation of

the choke coil ?

a) Self induction

b) Mutual inductance

c) Eddy currents


104. Which of the following helps in raising the

efficiency transformer as a machine ?

a) Sinusoidal nature of ac

b) High voltage

c) Absence of moving parts

d) Absence of direct electrical connection of the

primary and the secondary coils

105. The transformer varies the output :

a) energy b) power

c) frequency d) current

106. The core of the transformer is laminated to :

a) produce eddy currents

b) reduce self induction

c) increase the efficiency

d) decrease the weight of the transformer

107. Which of the following does not cause loss of

energy in a transformer ?

a) Heating b) Eddy currents

c) Mechanical motion d) Hysteresis

108. The core of the transformer is laminated to avoid

loss of energy due to :

a) heating b) eddy current

c) flux leakage d) hysteresis

109. Iron core decreases the loss of energy due to :

a) heating b) eddy current

c) flux leakage d) hysteresis

110. Which of the following decreases the efficiency

of the transformer ?

a) Laminating the core

b) Use of iron core

c) Core made of material having narrow hysteresis

loop


111. A choke coil should have :

a) high resistance low inductance

b) high resistance high inductance

c) low resistance high inductance

d) low resistance low inductance

112. Electromagnetic waves of wavelength 300 m are

to be received with a circuit having capacitance

2 F. What should be the self inductance of the

coil in the circuit ?

a) 12.67 H b) 12.67 mH

c) 12.67 H d) 12.67 nH

Alternating Current

113. What is the phase difference between the flux

linked with a coil rotating in a magnetic field and

the induced emf produced in it ?

a) 0 b) / 4

c) / 2 d)





114. If R, C and L be the resistance, capacitance and

inductance in a circuit in which ac of frequency f

is set up, then which of the following has the

dimensions of R ?

a) f C b) f L

c) C

fd)

L

f

115. For long distance transmission, the ac is stepped

up because transmission at high voltage is :

a) faster b) economical

c) not damped d) not dangerous

116. Large value of which of the following does not

allow electrical oscillations in the LCR circuit.

a) Capacitance b) Inductance

c) Resistance d) Electromotive force

117. Which of the following is independent of the

frequency of ac ?

a) Resistance

b) Inductive reactance

c) Capacitive reactance

d) Impedance

118. Through which of the ae circuit elements both

the emf and current are in phase ?

a) Impedance

b) Inductive reactance

c) Capacitive reactance

d) Resistance

119. The current and emf through an inductance differ

in phase by :

a) 4

b)

2

c) 34

d)

120. The ae cannot be used for :

a) heating

b) lighting

c) electrolysis

d) generate mechanical energy

121. What is the average value of ac over a complete

cycle ?

a) zero b) 0I

2

c) 02 I


122. Which of the following is zero in a watt-less

circuit ?

a) Inductance b) Capacitance

c) Resistance d) None of the above

123. For the current in LC circuit to be maximum, the

angular frequency should be related to L and C

as :

a) 2 LC b) 2 1

LC

c) LC d) 1

LC

124. What converts ac to dc ?

a) Transformer b) Generator

c) Rectifier d) None of the above

125. In an ac circuit, the current :

a) always leads the voltage

b) always lags behind the voltage

c) is always in phase with voltage

d) may lead or leg behind or be in phase with

voltage

126. A resistor, capacitor and inductor are connected

in series with a source of ac. Which of the following

is true ?

The current in resistor lags behind the :

a) current in capacitor

b) current in inductor

c) voltage across capacitor

d) voltage across inductor

127. The current in ae circuit will be wattless when :

a) inductance is zero

b) capacitance is zero

c) resistance is zero

d) capacitance = inductance

128. The hot wire instrument measures :

a) peak voltage b) average voltage

c) rms voltage d) none of the above

129. The instantaneous current in a circuit is

I 2 sin( t ) ampere.

What is the rms value of the current ?





a) 2 A b) 2

c) 1 A d) 1

A2

130. If R, C and L denote resistance, capacitance and

inductance. Which of the following will NOT

have the dimensions of frequency ?

a) RL–1 b) R–1 C–1

c) L–1/2 C–1/2 d) RCL

131. What generates the restoring tendency in the LCR

oscillating circuit ?

a) Capacitor b) Inductor

c) Resistor d) Cell

132. For quick discharge of a capacitor through a

resistor, which of the following should be large ?

a) Capacitance b) Resistance

c) Both resistance and capacitance

d) Neither resistance nor capacitance

133. How does the current in an RC circuit vary when

the charge on the capacitor builds up ?

a) It increases linearly

b) It increases exponentially

c) It decreases linearly

d) It decreases exponentially

134. The alternating current in RCL series circuit is

maximum when :

a) XL = 0 b) X

C = 0

c) XL = X

Cd) 2 2

L CX X 1

135. Hot wire anuneters can measure :

a) only ac b) only dc

c) both ac and dc d) neither ac nor dc

136. In an ac circuit capacitive reactance = inductive

reactance. The phase difference between the

current and voltage will be :

a) zero b) 4

c) 2

d)

137. The frequency of ac is 50 Hz. How many times

in one second does the voltage in the circuit

becomes zero ?

a) 25 b) 50

c) 100 d) 150

138. Capacitive reactance of a capacitor varies directly

as :

a) capacitance b) frequency of ac

c) both capacitance and frequency of ac


139. Why 220 V ac is more dangerous than 220 V dc ?

a) The dc attracts

b) Peak voltage for ac is much larger

c) The body offers less resistance to ac

d) Due to some other reason

140. An ac circuit contains a resistance R, capacitance

C and inductance L in series with a source of

emf = 0 sin (t + ). The current through the

circuit is maximum, when :

a) R L C b) 1

LC

c) 2 LC d) RLC

141. The choke coil of resistance R and inductance L

is connected across a battery of emf . The final

current in the choke depends on :

a) R and L b) L and

c) and R d) R, L and

142. What is the nature of graph between inductive

reactance and frequency of ac for series RCL

circuit ?

a) Straight line b) Parabola

c) Hyperbola d) Bell shaped

143. What is the nature of graph between impedance

and frequency of ac for series RCL circuit ?



144. What is the nature of graph between inductive

reactance and frequency of ac for series RCL

circuit ?



145. In a series RCL circuit the frequency of ac is

varied. At the resonant angular frequency 0, the

impedance of the circuit is :

a) R b) Less than 0L

c) More than 0L

d) Between 0L and

0

1

C





146. In the above question what is the current in the

circuit, if applied emf be E ?

a) More than E

Rb) Less than

E

R

c) Equal to E

R

d) Depends on the values of L and C

147. A pure resistance R, pure capacitance C and pure

inductance L are connected in series and the

impedance of the circuit at resonance is Z0. If

they are connected in parallel to each other, the

maximum impedance at resonance will be :

a) Less than R

b) More than R

c) Equal to Z0

d) dependent on the values of C and L

148. The ohm second =

a) henry b) siemns

c) weber d) tesla

149. The impedance of a 10 ohm resistance to 50 Hz

ac is :

a) 500 b) 250

c) 50 d) 10

150. A 10 F capacitor is connected across a 200 V,

50 Hz ac supply. The peak current through the

circuit is :

a) 0.6 A b) 0.6 2 A

c) 0.6

A2

d) 0.6

2A

151. In a transformer the voltage is stepped up from

220 V to 440 V. If the current in the primary was

1.0 ampere, that in the secondary should be :

a) 0.5 A

b) between 0.5 and 1 A

c) 1 A

d) more than 1 A

152. A hot wire ammeter reads 10 A in an ac circuit.

The peak value of the current is :

a) 10 2 A b) 10

A2

c) 5 A d) 20

A

153. The impedance of a 10 microfarad capacitor for

50 Hz ac is :

a) 2 b) 20

c) 200 d) none of the above

154. The reading of ac voltmeter is 220 V. What is

the peak voltage ?

a) 200 V b) 220 V

c) 240 V d) none of the above

155. An inductance coil and capacitor are connected

in series and the current through the combination

is maximum for ac of frequency f. If they are

connected in parallel, at what frequency the

current through the combination is minimum ?

a) f b) f / 2

c) 2 f d) none of the above

156. In a RCL circuit capacitance is changed from C

to 2 C. For the resonant frequency to remain

unchanged, the inductance should be changed

from L to :

a) 4 L b) 2 L

c) L / 2 d) L / 4

157. In a series resonant circuit the ae voltages across

resistance R, inductance L and capacitance C

are 5 V, 10 V & 10 V respectively. The ae voltage

applied to the circuit will be :

a) 25 V b) 20 V

c) 10 V d) 5 V

158. A 1.0 mH inductance, a 10 F capacitance and a

5.0 ohm resistance are connected in series to an

a.c. source. It is found that the inductor and the

capacitor show equal reactances. The reactance

should be nearest to :

a) 100 ohm b) 32 ohm

c) 10 ohm d) 3.2 ohm

159. In a circuit resistance R, capacitance C, and

inductance L are in series with a sinusoidal power

source. If the voltage across R, C and L are 80 V,

10 V & 70 V respectively, then the voltage across

the source terminals will be :

a) 100 V b) 110 V

c) 140 V d) 160 V

160. The ratio of the mean value over half cycle to

the r.m.s. value of an A.C. is :

a) 2 : b) 2 2 :

c) 2 : d) 2 :1





161. In a step-up transformer the turn ratio is 3 : 2.

A battery (e.m.f. 4.5 V) is connected across the

primary. The voltage developed in the secondary

would be :

a) 4.5 V b) 3.0 V

c) 1.5 V d) zero

162. A capacitor of capacitance 1 F and a resistor of

resistance 105 ohm are connected in series with

a battery of e.m.f. 100 volt and negligible internal

resistance. Then the time constant of the circuit

is :

a) 10–6 s b) 10–4 s

c) 10–1 s d) 1000 s

163. The ratio of induced emf in a coil of 50 turns and

area A oscillating at frequency 50 Hz to that in a

coil of 100 turns and same area oscillating at

frequency 100 Hz is :

a) 0.25 b) 0.50

c) 0.75 d) 1.00

164. A lamp of 220 V and 100 W is first connected in

dc circuit of 200 V and then in ae circuit of 200 V.

