Electromagnetic Induction and Alternating Currents Notes and MCQs

Notes 23 Pages

Joint Entrance Examination (Main)

Physics

Contributed by

Gulzar Dubey

174
SUMMERY
1. Net flux through the surface 
B dA
 



= BA cos
= angle between area vector
A

& magnetic field
B

• if = 0 then max = BA
• if = 90 then  = 0
2. Unit of magnatic flux is weber (wb) in SI unit and maxwell or Gauss x cm
2
in CGS unit where 1wb = 10
8
maxwell
• other units = tesla  m
2
=
Nm
A
=
Joule
A
=
Volt Coulomb
A

= Volt x sec = ohm x coulomb = henery x AA
• Its dimensional formula = M
1
L
2
T
–2
A
–1
3. Faraday’s Law
• The induced emf  = – N
d
dt

= – N
d
dt
(AB cos t)
• If A alone is changing  = – NB cos t
dA
dt
• If B alone is changing  = – NA cos t
dB
dt
• If  alone is changing  = + NABsin t
4. Motional emf  = – Bvl sin where,  = angle between

v


B
5. If conducting rod moves on two parallel conducting rails placed in magnetic field perpendicular to plane
of close loop.
• induced emf  = – Bvl
• induced current I =  =
B
R

vl
• magnetic force F = IlB =
2 2
B
R

vl
• power dessipated P =
2 2
B
R
2
v l
= F
m
• v
wherel = distance between two rails
R = Resistance of the loop
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175
6. Self induction
• self inductance L =
N

• induced emf  = – L
dI
dt
• unit of L is
wb
A
= ohm x sec = Henery
• dimensional formula of L is M
1
L
2
T
-2
A
-2
• magnetic potential energy of inductor U =
1
2
LI
2
• magnetic energy density S
m
=
U
Al
=
2
0
B
2

7. Mutual Induction
• Mutual inductance M =
1 1
2
N
I

=
2 2
1
N
I

• induced emf = 
2
= – M
1
dI
dt
OR 1 = – M
2
dI
dt
8. Relation between M, L, & L
2
For two magnetically coupled coils M = k
1 2
L L
where k = coefficient of coupling or coupling factor
(0 k 1)
k =
magnetic flux linked in sec ondary
magnetic flux linked in primary

9. Combination of inductances
• series L
s
= L
1
+ L
2
if they are situated close to each other then L
s
= L
1
+

L
2
+ 2M
• Parellel L
p
=
1 2
1 2
L L
L L
OR
p
1
L
=
1
1
L
+
2
1
L
if they are situated close to each other then
L
p
=
2
1 2
1 2
L L M
L L 2M

 
10. Growth & decay of current in LR circuit
• The value of current at time t after closing the circuit I =
Rt
L
0
I [1 e ]


Page 2
176
where I
0
= I
max
=
R

• The value of current at time t after opening from the steady state condition I =
Rt
L
0
I e


• Time constant  =
L
R
11. A.C. generator
• emf V = NAB sin t = V
m
sin t
• current I =
m
V
R
sin t = I
m
sin t
• A.C. current & voltage are positive for half the cycle & negative for the rest half. So aweerage
value of ac quantity is zero over a complete cycle.
• at t =
T
4
from the begining I or V reach their maximum value.
12. Series LCR circuit
• current I = I
m
cos (t – )
where I
m
=
m
V
z
 = phase difference between V & I
• Voltage V =
2
2
R L C
V (V V ) 
• Impedence
2 2 2 2
L C
1
z R (X X ) R ( L )
c
      

• Phase difference tan  =
L C L C
R
X X V V
R V
 

13. At resonance
• X
L
= X
C
then
z
= R then 
0
=
1
LC
then f
0
=
1
2 LC
• Half power band width  =
R
L
• Q-factor Q =
0


=
1 L
R C
Page 3
177
14. Power
• P = V
rms
I
rms
cos 
where cos  = power factor
15. Parellel LC circuit in series with R
•
z
=
2
2
1
R
1
( c )
L

 

• tan  =
1
1
R( c )
L
 

16. Transformer
•
p
s s
p s p
I
N
I N

 

