CHAPTER 39 ELECTROMAGNETIC INDUCTION
EXERCISE 182, Page 412
1. A conductor of length 15 cm is moved at 750 mm/s at right-angles to a uniform flux density of
1.2 T. Determine the e.m.f. induced in the conductor.
Length,  = 15 cm = 0.15 m and velocity, v = 750 mm/s = 0.75 m/s
Induced e.m.f., E = B  l v sin  = 1.2 × 0.15 × 0.75 × sin 90º = 0.135 V
2. Find the speed that a conductor of length 120 mm must be moved at right angles to a magnetic
field of flux density 0.6 T to induce in it an e.m.f. of 1.8 V.
Induced e.m.f., E = B  v from which, speed, v =
E
1.8

= 25 m/s
B  0.6  0.12
3. A 25 cm long conductor moves at a uniform speed of 8 m/s through a uniform magnetic field of
flux density 1.2 T. Determine the current flowing in the conductor when (a) its ends are opencircuited, (b) its ends are connected to a load of 15 ohms resistance.
Induced e.m.f., E = B  v = 1.2  0.25  8 = 2.4 V
(a) If the conductor is open circuited, then no current will flow.
(b) Current, I =
E 2.4

= 0.16 A
R 15
4. A straight conductor 500 mm long is moved with constant velocity at right angles both to its length
and to a uniform magnetic field. Given that the e.m.f. induced in the conductor is 2.5 V and the
velocity is 5 m/s, calculate the flux density of the magnetic field. If the conductor forms part of a
closed circuit of total resistance 5 ohms, calculate the force on the conductor.
412
© John Bird Published by Taylor and Francis
Induced e.m.f., E = B  v
i.e. 2.5 = B × 0.500 × 5 × sin 90º
from which, flux density, B =
2.5
=1T
0.500  5  sin 90
E
 2.5 
Force on conductor, F = B I  sin  = B       sin  = (1) 
 (0.500)(sin 00)
 5 
R
= 0.25 N
5. A car is travelling at 80 km/h. Assuming the back axle of the car is 1.76 m in length and the
vertical component of the earth’s magnetic field is 40 T, find the e.m.f. generated in the axle
due to motion.
Generated e.m.f, E = B  v = 40 106 1.76 
80 103
= 1.56 mV
60  60
6. A conductor moves with a velocity of 20 m/s at an angle of (a) 90 (b) 45 (c) 30, to a magnetic
field produced between two square-faced poles of side length 2.5 cm. If the flux on the pole face
is 60 mWb, find the magnitude of the induced e.m.f. in each case.
Induced e.m.f., E = B  v sin 
(a) When  = 90, E = B  v sin 90 =

60  103
 l  v  sin 90 
 2.5 102  20  sin 90 = 48 V
2
4
A
2.5
10
 
(b) When  = 45, E = B  v sin 45 = 48 sin 45 = 33.9 V
(c) When  = 30, E = B  v sin 30 = 48 sin 30 = 24 V
7. A conductor 400 mm long is moved at 70 to a 0.85 T magnetic field. If it has a velocity of
115 km/h, calculate (a) the induced voltage, and (b) force acting on the conductor if connected to
a 8  resistor.
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© John Bird Published by Taylor and Francis
 115 1000 
(a) Induced voltage, E = B  v sin  = (0.85)(0.4) 
 (sin 70) = 10.206 V or 10.21 V
 60  60 
E
 10.206 
(b) Force on conductor, F = B I  sin  = B       sin  = (0.85) 
 (0.4)(sin 70)
 8 
R
= 0.408 N
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© John Bird Published by Taylor and Francis
EXERCISE 183, Page 414
1. The mutual inductance between two coils is 150 mH. Find the magnitude of the e.m.f. induced in
one coil when the current in the other is increasing at a rate of 30 A/s.
The magnitude of the e.m.f. induced, E 2  M
dI1
 30 
 150 103   = 4.5 V
dt
 1 
2. Determine the mutual inductance between two coils when a current changing at 50 A/s in one
coil induces an e.m.f. of 80 mV in the other.
E2  M
E
dI1
80 103
hence, mutual inductance, M = 2 
= 1.6 mH
dI1
dt
50
dt
3. Two coils have a mutual inductance of 0.75 H. Calculate the magnitude of the e.m.f. induced in
one coil when a current of 2.5 A in the other coil is reversed in 15 ms.
Induced e.m.f., E 2  M
dI1
 2.5  2.5 
  0.75  
= 250 V
3 
dt
 15  10 
4. The mutual inductance between two coils is 240 mH. If the current in one coil changes from
15 A to 6 A in 12 ms, calculate (a) the average e.m.f. induced in the other, (b) the change of flux
linked with the other if it is wound with 400 turns.
(a) Induced e.m.f., E 2  M
(b) E = N
d
dt
dI1
 15  6 
   240 103  
= - 180 V
3 
dt
 12 10 
from which, change of flux, d 
Edt 180  12  103

