Test: Inductances

QUESTION: 1

Calculate the emf of a coil with turns 100 and flux rate 5 units.

A.
20
B.
-20
C.
500
D.
-500

Solution:

Answer: d
Explanation: The emf is the product of the turns of the coil and the flux rate. Thus e = -N dφ/dt, where the negative sign indicates that the emf induced is opposing the flux. Thus e = -100 x 5 = -500 units.

QUESTION: 2

The equivalent inductances of two coils 2H and 5H in series aiding flux with mutual inductance of 3H is

A.
10
B.
30
C.
1
D.
13

Solution:

Answer: d
Explanation: The equivalent inductance of two coils in series is given by L = L1 + L2 + 2M, where L1 and L2 are the self inductances and M is the mutual inductance. Thus L = 2 + 5 + 2(3) = 13H.

QUESTION: 3

The expression for the inductance in terms of turns, flux and current is given by

A.
L = N dφ/di
B.
L = -N dφ/di
C.
L = Niφ
D.
L = Nφ/i

Solution:

Answer: a
Explanation: We know that e = -N dφ/dt and also e = -L di/dt. On equating both we get, L = Ndφ/di is the expression for inductance.

QUESTION: 4

The equivalent inductance of two coils with series opposing flux having inductances 7H and 2H with a mutual inductance of 1H.

A.
10
B.
7
C.
11
D.
13

Solution:

Answer: b
Explanation: The equivalent inductance of two coils in series with opposing flux is L = L1 + L2 – 2M, where L1 and L2 are the self inductances and M is the mutual inductance. Thus L = 7 + 2 – 2(1) = 7H.

QUESTION: 5

A coil is said to be loosely coupled with which of the following conditions?

A.
K>1
B.
K<1
C.
K>0.5
D.
K<0.5

Solution:

Answer: d
Explanation: k is the coefficient of coupling. It lies between 0 and 1. For loosely coupled coil, the coefficient of coupling will be very less. Thus the condition K<0.5 is true.

QUESTION: 6

With unity coupling, the mutual inductance will be

A.
L1 x L2
B.
L1/L2
C.
√(L1 x L2)
D.
L2/L1

Solution:

Answer: c
Explanation: The expression for mutual inductance is given by M = k √(L1 x L2), where k is the coefficient of coupling. For unity coupling, k = 1, then M = √(L1 x L2).

QUESTION: 7

The inductance is proportional to the ratio of flux to current. State True/False.

A.
True
B.
False

Solution:

Answer: a
Explanation: The expression is given by L = Ndφ/di. It can be seen that L is proportional to the ratio of flux to current. Thus the statement is true.

QUESTION: 8

Calculate the mutual inductance of two tightly coupled coils with inductances 49H and 9H.

A.
21
B.
58
C.
40
D.
49/9

Solution:

Answer: a
Explanation: For tightly coupled coils, the coefficient of coupling is unity. Then the mutual inductance will be M = √(L1 x L2)= √(49 x 9) = 21 units.

QUESTION: 9

Find the inductance of a coil with turns 50, flux 3 units and a current of 0.5A

A.
150
B.
300
C.
450
D.
75

Solution:

Answer: b
Explanation: The self inductance of a coil is given by L = Nφ/I, where N = 50, φ = 3 and I = 0.5. Thus L = 50 x 3/0.5 = 300 units.

QUESTION: 10

The inductance of a coaxial cable with inner radius a and outer radius b, from a distance d, is given by

A.
L = μd ln(b/a)/2π
B.
L = 2π μd ln(b/a)
C.
L = πd/ln(b/a)
D.
L = 0

Solution:

Answer: a
Explanation: The inductance of a coaxial cable with inner radius a and outer radius b, from a distance d, is a standard formula derived from the definition of the inductance. This is given by L = μd ln(b/a)/2π.