PEMI – 1
S y l l a b u s :
Electromagnetic induction; Faraday’s law, induced emf and current; Lanz’s Law, Eddy currents. Self and mutual inductance. Alternating currents, peak and rms value of alternating current/voltage; reactance and impendence; LCR series circuit, resonance; Qualify factor, power in AC circuit, wattless current.
AC generator and transformer.
Einstein Classes ,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111

PEMI – 2
C O N C E P T S
C1 Magnetic Flux
Like electric flux, magnetic flux, 
B
, through a surface then B =
 d S is defined as 
B

S


B .
 d S . If

B

.
S and it represents total lines of induction crossing through a given surface S.

B is uniform
C2 Magnetic Induction and Faraday’s Laws
If the magnetic flux through a circuit or closed loop changes, an emf and a current are induced in the circuit.
This phenomenon is known as electromagnetic induction and the law which governs this phenomenon is known as Faraday’s Law. This law states that the magnitude of induced emf in a circuit is equal to the time rate of change of the magnetic flux. Mathematically, | e d 
|  . As dt
 

B

.
A  BA cos  . Hence if there is any change in magnetic field (B) or area (A) or orientation (  ) then there is induced emf. If some situation, more than one of these may contribute in induced emf, in this case magnitude of induced emf is written as
1.
| e |  d dt
( BA cos  )  ( A cos  ) dB dt
 ( B cos  ) dA dt
 BA sin  d  dt
This induced emf creates an induced current in the circuit whose magnitude is given as
I  net induced emf resistance of circuit

| e |
R
. Also the charge flown =
 
.
R
Practice Problems :
A magnet is moved with a high speed towards a coil at rest. Due to this, the induced emf, the induced current and the induced charge in the coil are E, I and Q respectively. If the speed of the magnet is doubled, the incorrect statement is
2.
(a) The induced current become 2I (b) The induced emf becomes 2E
(c) The induced charge remains same (d) The induced charge is 2Q
A thin circular ring of area A is held perpendicular to a uniform magnetic field of induction B.
A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is R. When the ring is suddenly squeezed to zero area, the charge flowing through the galvanometer is
(a) 2AB/R (b) AB/R (c)
AB
4 R
(d)
AB
3 R
[Answers : (1) d (2) b]
C3 Lenz’s Law
The direction of induced emf is governed by Lenz’s Law. This law states that an induced emf is always in the direction that opposes the change of magnetic flux that induced it. Incorporating this law into Faraday’s
Law, the induced emf is given by e   d  dt
. The negative sign indicates that the induced emf opposes the change of the flux.
Einstein Classes ,
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1.
PEMI – 3
Note the Lenz’s Law is based on conservation of energy principle.
Practice Problems :
In the figure the flux through the loop perpendicular to the plane of the coil and directed into the paper is varying according to the relation   = 6t 2 + 7t + 1 where  is in milliweber and t is in seconds.
2.
3.
Choose the correct statement :
(a)
(b)
(c)
At time t = 2s, the current flowing through R is 10mA from left to right
At time t = 2s, the current flowing through R is 10mA from right to left
The current through R is always increasing linearly
(d) both (a) and (c) are correct
A rectangular coil (having resistance per unit length 10/3  /m) of 100 turns and size 0.1 m × 0.05 m is placed perpendicular to a magnetic field of 0.1 T. If the field drops to 0.05 T in 0.05 s then
(a)
(b)
(c) the magnitude of average induced current is 4mA the total charge flown in the coil is 5µC the total charge flown in the coil isindependent of time during which the field will change
(d) both (a) and (c) are correct
A solenoid has 2000 turns wound over a length of 0.3 m. Its cross-sectional area is 1.2 × 10 –10 m 2 .
Around its central section a coil of 300 turns is wound. If an initial current of 2A flowing in the solenoid is reversed in 0.25 s, the emf induced in the coil will be
(a) 6.0 × 10 –4 V
[Answers : (1) d (2) c (3) d]
(b) 6.0 × 10 –2 V (c) 4.8 × 10 –4 V (d) 4.8 × 10 –2 V
C4 Motional Electromotive Force
1.
If a conductor with length L moves with speed v in a uniform magnetic field with magnitude B, and if the length and velocity are both perpendicular to the field, the induced emf is e = vBL. More general, when a conductor moves in a magnitude field