It will light brighter in :

a) dc circuit

b) ac circuit

c) none of the above

d) dc or ac circuit depending on the nature of

filament

165. In the series RCL circuit at resonance the applied

ac voltage is 220 V. The potential drop across

the inductance is 110 V, what is the potential drop

across the resistance ?

a) 110 V b) 110 2 V

c) 220 V d) 220 2 V

166. In the above question, what is the potential drop

across the capacitor ?

a) 110 V b) 110 2 V

c) 220 V d) 220 2 V

167. A capacitor of 5 F is charged to a potential

difference of 200 V. If it is discharged through

two resistors of 700 and 300 ohms, what is the

energy dissipated in each of the two resistors ?

a) 0.07 J, 0.03 J b) 0.03 J, 0.07 J

c) 0.7 J, 0.3 J d) 0.3 J, 0.7 J

168. In an RCL series circuit, the capacitance is made

four times. To keep the resonant frequency

unchanged, by how many times the inductance

be changed ?

a) 4 b) 2

c) 1

2d)

1

4

169. The inductance of a coil is 5 H. What is its

effective reactance in dc circuit ?

a) 0 b)

c) 5 W d) 0.2 W

170. A coil of 10 and 10 mH is connected in parallel

to a capacitor of 0.1 F. The impedance of the

circuit at resonance is :

a) 102 b) 103

c) 104 d) 106

171. In an ac circuit, the capacitive reactance equals

the inductive reactance. What is the phase

difference between the voltage and current ?

a) 0° b) 30°

c) 45° d) 60°

172. What will be the impedance of the circuit shown

below ?

a) 5 b) 10

c) 25 d) 75

173. What will be the impedance of the circuit shown

below ?

a) zero b) 1

c) 100 d)

174. In the above circuit, what is the current drawn

from the circuit ?

a) zero b) 1 A

c) 10 A d)

175. The alternating current is given by,

1 2I I cos t I sin t

What is the rms current in the circuit ?





a) 1 2I I

2

b)

1 2I I

2

c) 2 2

1 2I I

2

d)

2 2

1 2I I

2

176. A capacitor and 25 resistor are connected in

series. When they are connected across 250 V

a.c. supply then the current through the circuit is

2 A. What is the potential difference across the

capacitor ?

a) 2 100 V b) 2.5 100 V

c) 3 100 V d) 6 100 V

177. What will be the approximate time taken by an

a.c. of frequency 60 Hz to go from zero to

maximum or peak value ?

a) 0.004 s b) 0.005 s

c) 0.04 s d) 0.05 s

178. At what angular frequency the inductive reactance

of 2 H inductance will be equal to the capacitive

reactance of a capacitor of 2 F ?

a) 5 rad/s b) 50 rad/s

c) 500 rad/s d) 5000 rad/s

179. A capacitor of capacitance 16 F is connected

to an a.c. power supply of 200 V & 50 Hz. What

is the current through the capacitor ?

a) 10 A b) 5 A

c) 3 A d) 1 A

180. Two lamps are marked 220 V, 100 W and 220 V,

40 W. When they are operated on 220 V, what is

the ratio of the heat produced in them ?

a) 0.2 b) 0.4

c) 4 b) 2

181. Two electric lamps are marked 220 V, 100 W and

220 V, 50 W. If they are operated on 110 V, what

will be the ratio of the heat produced in them ?

a) 0.05 b) 0.5

c) 2 d) 20

182. The peak value of a.c. is 5 2 ampere. What is

its apparent value ?

a) 10 A b) 5 2 A

c) 5 A d) 5

A2

183. What is the equation of an alternating current of

frequency 60 Hz and rrns value 10 A ?

Given that a.c. = 0 at t = 0 :

a) I 10sin (120 t)

b) I 10cos (120 t)

c) I 10 2 sin (120 t)

d) I 10 2 cos (120 t)

184. What will be the value of voltage applied in the

following circuit ?

a) 220 V b) 140 V

c) 120 V d) 100 V

185. A resistance of 5 and an inductance of 50 mH

are connected in series with an a.c. I = 100 sin

(100 t). What is the phase difference between

the instantaneous current and voltage ?

a) 300 b) 450

c) 600 d) 900

186. In an RCL series circuit. the values of R. XL, X

C

are respectively : 120 , 180 , 130 . What is

the impedance of the circuit ?

a) 120 b) 130

c) 180 d) 330

187. An alternating power supply of 200 V is connected

across resistance 20 . capacitance 16 F and

inductance 2 H in series. What is the current in

the circuit for frequency of a.c. equal to zero and

infinity ?

a) 10 A, 0 A b) 0 A, 10 A

c) 10 A, 10 A d) 0 A, 0 A

188. An electric lamp is marked 100 W, 250 V a.c.

What is the resistance of the lamp ?

a) 484 b) 625

c) 48.4 d) 62.5

189. The self inductance of the motor of an electric

fan is 10 H. In order to impart maximum power

at 50 Hz, it should be connected to a capacitance

of :

a) 1 F b) 2 F

c) 4 F d) 8 F





190. The impedance of an a.c. circuit is 200 and

the phase angle between current and emf is 600.

What is the resistance of the circuit ?

a) 50 b) 100

c) 100 3 d) 300

191. The a.c. in a circuit leads the emf by 4

rad. The

component of the circuit are :

a) R alone b) R, C

c) RL d) LC

192. The phase difference between the a.c. and emf

is 2

. Which of the following cannot be the

constituent of the circuit ?

a) L, C b) L alone

c) C alone d) R, L

193. A de voltmeter is connected across a 220 V ac

power supply. What will be the reading of the

voltmeter ?

a) 220 V b) 220 2 V

c) 220

V2

d) zero

194. In series RCL circuit the reactance of inductor

as well as capacitor is 10 . If the resistance in

the circuit be 10 and 100 V power supply is

connected across it, then, what is the current in

the circuit ?

a) 5 A b) 10 A

c) 15 A d) 25 A

195. The capacitive and inductive reactance of a series

circuit are XC and X

L. What is the resultant

reactance ?

a) L CX X b)

L CX X

c) 2 2

L CX X d) 2 2

L CX X

196. The capacitive and inductive reactance of a

parallel circuit are XC and X

L. What is the net

reactance ?

a) L C

1 1

X X b)

L C

1 1

X X

c)

1/ 2

2 2

L C

1 1

X X

d)

1/ 2

2 2

L C

1 1

X X

197. For a choke coil the resistance is R and reactance

is X. Which of the following relations is valid ?

a) R > X b) R = X

c) R X d) R << X

198. After the time equal to the time constant on

closing the RC circuit, the charge grows to :

[q0 = peak charge]

a) 0.37 q0

b) 0.63 q0

c) 02 q d)

0q

2

199. What is the nature of RCL series circuit for

frequency less than the resonant frequency ?

a) Resistive b) Inductive

c) Capacitive d) None of the above

200. If the power factor changes from 1

2 to

1

4 then

what is the increase in impedance in A.C. ?

a) 20 % b) 50 %

c) 25 % d) 100 %

201. What is the expression for the resonant angular

frequency of the following circuit ?

a) 1

LCb) LC

c)

2

2

1 R

LC L d)

2

2

1 R

LC L

202. What is the impedance of a purely antiresonant

circuit at resonance ?

a) zero b) R

c) 2 R d) 203. What is the expression for the resonant angular

frequency of the following circuit ?





a) 1

LCb) LC

c)

2

2

1 R

LC L d)

2

2

1 R

LC L

Power factor

204. No current is drawn from the secondary of ideal

transformer. What is the power factor of the

primary coil ?

a) 1

2b) 1

c) d) zero

205. The power factor varies between :

a) zero to 0.5 b) 0.5 to 1

c) zero to 1 d) 1 and 2

206. The current in an ac circuit is I = I0 sin t and the

emf is = cos t. The power dissipation in the

circuit is :

a) zero b) 0 0I

2

c) 0 0I d) none of the above

207. What is the power dissipated in inductance L

when the current through it is I ?

a) 21

LI2

b) LI2

c) zero d) none of the above

208. The maximum current through a pure capacitor

of capacitance C is I0, The maximum emf is

0.

