Two coils, A and B, are arranged parallel to each other. When the current in coil A increases at the rate of 20 A/s and current in coil B is 5 A/s, the induced emf in coil B is 60 mV. The mutual inductance of the two coils is:

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Question

This question was previously asked in

AAI ATC Junior Executive 27 July 2022 Shift 2 Official Paper

Answer 1

Concept:

When two coils are arranged in such a way that a change of current in one coil causes an emf to be induced in the other, the coils are said to have mutual inductance.
The mutual inductance is denoted letter M and measured in Henry.
Induced emf in coil A due to the change in current in coil B is \(e_A = \left(\frac{Mdi}{dt}\right)_B\)
Where, di = change in current, dt = change in time, M = mutual inductance

Calculation:

Given, \((\frac {di}{dt})_A\) = 20 A/s, \((\frac {di}{dt})_B\) = 5 A/s, e_B = 60 mV

From coil B, from the Reciporicity theorem \(e_B = \left(\frac{Mdi}{dt}\right)_A\)

⇒ 60 = M × 20

⇒ M = 3 mH