B , the induced emf in the direction is given by e  a b
 (
 v 

B ).
d
 l
Practice Problems :
An electric potential difference will be induced between the ends of the conductor shown in the diagram when it moves in the direction
Einstein Classes ,
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PEMI – 4
2.
(a) P (b) Q (c) L (d) M
A conducting square loop ABCD of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A magnetic induction B, constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere, then
(a)
(b)
(c)
The current induced in the loop is zero
There is no induced emf in the rod BC and AD
There is an induced emf BLv in each rod AB and CD
(d) All the above statements are correct
[Answers : (1) d (2) d]
C5A Self-Inductance and Inductors
Any circuit that carries a varying current will have an emf induced in it by the variation in its own magnetic field. Such an emf is called a self-induced emf. Self-induced emf’s can occur in any circuit, since there will always be some magnetic flux through the closed loop of a current-carrying circuit. But the effect is greatly enhanced if the circuit contains a coil with N turns of wire. As a result of the current i, there is an average magnetic flux 
B
, through each turn of the coil. Here we defined the self inductance L of the circuit as follows L 
N 
B
I
The SI unit of inductance is the henry (H).
C5B Selfinductance of the solenoid
The inductance per unit length near the middle of a long solenoid of cross-sectional area A and n turns per unit length is
L l
 µ
0 n
2
A
C5C Selfinduced emf
1.
2.
The self-induced emf, using Faraday’s law, is given by e   L dI dt
Practice Problems :
The current in a coil changes from 0 to 2A in 0.05 s. If the induced emf is 80 V, the self-inductance of the coil is
(a) 1 H (b) 0.5 H (c) 1.5 H (d) 2 H
A torodial solenoid with an air core has an average radius of 15 cm, area of cross-section 12 cm 2 and
1200 turns. Ignoring the field variation across the cross-section of the toroid, the self-inductance of the toroid is
Einstein Classes ,
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3.
PEMI – 5
(a) 4.6 mH (b) 6.9 mH (c) 2.3 mH (d) 9.2 mH
A coil is wound on a frame of rectangular cross-section. If all the linear dimensions of the frame are increased by a factor 2 and the number of turns per unit length of the coil remains the same, selfinductance of the coil increases by a factor of
(a) 4 (b) 8 (c) 12 (d) 16
[Answers : (1) d (2) c (3) b]
C6 Energy Stored in an Inductor
If an inductor L carries a current i. the inductor’s magnetic field stores an energy given by
U 
1
2
Li 2
C7 Energy Density of a Magnetic Field
If B is the magnitude of a magnetic field at any point (in an inductor or anywhere else), the density of stored
B
2 magnetic energy at that point is u 
B
2 µ
0
.
C8 Mutual Induction
When a changing current i
1
in one circuit causes a changing magnetic flux in a second circuit, an emf e induced in the second circuit; likewise, a changing current i
2 first circuit. This is called mutual induction.
in the second circuit induced an emf e
is
1
2
in the e
2
  M di
1 dt and e
1
  M di
2 dt
The constant M, called the mutual inductance, depends on the geometry of the two coils and on the material between them. If the circuits are coils of wire with N
1
and N
2
turns, respectively, the mutual inductance can be expressed in terms of the average flux 
B2
through each turn of coil 2 that is caused by the current i
1
in
: coil 1 or in terms of the average flux 
B1
through each turn of coil 1 that is caused by the current i
2
in coil 2
M 
N
2

B 2 i
1

N
1

B 1 i
2
The SI unit of mutual inductance is the henry, abbreviated H. Equivalent units are
1 H = 1 Wb/A = 1V.s/A = 1  .s.
Mutual inductance of two solenoids one surrounding the other is given by µ
0 n p n s
A l where n p
and n s
are number of terms per unit length for primary and secondary coils and A is the cross-sectional area of primary coil and l is the length of the primary coil.
C9 LC Circuit
An L-C circuit, which contains inductance L and capacitance C, undergoes electrical oscillations with angular frequency  :
 