If the frequency is 50 Hz, the average power

dissipated through the capacitor is :

a) 0 2I

2

b) zero

c) 0 0I d) 2I /100 C

209. There is a current of 20 milliampere through an

ideal choke coil of 1.5 H when connected to

220 volt, 50 hertz ac supply. The power consumed

is :

a) zero

b) 220 20 10–3 watt

c) 220 50 watt d) 220 20 1.5 watt

210. The rms current in an a.c. circuit is 2 A. If the

wattless current be 3A, what is the power

factor ?

a) 1

3b)

1

2

c) 1

2d)

1

3

211. When an emf E = 7 cos t is applied across a

circuit, the current is I = 5 cos t. What is the

power factor for the circuit ?

a) zero b) 1

c) 5

7d)

212. The power factor of an RL circuit is 1

.2

If the

frequency of a.c. is doubled, what will be the

power factor ?

a) 1

3b)

1

5

c) 1

7d)

1

11

213. In a circuit, the reactance X and resistance R

are equal. What is the power factor ?

a) 1 b) 1

2

c) 1

2d) 2

214. The values of L, C and R for a circuit are 1 H,

9 F and 3 . What is the quality factor for the

circuit at resonance ?

a) 1 b) 9

c) 1

9d)

1

3

215. In n lamps of same type are connected in series,

then the power of combination

......power of each lamp

a) 1

nb) 2

1

n

c) n d) n2





216. The values of resistance and inductive reactance

of a choke coil are 8 & 6 respectively. What

is the power factor of the coil ?

a) 0.3 b) 0.4

c) 0.3 d) 0.8

217. In which of the following cases, the power factor

is not equal to 1 :

a) Z = R b) XL = X

C

c) SC = S

Ld) L = C

218. The current and emf in a circuit are :

0 0I I sin t, E E cos t

What is the power dissipated ?

a) zero b) 0 0E I

2

c) 0 0E I d)

219. What is the power factor of RCL series circuit at

resonance ?

a) 0 b) 1

c) Between 0 and 1 d) More than 1

Recent Questions form MH-CET Exams.

220. A current in a coil changes from 0 to 2 A in 0.05

sec. If the induced e.m.f. is 80 V, the self-

inductance of the coil is :

a) 1 H b) 1.5 H

c) 2 H d) 2.5 H

221. D.C. ammeter is connected in a circuit through

which an A.C. of 50 Hz flows. The ammeter

would read :

a) peak value of the current

b) zero

c) average current

d) R.M.S. value of current

222. The induced e.m.f. in a coil is independent of :

a) number of turns in the coil

b) time

c) resistance of the circuit

d) change in the magnetic flux

223. Two coils A and B are placed in a circuit. When

current changes by 8 amperes in the coil A, the

magnetic flux change of 1.6 weber occurs in B.

Then the mutual inductance of the coils is :

a) 12.8 H b) 5.0 H

c) 0.2 H d) 0.025 H

224. In a LCR circuit the capacitance is changed from

C to 4 C. For the same resonant frequency the

inductance should be changed from L to :

a) L

2b)

L

4

c) 2 L d) 4 L

225. Which of the following graphs best represents

the relation between impedance (z) and frequency

for the given circuit ?

a) b)

c) d)

226. The magnetic flux through a coil as a function of

time, is given by 10/t Webers. The e.m.f. induced

in the coil is :

a) – 10 loge t volts b)

6.93volts

t

c) 2

10volts

t

d) – 10 t volts

227. In the adjacent circuit,

a) V < VL + V

Lb) V = V

L + V

R

c) V > VL + V

Rd) V = V

R

228. If an AC main supply is given to be 220 V. What

would be the average emf during a positive half

cycle ?

a) 198 V b) 386 V

c) 256 V d) none of these





229. The current in a coil of inductance 5 H decrease

at the rate of 2 A/s. The induced emf is :

a) 2 V b) 5 V

c) 10 V d) – 10 V

230. Resonance of a capacitor of capacitance C F

for A.C. frequency 100

Hz is 25 . The value

C is :

a) 50 F b) 25 F

c) 100 F d) 75 F

231. In a coil of area 20 cm2 & 10 turns with magnetic

field directed perpendicular to the plane changing

at the rate of 104 T/s. The resistance of the coil

is 20 . The current in the coil will be :

a) 10 A b) 20 A

c) 0.5 A d) 1.0 A

232. In an purely capacitive circuit current in capacitor?

a) leads e.m.f. by /2

b) lags e.m.f. by /2

c) both are in same phase

d) both are out of phase

233. If 1 = 5 Wb,

2 = 2 Wb, t = 2s. What is the

value of e.m.f. induced if number of turns is 100 ?

a) 50 volt b) 100 volt


234. A helicopter rises vertically with a speed of

100 m/s. If helicopter has length 10 m and

horizontal component of earth's magnetic field is

5 10–3 Wb/m2, then the induced emf between

the tip of nose and tail of helicopter is :

a) 50 V b) 0.5 V

c) 5 V d) 25 V

235. The current which does not contribute to the

power consumed in an A.C. circuit is called :

a) non ideal current

b) wattless current

c) convectional current

d) inductance current

236. Induction coil is used to convert a small d.c.

voltage into :

a) a.c. voltage

b) sinusoidal voltage

c) high unidirectional and intermittent voltage

d) pulsating d.c. voltage

237. A metal disc of radius r rotates with an angular

velocity about an axis perpendicular to its plane

passing through its centre in a magnetic field of

induction B acting perpendicular to the plane of

the disc. The induced emf between rim and axis

of disc is :

a)

2BR

2

b)

2 2

2

2B R

c) 2B R d) 2B R 238. Resistor of 2 , inductor of 100 H and capacitor

of 400 pF are connected in series across a source

of erms

= 0.1 volt. At resonance voltage drop

across inductor is :

a) 25 volt b) 2.5 volt


239. A wire of length 2.5 km is part of circuit of

resistance 35 orient along E-W direction falls

under gravity to group from, a height of 10 m then

current in the wire is :

[g = 9.8 m/s2 and BH = 2 cot 5 10–5 T]

a) 0.2 A b) 0.02 A

c) 0.04 A d) 2 A

240. Peak current is given Ip, in a resistive circuit of

resistance R. Average power over complete cycle

is :

a) 2

P

1I R

2b) 2

PI R

c)

2

PI Rcos

2 d) pI R cos

241. An inductor of 9 mH and capacitor of 10 F are

in series and XL = X

C. Calculate resonant

frequency.

a) 0.53 kHz b) 5.3 kHz

c) 0.53 Hz d) 5.3 Hz

242. A rod of length is rotated about one of its ends

with angular speed '' in magnetic field of '',

then, e.m.f. induced will be :

a)

2

2

b)

2

c)

2

2

d) 2

243. Henry is equivalent to :

a) Ampere/second b) Ampere second

c) Ohm/second d) Ohm second





244. In the purely resistive AC. circuit :

a) current leads e.m.f. by a phase angle of radians

b) current leads e.m.f. by a phase angle of /2

radians

c) current and e.m.f. are in phase

d) current lags behind e.m.f. by a phase angle of

/2 radians

245. In LCR series circuit, at resonance, the power

facotor is :

a) zero b) 0.5

c) 1 d)

246. When a current of 2 A is passed through a coil of

100 turns flux associated with it is 5 10–5 Wb.

Find the self inductance of the coil :

a) 4 10–3 H b) 4 10–2 H

c) 2.5 10–3 H d) 10–3 H

247. Average power in the L-C-R circuit depends upon :

a) current

b) phase difference only

c) e.m.f.

d) current, e.m.f. and phase difference

248. A transformer is having 2100 turns in primary

and 4200 turns in secondary. An ac source of

120 V, 10 A is connected to its primary. The

secondary voltage and current are :

a) 240 V, 5 A b) 120 V, 10 A

c) 240 V, 10 A d) 120 V, 20 A

249. When the number of turns and length of a solenoid

are doubled keeping the area of cross section

same, the inductance becomes :

a) half b) zero

c) two times d) four times

250. If the current through the coil changes from +2 A

to –2 A in 0.05 sec and 8 V emf is developed in

the coil then the self inductance of the coil is :

a) 0.05 H b) 0.1 H

c) 0.2 H d) 0.4 H

251. An emf e 200 2 sin (100 t) volt is applied

across capacitor of capacitance 2 F then current

through capacitor is :

a) 4 mA b) 40 mA

c) 2 mA d) 3 mA

252. In LCR series circuit power factor at resonance

is :

a) less than one

b) greater than one

c) unity/one

d) can not be predicted

253. In series LCR circuit at resonance :

a) current is maximum and voltage is minimum

b) current is maximum and voltage is maximum

c) current is minimum and voltage is maximum

d) current is minimum and voltage is minimum

254. The self inductance of coil of 400 turns is 8 mH,

If current of 5 mA flows in it, then flux associated

with the coil is :

a) 0

4

b) 0

c) 0

100

d)

0

4

255. In LCR series circuit an ac emf of 2 volt and

frequency 50 Hz is applied across the combination.

If resistance is 4 , capacitance is 8 F and

inductance is 10–2 H then the voltage across

inductor will be :

a) 3

V5

b) 5

V3

c) 2

V3

d) 0.02 V

256. If 'N' is the number of turns in a circular coil then

the value of self inductance varies as :

a) N0 b) N

c) N2 d) N–2

257. In LCR series circuit, an alternating e.m.f. 'e' and

current 'i' are given by the equations

e 100sin(100t)volt,

i 100sin 100t mA.3

The average power dissipated in the circuit will

be :

a) 100 W b) 10 W

c) 5 W d) 2.5 W





258. In electromagnetic wave, according to Maxwell,

changing electric field gives :

a) stationary magnetic field

b) conduction current

c) eddy current

d) displacement current

259. Same current is flowing in two a.c. circuits. First

contains only inductance and second contains only

capacitance. If frequency of a.c. is increased for

both, the current will :

a) increase in first circuit and decrease in second

b) increase in both circuits

c) decrease in both circuits

d) decrease in first circuit and increase in second

260. Two coils A and B have mutual inductance

2 10–2 henry. If the current in the primary is

i = 5 sin (10 t) then the maximum value of e.m.f.

induced in coil B is :

a) volt b) volt2

c) volt3

d) volt

4







REVISION OUESTIONS

from Competitive Exams

1. In a coil of area 10 cm2 & 10 turns with magnetic

field directed perpendicular to the plane and is

changing at the rate of 108 gauss/second. The

resistance of the coil is 20 ohm. The current in

the coil will be :

a) 5 A b) 0.5 A

c) 0.05 A d) 5 108 A

2. The potential difference V across and the current

I flowing through an A.C. circuit are given by,

V = 5 cos t volt, I = 2 sin t ampere.

