Two coils A and B are arranged parallel to each other. When the current in coil B increases at the rate of 20 A/s and initial current in coil A is zero, the induced emf in coil A is 100 V. The mutual inductance of the two coil is:

Question

Question

This question was previously asked in

AAI ATC Junior Executive 27 July 2022 Shift 1 Official Paper

Answer 1

Concept:

When two coils are brought in proximity to each other the magnetic field in one of the coils tends to link with the other.
This further leads to the generation of voltage in the second coil.
This property of a coil that affects or changes the current and voltage in a secondary coil is called mutual inductance.

F1 Madhuri Defence 20.12.2022 D1

The emf induced in the coil is given as, \(e = -M\frac{dI}{dt}\) where M = mutual inductance, e = emf induced in the coil, i = current

Calculation:

Given,

The current in coil B increases at the rate, \(\frac{dI_B}{dt}=20 A/s\)

The initial current in coil A, I_A = 0A

The induced emf in a coil A, e_A = 100 V

The mutual inductance of the two coils is calculated as, \(e=-M\frac{di}{dt} \)

\(e_A=-M\frac{d(I_A-I_B)}{dt}\)

\(e_A=-M(\frac{dI_A}{dt}-\frac{dI_B}{dt})\)

\(100=-M(0-20)\)

\(M=\frac{100}{20}=5 H\)

Hence, the mutual inductance of the two coils is 5 H.