1
LC
Such a circuit is analogous to a mechanical harmonic oscillator, with inductance L analogous to mass m, the reciprocal of capacitance 1/C to force constant k, charge q to displacement x, and current i to velocity v.
Einstein Classes ,
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New Delhi – 110 018, Ph. : 9312629035, 8527112111

1.
2.
PEMI – 6
Practice Problems :
A capacitor of capacitance 1 µ F is charged upto 10V and then connected across an ideal inductor of
10 mH. Choose the correct statement :
(a) The angular frequency of LC oscillation is 10 4 rad/s
(b)
(c)
At any moment total energy is 50µJ
The current in the circuit changes with time sinusoidally
(d)
(d)
All are correct
A capacitor of 1 µ F initially charged to 10 V is connected across an ideal inductor of 0.1 mH. The maximum current in the circuit is
(b) 1 A (c) 1.5 A (d) 2 A (a)
(b)
0.5 A
[Answers : (1) d (2) b)
C10 Back EMF in D.C. Motor : A motor is the reverse of generator – it converts electrical energy into mechanical energy. When currents is passed through a coil placed in a magnetic field, it rotates. As the coil rotates, the magnetic flux linked with changes, giving rise to an induced emf. This emf opposes the applied emf (  ) and is, therefore, called back emf (e). If R is the resistance of the coil, the current through it is given by I 
  e
.
R
1.
Practice Problems :
In a dc motor, if E is the applied emf and e is the back emf, then the efficiency is
(a)
E  e
E
[Answers : (1) b]
(b) e
E
(c)
 E 

 E e 


2
(d)


 e
E

2


C11 Eddy Currents
When a metallic body is moved in a magnetic field in such a way that the flux through it changes or is placed in a changing magnetic field, induced currents circulate throughout the volume of the body. These are called eddy currents.
C12 Alternating Current
An alternator or ac source produces an emf that varies sinusoidally with time.
Production of A.C.
Production of A.C. is based on Faraday’s law of electromagnetic induction. Suppose a coil of N turns, and area A is rotated in a uniform magnetic field B with angular velocity  . As the coil rotates, the flux through it changes and therefore an emf is induced in it, given by  = 
0
sin  t where 
0
= NBA  .
A sinusoidal voltage or current can be represented by a phasor, a vector that rotates counterclockwise with constant angular velocity  equal to the angular frequency of the sinusoidal quantity. Its projection on the horizontal axis at any instant represent the instantaneous value of the quantity.
C13 Average and root mean square value of a.c.
For a sinusoidal current the average and rms (root-mean-square) currents are related to the current amplitude I
0
by
I av

2
I
0

 0 .
637 I
0
,
I rms

I
0
2
.
In the same way, the rms value of the snusoidal voltage is related to the voltage amplitude V
0
by
V rms