The power dissipated in the instrument is :

a) 0 watt b) 10 watt

c) 5 watt d) 2.5 watt

3. To reduce the loss of energy as heat due to eddy

currents, the soft iron core is laminated. The angle

between the plane of these sheets and the

magnetic induction should by :

a) zero b) 450

c) 600 d) 900

4. A coil is wound on a former of rectangular cross-

section. If all the linear dimensions of the former

are increased by a factor of 3 and the numbers

of turns per unit length remains the same, the

self-inductance increases by a factor of :

a) 3 b) 9

c) 27 d) 81

5. When the number of turns in a solenoid is doubled

without any change in the length of the solenoid,

its self-inductance will be :

a) Four times b) Doubled

c) Halved d) Squared

6. The average e.m.f. induced in a coil in which the

current changes from 2 ampere to 4 ampere in

0.05 second is 8 volt, what is the self inductance

of the coil ?



7. Using an A.C. voltmeter, the potential difference

in the elecrical line in a house is read to be

234 volt. If the line frequency is known to be

50 cycles per second, the equation for the line

voltage is :

a) V = 165 sin (100 t)

b) V = 331 sin (100 t)

c) V = 234 sin (100 t)

d) V = 440 sin (100 t)

8. A 20 volt A.C. is applied to a circuit consisting of

a resistance and a coil with a negligible resistance.

If the voltage across the resistance is 12 volt, the

voltage across the coil is :


c) 8 volt d) 6 volt

9. With the decrease of current in the primary coil

from 2 ampere to zero value in 0.01 second, the

e.m.f. generated in the secondary coil is 1000

volt. The mutual inductance of the two coil is :



10. The peak value of an alternating e.m.f. E given

by E = E0 cos t is 10 volt and its frequency is

50 Hz. At a time t = 1

600s the instantaneous value

of the e.m.f. is :

a) 10 volt b) 5 3 volt

c) 5 volt d) 1 volt

11. In a region of uniform magnetic induction B = 10–2

tesla, a circular coil of radius 30 cm and resistance

2 ohm is rotated about an axis which is perpen-

dicular to the direction of B and which forms a

diameter of the coil. If the coil rotates at 200 rpm

the amplitude of the alternating current induced

in the coil is :

a) 4 2 mA b) 30 mA

c) 6 mA d) 200 mA

12. A generator produces a voltage that is given by

V = 240 sin 120 t volt where t is in seconds. The

frequency and rms voltage are :

a) 60 Hz and 240 volt

b) 19 Hz and 120 volt

c) 19 Hz and 170 volt

d) 754 Hz and 170 volt

13. When 100 volt D.C. is applied across a solenoid,

a current of 1.0 ampere flows in it. When 100

volt A.C. is applied across the same coil, the

current drops to 0.5 ampere. If the frequency of

A.C. source is 50 Hz the impedance & inductance

of the solenoid are :





a) 200 ohm and 0.55 henry

b) 100 ohm and 0.86 henry

c) 200 ohm and 1.0 henry

d) 100 ohm and 0.93 henry

14. The current in a self inductance L = 40 mH is to

be increased uniformly from 1 A to 11 A in 4 milli

seconds. The induced e.m.f. produced in L during

this process will be :

a)100 volt b) 0.4 volt


15. The frequency of a resonant LC combination

(L = 10 mH and C = 1.0 F) is :

a) 1.0 104 radian per second

b) 1.0 10–4 hertz

c) 1.0 10–4 radian per second

d) 1.0 104 hertz

16. When the current in a coil changes from 8 ampere

to 2 ampere in 3 10–2 seconds the e.m.f. induced

in the coil is 2 volt. The self-inductance of the

coil, in rnilli henry, is :

a) 1 b) 5

c) 20 d) 10

17. The number of turns in the primary and the

secondary of a transformer are 1000 and 3000

respectively. If 80 volt A.C. is applied to the

primary coil of the transformer, then the potential

difference per turn of the secondary coil would

be :


c) 0.24 volt d) 0.80 volt

18. In an A.C. circuit the potential V and the current

are given respectively by,

V = 100 sin (100 t) volt and

1= 100 sin 100t3

mA.

The power dissipation in the circuit will be :

a) 104 watt b) 10 watt

c) 2.5 watt d) 5 watt

19. An A.C. circuit using an inductor and a capacitor

in series has a maximum current. If L = 0.5 henry

and C = 8 F, then the angular frequency of A.C.

voltage will be :

a) 500 b) 5 105

c) 4000 d) 5000

20. An alternating voltage (in volts) = 200 2 sin 100t

is connected to one microfarad capacitor through

an ac ammeter. The reading of the ammeter shall

be :

a) 10 mA b) 20 mA

c) 40 mA d) 80 mA

21. A galvanometer is connected to the secondary

coil. The galvanometer shows an instantaneous

maximum deflection of 7 divisions when current

is started in the primary coil of the solenoid. Now

if the primary coil is rotated through 180·, then

the new instantaneous maximum deflection will

be :

a) 7 units b) 14 units

c) 0 units d) 21 units

22. A 40 electric heater is connected to a 200 V,

50 Hz mains supply. The peak value of electric

current flowing in the circuit is approximately :

a) 2.5 A b) 5.0 A

c) 7 A d) 10 A

23. Dimensions of self-inductance are :

a) M L T–2 A–2 b) M L2 T–1 A–2

c) M L2 T–2 A–2 d) M L2 T–2 A–1

24. If the number of turns per unit length of a coil of

solenoid is doubled, the self-inductance of the

solenoid will :

a) remain unchanged b) be halved

c) be doubled d) become four times

25. Energy in a current carrying coil is stored in the

form of :

a) electric field b) magnetic field

c) dielectric strength c) heat

26. A rectangular coil has 20 turns and area of cross-

section 25 sq cm has a resistance of 100 ohm. If

a magnetic field which is perpendicular to the

plane of the coil changes at a rate of 1000 tesla

per second, the current in the coil is :

a) 1.0 ampere b) 50 ampere


27. The total charge, induced in a conducting loop

when it is moved in magnetic field, depends on :

a) the rate of change of magnetic flux

b) initial magnetic flux only

c) the total change in magnetic flux

d) final magnetic flux only





28. A 100 millihenry coil carries a current of 1 ampere.

Energy stored in its magnetic field is :

a) 0.5 J b) 1 J

c) 0.05 J d) 0.1 J

29. A magnetic field of 2 10–2 tesla acts at right

angles to a coil of area 100 cm2 with 50 turns.

The average emf induced in the coil is 0.1 V when

it is removed from the field in time 't', The value

of 't' is :

a) 0.1 second b) 0.01 second

c) 1 second d) 20 second

30. An alternating potential V = V0 sin t is applied

across a circuit.

As a result the current 0I I sin t2

flows in it. The power consumed in the circuit

per cycle is :

a) zero b) 0.5 V0I

0

c) 0.707 V0I

0d) 1.414 V

0I

0

31. Faraday's laws are consequence of conservation

of :

a) Energy

b) Energy and magnetic field

c) Charge

d) Magnetic field

32. A moving conductor coil produces an induced emf.

This is in accordance with :

a) Lenz's law b) Faraday's laws

c) Coulomb's law d) Ampere's law

33. When the number of turns and the length of the

solenoid are doubled keeping the area of cross-

section same, the inductance :

a) remains the same b) is halved

c) is doubled d) becomes four times

34. What is the self-inductance of a coil which

produces 5 V when the current changes from 3

amperes to 2 amperes in one millisecond ?

a) 5000 henry b) 5 mili-henry

c) 50 henry d) 5 henry

35. The north pole of a long horizontal bar magnet is

being brought closer to a vertical conducting plane

along the perpendicular direction. The direction

of the induced current in the conducting plane

will be :

a) horizontal b) vertical

c) clockwise

d) anticlockwise

36. In general in an alternating current circuit :

a) the average value of current is zero

b) the average value of square of the current is

zero

c) average power dissipation is zero.

d) the phase difference between voltage and

current is zero

37. A 12 ohm resistor and a 0.21 henry inductor are

connected in series to an AC source operating at

20 volts, 50 cycle. The phase angle between the

current and the source voltage is :

a) 300 b) 400

c) 800 d) 900

38. An e.m.f. of 15 volt is applied in a circuit coil

containing 5 henry inductance and 10 ohm

resistance. The ratio of the currents at time t = and at t = 1 seconds is :

a)

1/ 2

1/ 2

e

e 1b)

2

2

e

e 1

c) 11 e d) e 1

39. In a noiseless transformer an alternating current

of 2 amperes is flowing in the primary coil. The

number of turns in the primary and secondary

coils are 100 and 20 respectively. The value of

the current in the secondary coil is :

a) 0.80 A b) 0.4 A

c) 5 A d) 10 A

40. If resistance of 100 and inductance of 0.5 henry

and capacitance of 10 10–6 F are connected in

series through 50 Hertz AC supply then impedence

is :

a) 1.8765 b) 18.76

c) 187.6 d) 101.3

41. In an A.C. circuit, the current is,

i 5sin 100t amp2

and the A.C. potential

is V = 200 sin (100 t) volt. Then the power con-

sumption is :

a) 20 watts b) 40 watts

c) 1000 watts d) 0 watts





42. A step-up transformer is used on a 120 V line to

provide a potential difference of 2400 V. If the

primary coil has 75 turns, the number of turns in

the secondary coil is :

a) 150 b) 1200

c) 1500 d) 1575

43. In the circuit shown below, what will be the

readings of the voltmeter and ammeter ?

