# Electromagnetic Theory Questions and Answers – Inductances

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This set of Electromagnetic Theory Multiple Choice Questions & Answers (MCQs) focuses on “Inductance”.

1. Calculate the emf of a coil with turns 100 and flux rate 5 units.
a) 20
b) -20
c) 500
d) -500

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.

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

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.

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

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.
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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

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.

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

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.

6. With unity coupling, the mutual inductance will be
a) L1 x L2
b) L1/L2
c) √(L1 x L2)
d) L2/L1

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).

7. The inductance is proportional to the ratio of flux to current. State True/False.
a) True
b) False

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.

8. Calculate the mutual inductance of two tightly coupled coils with inductances 49H and 9H.
a) 21
b) 58
c) 40
d) 49/9

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.

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

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.

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

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.

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