V
0
2
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PEMI – 7
The voltage v in an ac circuit is represented by v = v
0 sin  t and current in a.c. circuit is represented by i = i
0 sin(  t +  ) where  is the phase angle between the current and voltage.
C14 A.C. Circuit
Pure resistive a.c. circuit
The voltage across a resistor R is in phase with the current, and the voltage and current amplitude are related by V
R
= IR
Pure inductive circuit
The voltage across an inductor L leads the current by 90 0 , the voltage and current amplitude are related by
V
L
= IX
L
, where X
L
=  L is the inductive reactance of the inductor.
Pure capacitive circuit
The voltage across a capacitor C lags the current by 90 0 ; the voltage and current amplitudes are related by where X
C
= 1/  C is the capacitive reactance of the capacitor.
LCR series circuit
V
C
= IX
C
,
In an ac circuit the voltage and current amplitudes are related by
V = IZ, where Z is the impedance of the circuit. In an L-C-R series circuit,
1.
2.
3.
Z  R
2
 ( X
L
 X
C
)
2
 R
2
 (  L  ( 1 /  C )]
2 , and the phase angle  of the voltage relative to the current is tan  
 L  1 /  C
R
Practice Problems :
A 40  electric heater is connected to 200 V, 50 Hz main supply. The peak value of the electric current flowing in the circuit is approximately
(a) 2.5 A (b) 5.0 A (c) 7 A (d) 10 A
(c)
An alternating voltage V = 200  2 sin 100 t, where V in volt and t seconds, is connected to a series combination of 1 µF capacitor and 10 k  resistor through an ac ammeter. The reading of the ammeter will be
(a)  2 mA (b) 10  2 mA (c) 2 mA (d) 20 mA
(b)
Choose the correct statement :
(a)
(b)
(c) the current leads the voltage in phase if an ac source is connected across a capacitor the current lags behind the voltage in phase if an ac source is connected across an inductor the current and voltage are in same phase if an ac source is connected across a resistor.
(d)
(d) all are correct
[Answers : (1) c (2) b (3) d]
C15 Power in A.C. circuit
The average power input P av
to an ac circuit is
P av

1
2
VI cos   V rms
I rms cos 
Einstein Classes ,
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New Delhi – 110 018, Ph. : 9312629035, 8527112111

1.
2.
3.
4.
PEMI – 8 where  is the phase angle of voltage with respect to current. The quantity cos  is called the power factor.
Practice Problems :
If a current I = I
0
sin (  t –  /2) flows in a circuit across which an alternating potential E = E has been applied, then the power consumed in the circuit depends on
0
sin  t
(a) E
0
(b) I
0
(c) both (d) none
In circuit 1, an alternating current of 2 A flows for 10 minutes. In another similar circuit 2, a direct current of 2 A flows for the same time. If the heat produced in circuit 1 is X then the heat produced in circuit 2 is
(a) 0.5 X (b) 1.5 X (c) X (d) 2X
A sinusodal alternating current flows through a resistor R. If the peak current is I p
, then the power dissipated is
(a) I p
2 R (b)
1
2
I
2 p
R
(c)
4

I
2 p
R
(d)
1

I
2 p
R
The impendence of a circuit consists of 3  resistance and 4  reactance. The power factor of the circuit is
(a) 0.4
(b) 0.6
(c) 0.8
(d) 1.0
[Answers : (1) d (2) c (3) b (4) b]
C16 Resonance in LCR Circuit
In an L-C-R series circuit the current becomes maximum (for a given voltage amplitude) and the impedance becomes minimum at an angular frequency 
0
= 1/(LC) 1/2 called the resonance angular frequency. This phenomenon is called resonance. At resonance the voltage and current are in phase, and the impedance Z is equal to the resistance R.
Practice Problems :
1.
In an LCR series circuit, the capacitance is changed from C to 4C. For the same resonant frequency, the inductance should be changed from L to
(a) 2L (b) L/2 (c) L/4 (d) 4L
[Answers : (1) c]
C17 Quality Factor
The Quality factor of an LCR series circuit is defined as Q 

0
L
where 
0
is the resonance angular
R frequency. It is an indicator of the sharpness of the current peak – higher the value of Q, sharper is the peak.
C18 Transformer
A transformer converts a low aleternating voltage to a high voltage and vice-versa. It is based on the principle of mutual induction. It consists of two coils wound on a soft iron core. The primary coil is connected to an a.c. source.The secondary coil is connected to the load which may be a resistor or any other electrical device.
If the primary resistance is zero, then E p
is equal to the applied voltage. Further, if there is no flux leakage, i.e., the same flux is linked with each turn of both the primary and secondary coils, then it can be shown that
E s
E p

N s
N p
.
If N s
> N p
, then E s
> E p
and the transformer is called a step-up transformer .
If N s
< N p
, then E s
< E p
and the transformer is called a step-down transformer .
For an ideal transformer, Input power = Output power  E p
I p
= E s
I s