a) 800 V, 2 A b) 300 V, 2 A

c) 220 V, 2.2 A d) 100 V, 2 A

44. In the non resonant circuit, what will be the nature

of the circuit for frequencies higher than the

resonant frequency ?

a) Resistive b) Capacitive

c) Inductance d) None of the above

45. Which of the following curves correctly represent

the variation of capacitive reactance (XC) with

frequency (f) ?

a) b)

c) d)

46. In a choke coil the reactance XL and resistance

R are :

a) XL = R b) X

L >> R

c) XL << R d) X

L =

47. In an induction coil with resistance, the induced

emf will be maximum when :

a) the switch is put on due to high resistance

b) the switch is put off due to high resistance

c) the switch is put on due to low resistance

d) the switch is put off due to low resistance

48. The mutual inductance of an induction coil is 5 H.

In the primary coil the current reduces from 5 A

to zero in 10–3 s. What is the induced emf in the

seconday coil ?

a) 2500 V b) 25000 V

c) 2510 V d) zero

49. The resonant frequency of a circuit is f. If the

capacitance is made 4 times the initial values, then

the resonant frequency will become :

a) f

2b) 2 f

c) f d) f

4

50. What will be the phase difference between virtual

voltage and virtual current, when the current in

the circuit is wattless ?

a) 90° b) 45°

c) 180° d) 60°

51. In the circuit given below, what will be the reading

of the voltmeter ?

a) 300 V b) 900 V

c) 200 V d) 400 V

52. An electric lamp is connected to 220 V, 50 Hz

supply. Then the peak voltage of current is :

a) 210 V b) 211 V

c) 311 V d) 320 V

53. In a L-R circuit, the value of L is 0.4

henry

and the value of R is 30 ohm. If in the circuit, an

alternating emf of 200 volt at 50 cycles per second

is connected, the impedance of the circuit and

current will be :

a) 11.4 ohm, 17.5 ampere

b) 30.7 ohm, 6.5 ampere

c) 40.4 ohm, 5 ampere

d) 50 ohm, 4 ampere





54. In only inductance circuit the relation of phase

between current and voltage is :

a) Voltage is leading by /2

b) Current is leading by /2

c) Both are in same phase

c) The phase difference is

55. In a coil of self-induction 5 henry, the rate of the

change of current is 2 ampere per second, then

EMF induced in the coil is :

a) 10 V b) 0 V

c) 5 V d) – 5 V

56. In an ac circuit containing only capacitance the

current :

a) leads voltage by 1800

c) remains in phase with voltage

c) leads voltage by 900

d) legs voltage by 900

57. During a current change from 2 A to 4 A in 0.05

second, 8 V of emf is developed in a coil. The

coefficient of self-induction is :

a) 0.1 H b) 0.2 H

c) 0·4 H d) 0.8 H

58. In an ac circuit with voltage V and current I the

power dissipated is :

a) VI

b) 1

VI2

c) 1

VI2

d) depends on the phase between V and I

59. The primary winding of transformer has 500

turns whereas its secondary has 5000 turns. The

primary is connected to an a.c. supply of 20 V,

50 Hz. The secondary will have an output of :

a) 200 V, 50 Hz b) 2 V, 50 Hz

c) 200 V, 500 Hz d) 2 V, 5 Hz

60. The number of turns in the primary coil of a

transformer is 200 and the number of turns in the

secondary coil is 10. If 240 volts ac are applied

to the primary, the output from the secondary will

be :

a) 48 A b) 24 V

c) 12 V d) 6 V

61. A coil of copper having 1000 turns is placed in a

magnetic field (B = 4 10–5) perpendicular to its

axis. The cross-sectional area of the coil is

0.05 m2. If it turns through 1800 in 0.01 second,

then the EMF induced in the coil is :

a) 0.4 V b) 0.2 V

c) 0.04 V d) 4 V

62. Weber/m2 is equal to :

a) volt b) henry

c) tesla d) all the these

63. If the rotational velocity of a dynamo armature is

doubled, then the induced emf will :

a) become half

b) become double

c) become quadruple

d) remain unchanged

64. Which quantity is increased in step-down

transformer ?

a) Current b) Voltage

c) Power d) Frequency

65. In L-C-R series A.C. circuit, the phase angle

between current and voltage is :

a) Any angle between 0 and 2

b) 2

c)

d) Any angle between 0 and 2

66. The average power dissipation in a pure capacitor

in AC circuit is :

a) 21

CV2

b) CV2

c) 2 CV2 d) zero

67. In an A.C. circuit, a resistance of R ohm is

connected in series with an inductance L. If phase

angle between voltage and current be 45°, the

value of inductive reactance will be :

a) R

4b)

R

2

c) R

d) cannot be found with the given data





68. In an L-R circuit, time constant is that time in

which current grows from zero to the value :

a) 0.63 I0

b) 0.50 I0

c) 0.37 I0

d) I0

[where I0 is the steady state current]

69. Quantity that remains unchanged in a transformer

is :

a) Voltage b) Current

c) Frequency d) None of these

70. The direction of induced current is such that it

opposes the very cause that has produced it. This

is the law of :

a) Lenz b) Faraday

c) Kirchhoff d) Fleming

71. A two meter wire is moving with a velocity of 1 m/s

perpendicular to a magnetic field of 0.5 Wb/m2.

The emf induced in it will be :

a) 0.5 volt b) 0.1 volt

c) I volt d) 2 volt

72. The north pole of a magnet is brought near a

metallic ring as shown in the figure. The direction

of induced current in the ring will be :

a) Anticlockwise

b) Clockwise

c) First anticlockwise and then clockwise

d) First clockwise and then anticlockwise

73. The expression for magnetic induction inside a

solenoid of length L, carrying a current I and

having N number of turns is :

a) 0 N

I4 L

b)

0 NLI

c) 0 NLI

4

d) 0

NI

L

74. A particle is moving in a uniform magnetic field,

then :

a) its momentum changes but total energy remains

the same

b) both momentum and total energy remain the

same

c) both change

d) total energy changes but momentum remains

same

75. A particle moving in a magnetic field has increase

in its velocity, then its radius of the circle :

a) decreases b) increases

c) remains the same d) becomes half

76. Two inductors each of inductance 'L' are joined

in parallel. What is the equivalent inductance ?

a) 2 L b) L

c) L

2d) zero

77. What is the coefficient of mutual inductance,

when the magnetic flux changes by 2 10–2 Wb,

and change in current is 0.01 A ?

a) 2 henry b) 3 henry

c) 1

2 henry d) zero

78. In an LCR series circuit, the capacitance is made

one-fourth, when in resonance. Then what should

be change, in inductance, so that the circuit remains

in resonance ?

a) 4 times b) 1

4 times

c) 8 times d) 2 times

79. A step-up transformer has transformation ratio

of 3 : 2. What is the voltage in secondary, if

voltage in primary is 30 V ?

a) 45 V b) 15 V

c) 90 V d) 300 V

80. A step-up transformer operates on a 230 V line

and supplies a load of 2 ampere. The ratio of the

primary and secondary winding is 1 : 25. The

current in the primary is :

a) 15 A b) 50 A

c) 25 A d) 12.5 A

81. Two coils have a mutual inductance 0.005 H.

The current changes in the first coil according

to equation I = I0 sin t where I

0 = 10 A and

= 100 radian/second. The maximum value

of e.m.f. in the second coil is :

a) 2 b) 5

c) d) 4





82. In an A.C. circuit the potential difference across

an inductance and resistance joined in series are

respectively 16 V and 20 V. The total potential

difference across the circuit is :

a) 20.0 V b) 25.6 V

c) 31.9 V d) 53.5 V

83. In a transformer, the number of turns of primary

coil and secondary coil are 5 and 4 respectively.

If 240 V is applied on the primary coil, then the

ratio of current in primary and secondary coil is :

a) 4 : 5 b) 5 : 4

c) 5 : 9 d) 9 : 5

84. In the given circuit the r.m.s. value of e is 5 V &

the r.m.s. value of voltage drop across L is 3 V.

The r m.s. value of the voltage across R will be :

a) 2 V b) 3 V

c) 4 V d) 0 V

85. Assertion : In series LCR circuit, the resonance

occurs at one frequency only.

Reasons : At resonance the inductive reactance

is equal and opposite to the capacitive reactance.

a) If both Assertion and Reason are true and the

Reason is correct explanation of the Assertion.

b) If both Assertion and Reason are true, but

Reason is not correct explanation of the Assertion.

c) If Assertion is true, but the Reason is false.

d) If Assertion is false and Reason is true.

86. Assertion : In series LCR circuit resonance can

take place.

Reason: Resonance takes place if inductive and

capacitive reactances are equal and opposite.

a) If both Assertion and Reason are true and the

Reason is correct explanation of the Assertion.

b) If both Assertion & Reason are true, but Reason

is not correct explanation of the Assertion.

c) If Assertion is true, but the Reason is false.

d) If Assertion is false and Reason is true.

