Question

Calculate the mutual inductance for a system defined below.

Two coils P and Q are kept in parallel planes, such that 70% of the flux produced by coil P links with coil Q. The number of turns in coil P is 10,000 and in coil Q is 12,000.

A current of 4 A in coil P produces a flux of 0.04 mWb while a current of 4 A in coil Q produces a flux of 0.08 mWb.

1. 1.25 H
2. 0.90 H
3. 0.08 H
4. 3.21 H

Answer 1

Correct Answer - Option 3 : 0.08 H

Concept:

Self-inductance of the coil is given by

\(L = \frac{N\phi}{I}\)

Where

N = Number of turns

I = current through the coil

ϕ = flux

Mutual inductance between two coils is given by 

M = K \(\sqrt {L_1L_2}\)

K = coupling coefficient

L₁ = self-inductance of the coil 1

L₂ = self-inductance of the coil 2

Calculation:

Given that

Coupling Coefficient K = 0.7

Self-inductance of the coil P is equal to L_P = (10000 × 10^-3 × 0.04)/4 = 0.1 H

Self-inductance of the coil Q is equal to L_Q = (12000 × 10^-3× 0.08)/4 = 0.24 H

⇒ M = 0.7 \(\sqrt {0.1 \times 0.24}\) = 0.1 ≈ 0.08 H