= r = transformation ratio
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178
MCQ
For the answer of the following questions choose the correct alternative from among
the given ones.
1. A coil having area 2m
2
is placed in a magnetic field which changes from 1 wb /m
2
to 4 wb/m
2
in an
interval of 2 second. The emf induced in the coil of single turn is....
(a) 4 v (b) 3 v (c) 1.5 v (d) 2 v
2. Two different loops are concentric & lie in the same plane. The current in outer loop is clockwise &
increasing with time. The induced current in the inner loop then, is..........
(a) clockwise (b) zero
(c) counter clockwise (d) direction depends on the ratio of loop radii
3. A ring of radius r is rotating about its diameter with angular velocity  in a perpendicular magnetic
field
B
It has 20turns.The emf induced is
(a)
wtSinrB20
2

(b)
wtcosrB20
2

(c)
2
rB210 
(d)
wtsinwrB20
2

4. A magnetic field
T102
2

acts at right angles to a coil of area 200 cm
2
with 25 turns. The average
emf induced in the coil is 0.1 v when it removes from the field in time t. The value of t is
(a) 0.1 sec (b) 1 sec (c) 0.01 sec (d) 20 sec
5. The magnetic flux linked with a coil, in webers, is given by the equation
7t3t4
2

. Then the
magnitude of induced emf at 2 sec will be ...
(a) 15 v (b) 19 v (c) 17 v (d) 21 v
6. A solenoid of 1.5 m long with inner diamter of 4 cm has three layers of windings of 1000 turns each
& carries a current of 2 A. The magnetic flux through a cross section of the solenoid is nearly.....
(a)
wb105.2
7

(b)
wb1031.6
6

(c)
wb101.2
6

(d)
wb101.4
5

7. A coil has an area of 0.05 m
2
& it has 800 turns. It is placed perpendicularly in a magnetic field of
strength , 4x10
–5
Wb/m
-2
. It is rotated through 90
o
in 0.1 sec. The average emf induced in the coil
is...
(a) 0.056 v (b) 0.046 v (c) 0.026 v (d) 0.016 v
Page 5
179
8. A bar magnet is moving along the common axis of two coils A &B towards A. current is induced in
(a) Only A (b) Only B
(c) both A& B in same direction (d) both A & B in opposite direction
9. A coil having n turns & resistance
R
is connected with a galvanometer of resistance 4R. This
combination is moved from a magnetic field W
1
Wb to W
2
Wb in t second. The induced current in
the circut is....
(a)


Rnt5
WW
12


(b)


Rt5
WW
n
12


(c)


Rnt
WW
12


(d)


Rt
WW
n
12


10.
When a train travels with a speed 360 km h
-1
along the track separated by 1 meter. The vertical
component of earth's magnetic field is
T101.0
4

.What is the value of induced emf between the
rails ?
(a)
V10
2
(b)
V10
4
(c)
V10
3
(d)
V1
11. An electron moves along the line AB,which lies in the same plane as a circular loop of conducting
wires as shown in figure. What will be the direction of current induced if any, in the loop ?
(a) No current will be induced
(b) The current will be clockwise
(c) The current will be anticlockwise
(d) The current will change direction as the electron passes by
12. A circular loop of radius R carrying current I lies in X-Y plane with its centre at origin. The total
magnetic flux through x-y plane is.....
(a) Directly proportional to I (b) Directly proportional to R
(c) Directly proportional to R
2
(d) zero
Page 6
180
13. Consider the situation shown in the figure. The wireAB is sliding on the fixed rails with a constant
velocity

. If the wire AB replaced by semi circular wire the magnitude of the induced current will.
(a) Increases (b) decreased
(c) Remain same (d) depending on whether the semicircle
bulge is towards the resistance or
away from it.
14. Two similar circular loops carry equal currents in the same direction.On moving the coils further
apart, the electric current will
(a) Remain unchanged (b) Increasing in both
(c) Increasing in one decreasing in other (d) Decreasing in both
15. When the number of turns in a coil is make four time without any change in length of the coil, its self
inductance becomes......
(a) unchanged (b) two times
(c) four times (d) sixteen times
16. A metal road moves at a constant velocity in a direction perpendicular to its length & a constant
uniform magnetic field too. Select the correct statement (s) from the following.
(a) The entire rod is at the same electrical potential
(b) There is an electric field in the rod
(c) The electric polential is highest at the centre of the rod.
(d) The electric polential is lowest at the centre of the rod.
17. Two co-axial solenoids are made by a pipe of cross sectional area 10 cm
2
and length 20 cm If one
of the solenoid has 300 turns and the other 400 turns, their mutual inductance is........
(a)
H108.4
4