I p
I s

E s
E p

N
N p s
.
Einstein Classes ,
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New Delhi – 110 018, Ph. : 9312629035, 8527112111

1.
2.
3.
4.
1.
2.
PEMI – 9
In actual transformers, there is some power loss. The main sources of power loss are :
I 2 R loss due to Joule heat in copper windings.
Heating produced due to Eddy currents in the iron core. This is reduced by using laminated core.
Hysteresis loss due to repeated magnetisation of the iron core.
Loss due to flux leakage.
When all the losses are minimized, the efficiency of the transformer becomes very high (90-99%).
Practice Problems :
In a step-down tranformer the input voltage is 22 kV and the output voltage is 550 V. The ratio of the number of turns in the secondary to that in the primary is
(a) 1 : 20 (b) 20 : 1 (c) 1 : 40 (d) 40 : 1
In a noiseless transformer an alternating current of 2 A 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) 0.08 A (b) 0.4 A (c) 5 A (d) 10 A
[Answers : (1) c (2) d]
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New Delhi – 110 018, Ph. : 9312629035, 8527112111

1.
2.
Choose the correct statement from the following :
(a) Electric field is produced by time-varying magnetic flux
(b)
(c)
Faraday’s law of electromagnetic induction is related to the law of conservation of energy
The direction of induced emf during electromanetic induction is given by
Lenz’s law which is consequence of conservation of energy
All are correct (d)
A circular coil (constant radius) of total length L having number of turns N is rotated about the diameter in a uniform magnetic field B with an angular velocity  . Initially the magnetic field is perpendicular to the plane of the coil. The maximum value of the emf induced in it is
(a)
BL
2

2  N
(b)
NBL
2

2 
3.
4.
(c)
BL
2

4  N
(d)
NBL
2

4 
A copper ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet is ‘a’ and acceleration due to gravity is g, then the relation between a and g is
(a)
(b) a = g at all time first a > g and then a < g
(c)
(d)
Consider the following two statement.
Statement 1 : Two identical coaxial circular loops carry a current i each circulating in the same direction. If the loops approach each other the current in each decreases.
Statement 2 : This is the consequence of Lenz’s law.
(a) a < g at all time can’t be decided
(b) both statements are correct and statement 1 is correct explanation for statement 2 both statements are correct and statement 1 is not correct explanation for statement 2
(c)
(d) only statement 1 is correct only statement 2 is correct
5.
PEMI – 10
Consider the following two statement.
Statement 1 :Two circular coils P and Q are arranged coaxially as shown. The sign convention adopted is that the currents are taken as positive when they flow in the direction of the arrows as shown in figure. If P carries a steady positive current and Q is moved towards P, a negative current is induced in Q.
6.
7.
8.
Statement 2 : If both the coils carry positive currents, the coils repeal each other.
(a) both statements are correct and statement 1 is correct explanation for statement 2
(b) both statements are correct and statement 1 is not correct explanation for statement 2
(c)
(d) only statement 1 is correct only statement 2 is correct
An ideal transformer steps down 220 V to 22 V in order to operate a device with an impendance of
220  . The current in the primary is
(a)
(c)
0.01 A
0.5 A
(b)
(d)
0.1 A
1.0 A
The same alternating voltage is applied in two circuits. The first circuit contains only inductance and the other contains only capacitance. If the frequency of the source is changed in both, the current
(a) changes in the first circuit linearly and hyperbolically in the other circuit
(b)
(c)
(d) changes lienarly in both circuit changes hyperbolically in both circuit changes in the first circuit hyperbolically and linearly in the other circuit
The time constant of an inductance coil is
2.0 × 10 –3 s. When a 90  resistance is joined in series, the time constant becomes 0.5 × 10 –3 s.
The inductance and resistance of the coil are
(a)
(c)
120 mH; 60  (b)
60 mH; 30  (d)
90 mH; 45
30 mH; 15


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9.
A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction

B . At the position MNQ the speed of the ring is V, and the potential difference developed across the ring is
(a)
(b)
(c)
(d)
PEMI – 11 zero
BV  R 2 /2 and M is at a higher potential
 RBV and Q is at a higher potential
2R BV and Q is at a higher potential.
1.
2.
A copper disc of radius R is rotated about its centre with n revolutions per second in a uniform magnetic field B with its plane. Choose the correct statement :
(a)
(b)
(c) If the field is perpendicular to the disc then the induced emf between the centre and the edge of the disc is  BnR 2 both (a) and (c) are correct (d)
A rectangular loop of sides 8 cm and 2 cm is lying in a uniform magnetic field of magnitude 0.5 T with its plane normal to the field. The field is now gradually reduced at the rate of 0.02 T/s. If the resistance of the loop is 1.6  , then the power dissipated by the loop as heat is
(a)
(c)
If the field is in the plane of the disc then the induced emf between the centre and the edge of the disc is zero
If the field is in the plane of the disc then the induced emf between the centre and the edge of the disc is non-zero
6.4 × 10 –10 W
6.4 × 10 –5 W
(b)
(d)
3.2 × 10 –10 W
3.2 × 10 –5 W
3.
4.
5.
A tranformer is used to light a 140 W, 24 V bulb from a 240 V A.C. mains. The current in the main cable is 0.7 A. The efficiency of the transformer is
(a) 63.8% (b) 83.3%
(c) 16.7% (d) 36.2%
The number of turns of primary and secondary coils of a transformer are 5 and 10 respectively and the mutual inductance of the transformes is 25 H.
If the number of turns in the primary and secondary are made 10 and 5 respectively, then the mutual inductance of the transformer will be
(a)
(c)
6.25 H
25 H
(b)
(d)
12.5 H
50 H
In an LCR circuit, choose the correct statement
(a) current and voltage are always in phase if  
1
LC
(b) current lags behind the voltage if
(c)
(d)
  1 / LC current leads the voltage if
  1 / LC
All are correct
1.
2.
3.
4.
5.
ANSWERS (
c a d c c
6.
7.
8.
9.
) c d a d
ANSWERS (
)
1.
2.
3.
4.
5.
a c b a d
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1.
2.
3.
4.
5.
6.
The inductance between A and D is
(a)
(c)
3.66 H
0.66 H
(b)
(d)
9 H
1 H
A conducting square loop of side L and resistance
R moves in its place with a uniform velocity v perpendicular to one of its sides. A magnetic induction B constant in time and space, pointing perpendicular and into at the loop exists everywhere with half the loop outside the field, as shown in figure. The induced e.m.f. is
7.
8.
PEMI – 12
The core of any transformed is laminated so as to
(a)
(b) make it robust and strong increase the secondary voltage
(a)
(b)
(c)
(c) reduce the energy loss due to eddy currents make it light weight (d)
Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon the materials of the wires of the coils the currents in the two coils
(d) the rates at which currents are changing in the two coils relative position and orientation of the two coils
(a) zero (b) RvB
(c) vBL/R (d) vBL
The power factor of an A.C. circuit having resistance (R) and inductance (L) connected in series and an angular velocity  is
(a)
(c)
R/  L
 L/R
(b)
(d)
R/(R 2 +  2 L 2 ) ½
R/(R 2 –  2 L 2 ) ½
In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current in primary is 4 A, then that in the secondary is
(a)
(c)
4 A
6 A
(b)
(d)
2 A
10 A
When the current from +2A to –2A in 0.05 second, an e.m.f. of 8 V is induced in a coil. The coefficient of self-induction of the coil is
(a)
(c)
0.8 H
0.2 H
(b)
(d)
0.1 H
0.4 H
In an oscillating LC circuit the maximum charge on the capacitor is Q. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is
(a)
Q
2
(b) Q
9.
Alternating current can not be measured by D.C.
ammeter because
(a)
(b)
(c)
A.C. cannot pass through D.C. ammeter
A.C. changes direction average value of current for complete cycle is zero
(d) D.C. ammeter will get damaged
[2004]
10.
In a LCR series a.c. circuit, the voltage across each of the components L, C and R is 50 V. The voltage across the LC combination will be
(a)
(c)
50 V
100 V
(b)
(d)
50  2 V
0 V (zero)
[2004]
11.
A coil having n tunes and resistance R  is connected with a galvanometer of resistance 4R  .
This combination is moved in time t seconds from a magnetic field W
1
weber to W
2
weber. The induced current in the circuit is
(a)