87. The best material for the core of a transformer,

is :

a) stainless steel b) mild steel

c) hard steel d) soft iron

88. A transformer works on the principle of :

a) convertor b) invertor

c) mutual induction d) self-induction

89. In a circuit given in figure, 1 and 2 are ammeter.

Just after key K is pressed to complete the circuit,

the reading is :

a) zero in both 1 and 2

b) maximum in both 1 and 2

c) zero in 1, maximum in 2

d) maximum in 1, zero in 2

90. The effective value of A.C. in a circuit is 10 A.

The peak value of current is :

a) 10 A b) 14.14 A

c) 0.707 A d) 5 A

91. An L.C. circuit contain 10 mH inductor and a

25 F capacitor. The resistance of the circuit is

negligible. The energy stored in the circuit is

completely magnetic at time (in milli seconds).

The time is measured from the instant when the

circuit is closed :

a) 1.57, 4.71, 7.85 b) 0, 3.14, 6.28

c) 0, 1.57, 4.71 d) none of these

92. Which of the following quantity remains constant

in a step-down transformer ?

a) Current b) Voltage

c) Power d) None of these

93. A magnet is freely falling inside a long hollow

pipe. The acceleration of the magnet is :

a) > g b) < g

c) = g d) none of these

94. The phase difference between the current and

voltage at resonance is :

a) 0 b) / 2

c) d) –

95. If the current is halved in a coil, then the energy

stored is how much times the previous value ?

a) 1 / 2 b) 1 / 4

c) 2 d) 4





96. The average e.m.f. induced in a coil in which. a

current changes from 0 to 2 A in 0.05 s is 8 V.

The self inductance of the coil is :

a) 0.1 H b) 0.2 H

c) 0.4 H d) 0.8 H

97. Output voltage of a transformer does not depend

upon :

a) number of turns in secondary coil

b) input voltage

c) number of turns in primary coil

d) A.C. frequency

98. In an A.C. source R = 36 ohm, frequency = 50 Hz

& L = 0.12 henry, then phase difference between

current and voltage is :

a) 90° b) 45°

c) 60° d) 75°

99. An inductance L having a resistance R is connected

to an alternating source of angular frequency .

The quality factor (Q) of the inductance is :

a) R

Lb)

1/ 2R

L

c)

2L

R

d) L

R

100. A circular loop of radius 0.3 cm lies parallel to a

much bigger circular loop of radius 20 cm. The

centre of the small loop is on the axis of the bigger

loop. The distance between their centres is 15 cm.

If a current of 2.0 A flows through the smaller

loop, then the flux linked with bigger loop is :

a) 6.6 10–9 weber

b) 9.1 10–11 weber

c) 6 19–11 weber

d) 3.3 10–11 weber

101. A coil of self-inductance L is connected in series

with a bulb B and an AC source. Brightness of

the bulb decreases when :

a) a capacitance of reactance XC = X

L is included

in the same circuit

b) an iron rod is inserted in the coil

c) frequency of the AC source is decreased

d) number of turns in the coil is reduced

102. The current (I) in the inductance is varying with

time according to the plot shown in figure.

Which one of the following is the correct variation

of voltage with time in the coil ?

a) b)

c) d)

103. A coil of resistance 400 is placed in a magnetic

field. If the magnetic flux (Wb) linked with the

coil varies with time t (sec) as,

= 50 t2 + 4

The current in the coil at t = 2 sec is :

a) 0.1 A b) 2 A

c) 1 A d) 0.5 A

104. A coil is suspended in a uniform magnetic field,

with the plane of the coil parallel to the magnetic

lines of force. When a current is passed through

the coil it starts oscillating it is very difficult to

stop. But if an aluminium plate is placed near to

the coil, it stops. This is due to :

a) electromagnetic induction in the aluminium

plate giving rise to electromagnetic damping

b) development of air current when the plate is

placed

c) induction of electrical charge on the plate

d) shielding of magnetic lines of force as aluminium

is a paramagnetic material.

105. A metallic rod oflength '' is tied to a string of

length 2 and made to rotate with angular speed

on a horizontal table with one end of the string

fixed. If there is a vertical magnetic field 'B' in

the region the e.m.f. induced across the ends of

the rod is :





a)

25 B

2

b)

22 B

2

c)

23 B

2

d)

24 B

2

Paragraph for Questions 106 and 107

A point charge Q is moving in a circular orbit of

radius R in the x-y plane with an angular velocity

. This can be considered as equivalent to a loop

carrying a steady current. A uniform magnetic

field along the positive z-axis is now switched on,

which increases at a constant rate from 0 to B in

one second. Assume that the radius of the orbit

remains constant. The application of the magnetic

field induces an emf in the orbit. The induced

emf is defined as the work done by an induced

electric field in moving a unit positive charge

around a closed loop. It is known that, for an

orbiting charge, the magnetic dipole moment is

proportional to the angular momentum with a

proportionality constant .

106. The change in the magnetic dipole moment

associated with the orbit, at the end of the time

interval of the magnetic field change, is :

a) 2 BQR b)

2BQR

2

c)

2BQR

2 d) 2 BQR

107. The magnitude of the induced electric field in the

orbit at any instant of time during the time interval

of the magnetic field change is :

a) BR

4b)

BR

2

c) BR d) 2 BR

108. A thin semicircular conducting ring (PQR) of

radius 'r' is falling with its plane vertical in a

horizontal magnetic field B, as shown in figure.

The potential difference developed across the ring

when its speed is , is :

a) 2 rBv and R is at higher potential

b) zero

c)

2Bv r

2

and R is at higher potential

d) rBv and R is at higher potential

109. In an electrical circuit R, L, C and a.c. voltage

source are all connected in series. When L is

removed from the circuit, the phase difference

between the voltage and the current in circuit is

.3

If instead, C is removed from the circuit the

phase difference is again .3

The power factor

of the circuit is :

a) 1

2b) 1

c) 3

2d)

1

2

110. A transformer having efficiency of 90% is working

on 200 V and 3 kW power supply. If the current

in the secondary coil is 6 A, the voltage across

the secondary coil and the current in the primary

coil respectively are :

a) 600 V, 15 A b) 300 V, 15 A

c) 450 V, 15 A d) 450 V, 13.5 A

111. In the given circuit the reading of voltmeter V1

and V2 are 300 volts each. The reading of the

voltmeter V3 and ammeter A are respectively :





a) 150 V, 2.2 A b) 220 V, 2.2 A

c) 220 V, 2.0 A d) 100 V, 2.0 A

112. The figure shows an experimental plot for

discharging of a capacitor in R-C circuit. The time

constant of this circuit lies between :

a) 100 sec and 150 sec

b) 150 sec and 200 sec

c) 0 and 50 sec

d) 50 sec and 100 sec

113. In an LCR circuit is shown below both switches

are open initially. Now switch S1 is closed, S

2

kept open. (q is charge on the capacitor and

= RC is capacitive time constant). Which of

the following statement is correct ?

a) At 1t , q CV(1 e )

2

b) Work done by the battery is half of the energy

dissipated in the resistor

c) At CV

t , q2

d) At 2t 2 , q CV(1 e )

Paragraph for Questions 114 and 115

A thermal power plant produces electric power

of 600 kW at 4000 V, which is to be transported

to a place 20 km away from the power plant for

consumers' usage. It can be transported either

directly with a cable of large current carrying

capacity or by using a combination of step-up and

step-down transformers at the two ends. The

drawback of the direct transmission is the large

energy dissipation. In this method using transformers

the dissipation is much smaller. In this method, a

step-up transformer is used at the plant side so

that the current is reduced to a smaller value. At

the consumers' end, a step-down transformer is

used to supply power to the consumers at the

specified lower voltage. It is reasonable to assume

that the power cable is purely resistive and the

transformers are ideal with a power factor unity.

All the currents and voltages mentioned are rms

values.

114. In the method using the transformers, assume that

the ratio of the number of turns in the primary to

that in the secondary in the step-up transformer

is 1 : 10. If the power to the consumers has to be

supplied at 200 V, the ratio of the number of turns

in the primary to that in the secondary in the step-

down transformer is :

a) 200 : 1 b) 150 : 1

c) 100 : 1 d) 50 : 1

115. If the direct transmission method with a cable of

resistance 0.4 km–1 is used, the power dissipation

(in %) during transmission is :

a) 20 b) 30

c) 40 d) 50

116. In the circuit shown here, the point 'C' is kept

connected to point 'A' till the current flowing

through the circuit becomes constant. Afterward,

suddenly, point' C' is disconnected from point 'A'

and connected to point 'B' at time t = 0. Ratio of

the voltage across resistance and the inductor at

Lt

R will be equal to :

a) e

1 eb) 1

c) – 1 d) 1 e

e





117. At time t = 0, terminal A in the circuit shown in

the figure is connected to B by a key and an

alternating current I(t) = I0 cos(t), with I

0 = 1 A

and = 500 rad s–1 starts flowing in it with the

initial direction shown in the figure. At 7

t ,6

the key is switched from B to D.