(b)
H108.4
5

(c)
H104.2
4

(d)
H108.4
4

18. The self inductance of a straight conductor is...
(a) zero (b) very large (c) very small (d)

19. Two coils of self inductances 2 mH & 8 mH are placed so close togather that the effective flux in one
coil is completely half with the other.The mutual inductance between these coils is.......
(a) 4 mH (b) 6 mH (c) 2 mH (d) 16 mH
20. In circular coil. when no. of turns is doubled & resistance becomes half of the initial then inductance
becomes....
(a) 4 times (b) 2 times (c) 8 times (d) No change
Page 7
181
21. In the figure the magnetic energy stored in the coil is
(a) zero (b) infinite (c) 25 J (d) 16 J
22. When the switch S turned off.
(a) Both B
1
and B
2
die out promptly
(b) Both B
1
and B
2
die out with some delay
(c) B
1
dies out promptly but B
2
with some delay
(d) B
2
dies out promptly but B
1
with some delay
23. A transformer of efficiency 90% draws an input power of 4 kW. An electrical applience connected
across the secondary draws a current of 6 A.The impedence of device is.........
(a)
60
(b)
50
(c)
80
(d)
100
24. The armature of dc motor has 20

resistance. It draws current of 1.5 A when run by 220 V dc
suppy. The value of back induced in it will be
(a) 150 V (b) 190 V (c) 170 V (d) 180 V
25. A thin semicircular conducting ring of radius R is falling in a magnetic field B. Which is in limited area
as shown in figure. At the position MNQ,the speed of ring is  and the potential difference developed
across the ring is
(a) zero (b)
2
R
B
2

and M is at higher potential
(c)
RB
and Q is at higher potential (d)
RB2
and Q is at higher potential
26. Two identical circular loops of metal wire are lying on a table near to each other without touching.Loop
A carries a current which increasing with time.In response the loop B.......
(a) Is repelled by loop A (b) Is attracted by loop A
(c) rotates about its centre of mass (d) remains stationary
Page 8
182
27. A wire of length 2m is moving at a speed 2ms
-1
keep its length perpendicular to uniform magnetic
field of 0.5 T. The resistance of circuit joined with this wire is
6
. The rate at which wolrk is being
done to keep the wire moving at constant speed is ..........
(a)
1
ω
3
(b)
2
ω
3
(c)
1
ω
6
(d) 2
28. Two identical magnets moving towards a coil, connecting a condenser at rear side shown in fig., with
equal speed from opposite sides Then
(a) Both plate will be positive
(b) There is no charging of condenser
(c) Plate 1 will be positive and 2 negative
(d) Plate 2 will be positive and 1 negative
29. A rectangular loop with a sliding rod of length 2m & resistance
2
. It moves in a uniform magnetic
field of 3T perpendicular to plane of loop. The external force required to keep the rod moving with
constant velocity of 2ms
-1
is
(a) 2N (b) 4N (c) 6N (d) 8N
30. A conducting rod PQ of length 4l is rotated about a point O in a uniform magnetic field
B
.
ThenPO 
(a)
2
Q P
Bω
V V
2
  

(b)
2
Q O
5
V V Bω
2
  
(c)
2
Q O
9
V V Bω
2
  
(d)
2
A Q
V V 4 Bω  
Page 9
183
31. As shown in figure after a long time the battery is disconnected and short circuiting the points A & B.
The current in circuit after 2ms after the short circuit is.
(a)
A
e
1
2
(b)
A
e
1
(c) 0.2A (d)
Ae
2
32. The variation of induced emf with time in a coil if a short bar magnet is moved along its axis with
constant velocity is.

(a) (b)
(c) (d)
33. A square loop of side 10 cm and resistance 2

is moved with velocity 
o
as shown in fig. The
uniform magnetic field is 3T with what speed should the loop be moved so that a steady current of
1.5 mA flows in the loop.
(a)
1
cms1

(b)
1
cms2

(c)
1
cms3

(d)
1
cms4

34. An inductor-resistor-battery circuit is switched on at t = 0. If the emf of battry is  find the charge
passes through the battery in one time constant .
(a)
max
i
e

(b)
 
max
-1 ie

(c)
max
i
e
(d)
max
τ i
Page 10

Electromagnetic Induction and Alternating Currents Notes and MCQs

Electromagnetic Induction and Alternating Currents Notes and MCQs

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