W
2
 W
5 Rnt
1
(b)
(c)
 n ( W
2

5 Rt
W
1
)
–
( W
2

Rnt
W
1
)
(d) – n ( W
2

Rt
W
1
)
[2004]
12.
In a uniform magnetic field of induction B a wire in the form of a semicircle of radius r rotates about the diameter of the circle with angular frequency
 . The axis of rotation is perpendicular to the field.
If the total resistance of the circuit is R the mean power generated per period of rotation is
(c)
Q
2
(d)
Q
3
Einstein Classes ,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111

PEMI – 13
(a)
B  r
2

2 R
(b)
( B  r
2
 )
2
8 R
( B  r  )
2
( B  r 
2
)
2
(c) (d)
2 R 8 R
[2004]
13.
In a LCR circuit capacitance is changed from C to
2C. For the resonant frequency to remain unchanged, the inductance should be changed from
L to
(a)
(c)
4 L
L/2
(b)
(d)
2 L
L/4
[2004]
14.
A metal conductor of length 1 m rotates vertically about one of its end at angular velocity 5 radians per second. If the horizontal component of earth’s magnetic field is 0.2 × 10 –4 T, then the e.m.f.
developed between the two ends of the conductor is
(a)
(c)
5 µV
5 mV
(b)
(d)
50 µV
50 mV
[2004]
15.
A coil of inductance 300 mH and resistance 2  is connected to a source of voltage 2 V. The current reaches half of its steady state value in
(a) 0.15 s (b) 0.3 s
(c) 0.05 s (d) 0.1 s
[2005]
16.
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)
(c)
1 µF
4 µF
(b)
(d)
2 µF
8 µF
[2005]
17.
A circuit has a resistace of 12 ohm and an impendence of 15 ohm. The power factor of the circuit will be
(a)
(c)
1.25
0.8
(b)
(d)
0.125
0.4
[2005]
18.
The phase difference between the alternating current 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
[2005]
19.
One conducting U tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed V, then the emf induced in the circuit in terms of B, l and V where l is the width of each tube, will be
(a)
(c) zero
B l V
(b)
(d)
2 B l V
–B l V
[2005]
20.
An inductor (L = 100 mH), a ressitor (R = 100  ) and a battery (E = 100 V) are initially connected in series as shown in figure. After a long time the battery is disconnected after short circuiting the points A and B. The current in the circuit 1 ms after the short circuit is
(a)
(c)
0.1 A
1/e A
(b)
(d)
1 A e A
21.
In a series resonant LCR circuit, the voltage across
R is 100 volts and R = 1 k  with C = 2 µF. The resonant frequency  is 200 rad/s. At resonance the voltage across L, is
(a) 250 V (b) 4 × 10 –3 V
(c) 2.5 × 10 –2 V (d) 40 V
22.
In an AC generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency  in a magnetic field B. The maximum value of emf generated in the coil is
(a)
(c)
NABR
NABR 
(b)
(d)
NAB
NAB

23.
The flux linked with a coil at any instant ‘t’ is given by  = 10t 2 – 50t + 250
The induced emf at t = 3s is
(a)
(c)
10 V
–190 V
(b)
(d)
190 V
–10 V
Einstein Classes ,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111