= 5.4 mWb
N
400
415
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EXERCISE 184, Page 416
1. A transformer has 600 primary turns connected to a 1.5 kV supply. Determine the number of
secondary turns for a 240 V output voltage, assuming no losses.
N1 V1

N 2 V2
V 
 240 
from which, secondary turns, N 2  N1  2    600  

 1500 
 V1 
= 96 turns
2. An ideal transformer with a turns ratio 2:9 is fed from a 220 V supply. Determine its output
voltage.
N1 2

and V1  220 V
N2 9
N1 V1

N 2 V2
N 
9
from which, output voltage, V2  V1  2    220    = 990 V
2
 N1 
3. An ideal transformer has a turns ratio of 12:1 and is supplied at 192 V. Calculate the secondary
voltage.
N1 V1

N 2 V2
N 
1
from which, secondary voltage, V2  V1  2   192   
 12 
 N1 
= 16 V
4. A transformer primary winding connected across a 415 V supply has 750 turns. Determine how
many turns must be wound on the secondary side if an output of 1.66 kV is required.
N1 V1

N 2 V2
V 
 1660 
from which, secondary turns, N 2  N1  2    750  
 = 3000 turns
 415 
 V1 
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© John Bird Published by Taylor and Francis
5. An ideal transformer has a turns ratio of 15:1 and is supplied at 180 V when the primary current
is 4 A. Calculate the secondary voltage and current.
N1 12

, V1  220 V and I1  4 A
N2 1
N1 V1

N 2 V2
N 
1
from which, output voltage, V2  V1  2   180    = 12 V
 15 
 N1 
N1 I 2

N 2 I1
N 
 15 
from which, secondary current, I 2  I1  1    4    = 60 A
1
 N2 
6. A step-down transformer having a turns ratio of 20:1 has a primary voltage of 4 kV and a load of
10 kW. Neglecting losses, calculate the value of the secondary current.
N1 20

and V1  4000 V
N2
1
N1 V1

N 2 V2
N 
 1 
from which, output voltage, V2  V1  2    4000    = 200 V
 20 
 N1 
Secondary power = V2 I 2 = 10000
from which,
i.e.
200 I 2 = 10000
secondary current, I 2 
10000
= 50 A
200
7. A transformer has a primary to secondary turns ratio of 1:15. Calculate the primary voltage
necessary to supply a 240 V load. If the load current is 3 A determine the primary current. Neglect
any losses.
N1 V1

N 2 V2
N 
1
from which, primary voltage, V1  V2  1    240    = 16 V
 15 
 N2 
N1 I 2

N 2 I1
N 
 15 
from which, primary current, I1  I 2  2    3   = 45 A
1
 N1 
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© John Bird Published by Taylor and Francis
8. A 20  resistance is connected across the secondary winding of a single-phase power
transformer whose secondary voltage is 150 V. Calculate the primary voltage and the turns ratio
if the supply current is 5 A, neglecting losses.
Secondary current, I 2 
N1 V1

N 2 V2
V2 150

= 7.5 A , I1  5 A and
R 2 20
V2 = 150 V
N 
I 
 7.5 
from which, primary voltage, V1  V2  1   V2  2   150  
 = 225 V
 5 
 N2 
 I1 
Turns ratio,
N1 I 2 7.5
3
 
= 1.5 or
N 2 I1
5
2
or 3:2
EXERCISE 185, Page 416
Answers found from within the text of the chapter, pages 408 to 416.
EXERCISE 186, Page 417
1. (c) 2. (b) 3. (c) 4. (a) 5. (d)
13. (d)
6. (a) 7. (b)
8. (c)
9. (d)
10. (a)
11. (b)
12. (a)
14. (b) and (c)
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