Now onwards only A and D are connected. A

total charge Q flows from the battery to charge

the capacitor fully. If C = 20 F, R = 10 and

the battery is ideal with emf of 50 V, identify the

correct statement(s).

a) Magnitude of the maximum charge on the

capacitor before 7

t6

is 1 10–3 C

b) The current in the left part of the circuit just

before 7

t6

is clockwise

c) Immediately after A is connected to D, the

current in R is 10 A

d) Q = 2 10–3 C

118. The electric field of an electromagnetic wave in

free space is given by

7 ˆE 10cos (10 t kx) j V/m,

where t and x are in seconds and metres

respectively. It can be inferred that :

1) the wavelength is 188.4 m

2) the wave number k is 0.33 rad/m

3) the wave amplitude is 10 V/m

4) the wave is propagating along +x direction

Which one of the following pairs of statements is

correct ?

a) (3) and (4) b) (1) and (2)

c) (2) and (3) d) (1) and (3)

119. The electric field associated with an e.m. wave

in vacuum is given by,

8ˆE i 40 cos (kz 6 10 t)

where E, z and t are in volt/m, meter and seconds

respectively. The value of wave vector k is :

a) 0.5 m–1 b) 6 m–1

c) 3 m–1 d) 2 m–1

120. A radar has a power of 1 kW and is operating at

a frequency of 10 GHz. It is located on a mountain

top of height 500 m. The maximum distance upto

which it can detect object located on the surface

of the earth (radius of earth = 6.4 106 m) is :

a) 64 km

b) 80 km

c) 16 km

d) 40 km

121. An electromagnetic wave in vacuum has the

electric and magnetic fields E & B,

which are

always perpendicular to each other. The direction

of polarization is given by X

and that of wave

propagation by k.

Then :

a) X || E and k || B E

b) X || B and k || B E

c) X || E and k || E B

d) X || B and k || E B

122. The magnetic field in a travelling electromagnetic

wave has a peak value of 20 nT. The peak value

of electric field strength is :

b) 3 V/m a) 12 V/m

c) 6 V/m d) 9 V/m

123. During the propagation of electromagnetic waves

in a medium :

a) Electric energy density is double of the magnetic

energy density.

b) Electric energy density is half of the magnetic

energy density.

c) Electric energy density is equal to the magnetic

energy density.

d) Both electric and magnetic energy densities

are zero.

124. Match List-I (Electromagnetic wave type) with

List-II (Its association/application) and select the

correct option from the choices given below in

the lists :





List-I List-II

a) Infrared i) To treat muscular

waves strain

b) Radio waves ii) For broadcasting

c) X-rays iii) To detect fracture

of bones

d) Ultraviolet iv) Absorbed by the

rays ozone layer of the

atmosphere.

(a) (b) (c) (d)

a) (iv) (iii) (ii) (i)

b) (i) (ii) (iv) (iii)

c) (iii) (ii) (i) (iv)

d) (i) (ii) (iii) (iv)

125. A conducting square frame of side 'a' and a long

straight wire carrying current I are located int he

same plane as shown in the figure. The frame

moves to the right with a constant velocity 'V'.

The emf induced in the frame will be proportional

to :

a) 2

1

(2x a) b) 1

(2x a)(2x a)

c) 2

1

xd) 2

1

(2x a)

126. An inudctor (L – 0.03 H) & a resistor (R = 0.15 k)

are connected in series to a battery of 15 V EMF

in a circuit shown. The key k1 has been kept closed

for a long time. Then at t = 0, K1 is opened and

K2 is closed simultaneously. At t = 1 ms, the current

in the circuit will be : 5(e 150)

a) 6.7 mA b) 0.67 mA

c) 100 mA d) 67 mA

127. An LCR circuit is equivalent to a damped pendulum.

In an LCR circuit the capacitor is charged to Q0

and then connected to the the L and R as shown

here.

If a student plots graphs of the sequare of maximum

charge (Q2

Max) on capacitor with time (t) for two

different values L1 and L

2 (L

1 > L

2) of L then

which of the following represents this graph

correctly ?

[Plots are schematic and not drawn to scale]

a) b)

c) d)

128. An series R-C circuit is connected to an alter-

nating voltage source. Consider two situations.

(a) When capacitor is air filled

(b) When capacitor is mica filled

Current through resistor is i and voltage across

capacitor is V then :

a) a bi i b)

a bV V

c) a bV V d)

a bV V

129. A electron moves on a straight line path XY as

shown. The abvd is a coil adjacent to the path of

electron. What will be the direction of current, if

any, induced in the coil ?





a) The current will reverse its direction as the

electron goes past the coil

b) No current induced

c) abcd

d) adcb

Brain Teasers

1. A step up transformer operates on a 230 volt line

and supplies a load of 2 ampere. The ratio of

primary and secondary windings is 1 : 25.

Determine the primary current.

a) 12.5 A b) 50 A

c) 8.8 A d) 25 A

2. An A.C. series circuit contains 40 ohm of resistance

and 30 ohm of inductive reactance. Then the

impedance of the circuit is :

a) 70 ohm b) 10 ohm

c) 50 ohm d) 70 ohm

3. The ratio of secondary to the primary turns in a

transformer is 5. If the power output be P, the

input power neglecting all losses, must be equal

to :

a) 5 P b) 5 P

c) P

5d) none of the above

4. The switch connected to a 2 volt cell, a coil of

50 ohms resistance and self-inductance of

25 henries is closed. The final steady current value

is :

a) 4 A b) 0.4

c) 0.04 A d) 0.004 A

5. An alternating voltage of 220 V & 50 Hz is applied

across a circuit containing pure resistance (R)

inductance (L) & capacitance (C). Across which

of the following combinations the voltage can be

greater than 220 V ?

a) R, L and C b) L and C

c) R and L d) none of the above

6. An alternating voltage is applied across a series

circuit containing resistance R, inductance L and

capacitance C. The potential across R is 10 V,

that across L is 18 V and that across C is 8 V.

What is the total voltage across the circuit ?

a) 36 V b) 20 V

c) 10 2 V d) 16 V

7. The average value over one time period of the

output current (peak value I0) of the half wave

rectifier is :

a) 02 I

b)

0I





c) 0I

2d) zero

8. The average value over one time period of the

output current (peak value I0) of the full wave

rectifier is :

a) 02 I

b)

0I

c) 0I

2d) zero

9. In the above question what will be the average

value over half time period ?

a) 02 I

b)

0I

c) 0I

2d) zero

10. The nns value of the output voltage having peak

emf V0 of the half wave rectifier is :

a) 0V

2b)

0V

2

c) 0V d) V

0

11. The nns value of the output current (peak value I0)

for the full wave rectifier is :

a) 0I

2b)

0I

2

c) 0I

2d) I

0

12. In the above question what will be the nns value

when calculated over half time period ?

a) 0I

2b)

0I

2

c) I0

d) I0

13. The output current of a half wave rectifier is a

rectangular wave of peak value I0. What is the

rms value of the current ?

a) 0I

2b)

0I

2

c) 02 I d) I

0

14. The dimensional formula for the time rate of

change impedance is same as that of :

a) Inductance b) Conductance

c) Capacitance d) e.m.f.

15. The equation of an alternating current is

I 50 2 sin 400 t ampere then the frequency

and the root mean square of the current are

respectively :

a) 200 hertz, 50 ampere

b) 400 hertz, 50 2 ampere

c) 200 hertz, 50 2 ampere

d) 50 hertz, 200 ampere

16. A square wave current switching rapidly between

+0.5 ampere and –0.5 ampere is passed through

an A.C. ammeter. Then the reading shown by it,

is :


c) 0.5

ampere2

d) 0.5 2 ampere

17. An ideal choke takes a current of 10 ampere when

connected to an A.C. supply of 125 volt and 50

hertz. A pure resistor under the same conditions

takes a current of 12.5 ampere. If the two are

connected to an AC. supply of 100 2 volt and

40 hertz, then the current in a series combination

of the above resistor and inductor is :

a) 10 ampere b) 12.5 ampere

c) 20 ampere d) 25 ampere

18. A transformer steps down 200 volt to 20 volt to

operate a device with an impedance of 200 ohm.

Then the current drawn from the mains by the

primary of the transformer, is :



19. An inductive circuit contains a resistance of

10 ohm and an inductance of 2.0 henry. If an AC

voltage of 120 volt and frequency 60 Hz is applied

to this circuit, the current in the circuit would be

nearly :



20. A group of electric lamps having a total power

rating of 1000 watt is supplied by an A.C. voltage

E = 200 sin (310 t + 60°)

Then the r.m.s. value of the circuit current is :

a) 10 A b) 10 2 A

c) 20 A d) 20 2 A





21. A coil of resistance 300 ohm and self inductance

1.5 henry is connected to an A.C. source of

frequency 100

hertz. The phase difference

between voltage and current is :

a) 0° b) 30°

c) 45° d) 60°

22. The armature of a 10 polar dynamo rotates

making 600 r.p.m. What is the frequency of ac ?

a) 10 Hz b) 30 Hz

c) 50 Hz d) 60 Hz

23. A coil of 10 cm 10 cm having 50 turns is making

50 r.p.s. in a magnetic field of induction 2 tesla.