24.
An ideal coil of 10 H is connected in series with a resistance of 5  and a battery of 5V. 2 second after the connection is made, the current flowing in ampere in the circuit is
(a)
(c)
(1 – e –1 )
(1 – e)
(b)
(d) e e –1
1.
8.
15.
d
22.
b d a
2.
9.
16.
23.
a d d c
3.
10.
17.
24.
c a b d
4.
11.
18.
25.
d b b b
PEMI – 14
25.
In a ac circuit, the voltage applied is E = E
0
sin  t.
The resulting current in the circuit is I = I
0 sin



 t 

2



. The power consumption in the circuit is given by
(a) P  2 E
0
I
0
(b) P = zero
(c) P 
E
0
I
0
2
(d) P 
E
0
I
0
2
5.
12.
19.
b b b
6.
13.
20.
a c c
7.
14.
21.
c b a
1.
Consider the following two statement.
Statement 1 : A current-carrying wire is placed below a coil in its plane, with current flowing as shown.
2.
If the current increases then there is an induced current in the clockwise direction in the loop.
Statement 2 : This is the consequence of Lenz’s law.
(a)
(b)
(c) both statements are correct and statement 1 is correct explanation for statement 2 both statements are correct and statement 1 is not correct explanation for statement 2 only statement 1 is correct
(d) only statement 2 is correct
A circular coil is placed in a region having magnetic field B perpendicular to the plane of the coil. An emf will not be induced in the coil if the
(a)
(b)
(c) magnetic field is increased with time magnetic field is switched off coil is rotated about any diameter
3.
4.
5.
(d) coil is rotated about an axis perpendicular to the plane of the coil and passing through its centre
The time taken by the current to rise to half of its maximum value in a d.c. circuit containing inductance (L) and resistance (R) is
(a)
L
R ln 2 (b)
L
R
(c)
L
2
R
(d)
L
2
R ln2
Which of the following quantity do not have the dimension [M 0 L 0 T], symbols have their usual meaning ?
(a)
L
R
(b) RC
(c) LC (d)
L
CR
2
A low-loss transformer has 230 V applied to the primary and gives 4.6 V in the secondary. The secondary is connected to a load which draws
5 amperes of current. The current (in amperes) in the primary is
(a) 0.1
(b) 1.0
(c) 10 (d) 250
Einstein Classes ,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111

6.
7.
8.
9.
In general in an ac circuit
(a)
(b) the average value of current for complete cycle is zero the average value of the current is 2/  times of the peak value
(c) the rms current is 1/  2 times of peak current all the above statements are correct (d)
A jet plane having a wing span of 25 m is travelling horizontally towards the east with a speed of
1800 km/h. If the earth’s magnetic field at the location is 5 × 10 –4 T and the angle of dip is 30 0 , then the potential difference between the ends of the wing is
(a)
(c)
3.1 V
6.2 V
(b)
(d)
0.31 V
0.62 V
A player with 3 metre long iron rod runs towards east with a speed of 30 km/hr. Horizontal component of earth’s magnetic field is
4 × 10 –5 Wb/m 2 . If he runs with the rod in horizontal and vertical positions, then the potential difference induced between the two ends of the rod in the two cases will be
(a) zero in vertical position, 1 × 10 –3 V in horizontal position
(b) 1 × 10 –3 V in vertical position, zero in horizontal position
(c)
(d) zero in both positions
1 × 10 –3 V in both positions
A square metal loop of side 10 cm and resistance
1 ohm is moved with a constant velocity partly inside a uniform magnetic field of 2 Wb/m 2 , directed into the paper, as shown in the figure. The loop is connected to a network of five resistors each of value
3  . If a steady current of 1 mA flows in the loop, then the speed of the loop is
PEMI – 15
10.
In the given circuit R is a resistor, L is an inductor and B
1 off
and B
2
are two bulbs. If the switch S is turned
(a)
(b)
(c)
(d) both B
1
and B
2
die out promptly both B
1
and B
2
die out with some delay
B
1
dies out promptly but B
2
with some delay
B
2
dies out promptly but B
1
with some delay
(a)
(c)
0.5 cm/s
2 cm/s
(b)
(d)
1 cm/s
4 cm/s
3.
4.
5.
1.
2.
a d a a d
6.
7.
8.
9.
10.
b c c d a
A NS W ER S
Einstein Classes ,
Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road
New Delhi – 110 018, Ph. : 9312629035, 8527112111