The peak value of the induced e.m.f. is

approximately :



24. A 50 hertz alternating current of peak value

2 ampere flows through the primary coil of a

transformer. If the mutual inductance between

the primary and the secondary be 0.5 henry then

the peak value of the induced voltage, is :



25. A dynamo dissipates 25 watt when it supplies a

current of 5 ampere through it. If the terminal

potential difference is 220 volt then the e.m.f.

produced in volts is :

a) 210 b) 215

c) 225 d) 230

26. Voltmeters V1 and V

2 are connected in series

across a dc power supply. The voltmeter V1 reads

80 V and has per volt resistance of 200 . If the

total resistance of V2 be 32 k, then what is the

line voltage ?

a) 120 V b) 160 V

c) 200 V d) 240 V

27. The reactance of a coil is 10 and its resistance

is also 10 . What is the peak current in the circuit

when applied emf is 220 V ?

a) 44 A b) 22 2 A

c) 22 A d) 22

A2

28. A pure resistance (R) capacitance (C) & inductance

(L) are connected in parallel to a 220 V & 50 Hz

power supply. The maximum current drawn from

the power supply is 10 A The current through

which of the following can be more than 10 A ?

a) R b) L and C

c) R and C d) none of the above

29. In the above question if the current through R is

6 A, through C is 15 A, then what is the current

through L ?

a) 7 A b) 8 A

c) 9 A d) 10 A

30. At what value of the electric field strength in

vacuum the volume energy density is same as

that of the magnetic field of induction B = 1.0 T?

a) 3 N/C b) 108 N/C

c) 3 108 N/C d) none of the above

31. An electric motor runs on a dc source of emf 200V

and draws a current of 10 A If the efficiency be

40%, then the resistance of armature is :

a) 4 b) 8

c) 12 d) 16

32. In a purely resistive A.C. circuit, the current :

a) lags behind the e.m.f. in phase

b) is in phase with the e.m.f.

c) leads the e.m.f. in phase

d) leads the e.m.f. in half the cycle and lags behind

it in the other half

33. In the following figure which voltmeter reads zero,

when is equal to the resonant frequency of the

RCL combination ?

a) V1

b) V2

c) V3

d) none of them

34. In the circuit shown below what is the value of I1

just after pressing the key K ?





a) 5

A7

b) 5

A11

c) 1 A d) none of the above

35. In Q-34, what is the value of current I1 long after

the pressing of key K ?

a) 5

A7

b) 5

A11


36. In Q-34 what is the value of I2 long after the

pressing of the key K ?

a) 5

A7

b) 5

A11


37. An inductor of 10 mH and a capacitor of 16 F

are connected in the circuit as shown in the figure.

The frequency of the power supply is equal to

the resonant frequency of the circuit. Which

ammeter will read zero ampere ?

a) A1

b) A2

c) A3

d) none

38. In the circuit shown below what is the reading of

the ammeter after closing the key ?

a) 1 A b) 2 A

c) 4

A3

d) 3

A4

39. A simple electric motor has an armature resistance

of 1 and runs from a dc power supply of 12 V.

When unloaded it draws a current of 2 A. When

certain load is connected, its speed becomes one

half of its unloaded speed. Then the current

drawn in ampere is :

a) 4 A b) 5 A

c) 6 A d) 7 A

40. What is the reading of the voltmeter V2 in the

circuit below, if the reading of V1 is 3 V ?

a) 2 V b) 3 V

c) 4 V d) 5 V

41. In the circuit shown here a 30 V d.c. source gives

a current 2.0 A, & a 30 V a.c. source of frequency

100 Hz gives a current 1.2 A. The inductive

reactance is :

a) 10 ohm b) 20 ohm

c) 5 34 ohm d) 40 ohm

42. A transformer is used to light up a 100 W, 110 V

lamp from a 220 V supply. If the supply current

is 0.5 A, the efficiency of the transformer is very

near to :

a) 30 % b) 45 %

c) 60 % d) 90 %

43. In the circuit given below the lamp L will suddenly

become bright, when the key K is :

a) first closed b) opened

c) opened or closed d) is closed for long time



DINESH [MHT - CET] PHYSICS


Answer Key

MH Text Book Based MCQ's

01. (a)

02. (d)

03. (d)

04. (a)

05. (a)

06. (c)

07. (c)

08. (c)

09. (d)

10. (b)

11. (b)

12. (c)

13. (c)

14. (a)

15. (d)

16. (c)

17. (a)

18. (c)

19. (a)

20. (b)

21. (a)

22. (b)

23. (c)

24. (b)

25. (c)

26. (b)

27. (c)

28. (d)

29. (d)

30. (b)

31. (b)

32. (c)

33. (c)

34. (d)

35. (c)

36. (a)

37. (d)

38. (b)

39. (a)

40. (c)

41. (c)

42. (d)

43. (c)

44. (a)

45. (c)

46. (a)

47. (b)

48. (b)

49. (c)

50. (d)

51. (d)

52. (b)

53. (a)

54. (b)

55. (c)

56. (d)

57. (c)

58. (a)

59. (d)

60. (d)

61. (d)

62. (d)

63. (b)

64. (c)

65. (c)

66. (c)

67. (c)

68. (a)

69. (c)

70. (c)

71. (b)

72. (d)

73. (c)

74. (b)

75. (c)

76. (c)

77. (d)

78. (c)

79. (d)

80. (c)

81. (b)

82. (b)

83. (d)

84. (b)

85. (a)

86. (d)

87. (a)

88. (b)

89. (a)

90. (b)

91. (c)

92. (b)

93. (c)

94. (a)

95. (d)

96. (c)

97. (b)

98. (d)

99. (a)

100. (c)

101. (c)

102. (d)

103. (a)

104. (c)

105. (b)

106. (c)

107. (c)

108. (b)

109. (c)

110. (d)

111. (c)

112. (d)

113. (c)

114. (b)

115. (b)

116. (c)

117. (a)

118. (d)

119. (b)

120. (c)

121. (a)

122. (c)

123. (b)

124. (c)

125. (d)

126. (d)

127. (c)

128. (c)

129. (c)

130. (d)

131. (a)

132. (d)

133. (d)

134. (c)

135. (c)

136. (a)

137. (c)

138. (d)

139. (b)

140. (b)

141. (c)

142. (a)

143. (d)

144. (c)

145. (a)

146. (c)

147. (c)

148. (a)

149. (d)

150. (b)

151. (a)

152. (a)

153. (d)

154. (d)

155. (a)

156. (c)

157. (d)

158. (c)

159. (a)

160. (b)

161. (d)

162. (c)

163. (a)

164. (b)

165. (c)

166. (a)

167. (a)

168. (d)

169. (a)

170. (c)

171. (a)

172. (c)

173. (d)

174. (a)

175. (d)

176. (d)

177. (a)

178. (c)

179. (d)

180. (b)

181. (b)

182. (c)

183. (c)

184. (d)

185. (b)

186. (b)

187. (d)

188. (b)

189. (a)

190. (b)

191. (b)

192. (d)

193. (d)

194. (b)

195. (b)

196. (a)

197. (d)

198. (b)

199. (c)

200. (d)

201. (c)

202. (d)

203. (a)

204. (d)

205. (c)

206. (a)

207. (c)

208. (d)

209. (a)

210. (c)

211. (b)

212. (b)

213. (c)

214. (c)

215. (a)

216. (d)

217. (d)

218. (a)

219. (b)

220. (c)

221. (b)

222. (c)

223. (c)

224. (b)

225. (b)

226. (c)

227. (a)

228. (a)

229. (d)

230. (a)

231. (a)

232. (a)

233. (c)

234. (c)

235. (b)

236. (c)

237. (a)

238. (a)

239. (b)

240. (c)

241. (a)

242. (a)

243. (d)

244. (c)

245. (c)

246. (c)

247. (d)

248. (a)

249. (c)

250. (b)

251. (b)

252. (c)

253. (a)

254. (c)

255. (d)

256. (c)

257. (d)

258. (d)

259. (d)

260. (a)



DINESH [MHT - CET] PHYSICS


Answer Key

REVISION QUESTIONS from Competitive Exams.

01. (a)

02. (a)

03. (a)

04. (c)

05. (a)

06. (b)

07. (b)

08. (a)

09. (c)

10. (b)

11. (c)

12. (c)

13. (a)

14. (a)

15. (a)

16. (d)

17. (d)

18. (c)

19. (a)

20. (b)

21. (b)

22. (c)

23. (c)

24. (d)

25. (b)

26. (c)

27. (c)

28. (c)

29. (a)

30. (a)

31. (a)

32. (b)

33. (c)

34. (b)

35. (d)

36. (a)

37. (c)

38. (b)

39. (d)

40. (c)

41. (d)

42. (c)

43. (c)

44. (c)

45. (c)

46. (c)

47. (b)

48. (d)

49. (a)

50. (c)

51. (a)

52. (c)

53. (d)

54. (a)

55. (a)

56. (c)

57. (b)

58. (d)

59. (a)

60. (c)

61. (a)

62. (c)

63. (b)

64. (a)

65. (a)

66. (d)

67. (c)

68. (a)

69. (c)

70. (a)

71. (c)

72. (a)

73. (d)

74. (a)

75. (b)

76. (c)

77. (a)

78. (a)

79. (a)

80. (b)

81. (b)

82. (b)

83. (a)

84. (c)

85. (a)

86. (a)

87. (d)

88. (c)

89. (b)

90. (b)

91. (b)

92. (c)

93. (b)

94. (a)

95. (b)

96. (b)

97. (d)

98. (c)

99. (d)

100. (b)

101. (b)

102. (c)

103. (d)

104. (a)

105. (a)

106. (b)

107. (b)

108. (a)

109. (b)

110. (c)

111. (b)

112. (a)

113. (d)

114. (a)

115. (b)

116. (c)

117. (c,d)

118. (d)

119. (d)

120. (b)

121. (c)

122. (c)

123. (c)

124. (d)

125. (b)

126. (b)

127. (c)

128. (d)

129. (a)

BRAIN TEASERS

01. (b)

02. (c)

03. (d)

04. (c)

05. (c)

06. (c)

07. (b)

08. (a)

09. (a)

10. (b)

11. (a)

12. (a)

13. (d)

14. (c)

15. (a)

16. (b)

17. (a)

18. (c)

19. (b)

20. (b)

21. (c)

22. (c)

23. (c)

24. (c)

25. (c)

26. (d)

27. (c)

28. (c)

29. (a)

30. (c)

31. (c)

32. (b)

33. (b)

34. (a)

35. (c)

36. (d)

37. (c)

38. (a)

39. (d)

40. (c)

41. (b)

42. (d)

43. (b)






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