Question

The current in a coil changes steadily from 3 A to 5 A in 0.2 s when an emf of 2 $\mu$V is induced in it. The self-inductance of the coil is

• A. 0.2 mH
• B. 20 $\mu$H
• C. 2 $\mu$H
• D. 0.2 $\mu$H

Hint:

The induced emf in a coil is related to its self-inductance and the rate of change of current. Use this formula to calculate the inductance when you know the emf and the current change.

Answer 1

The Correct Option is D

The self-inductance \( L \) of a coil is given by the formula: \[ \text{Induced emf} = L \cdot \frac{\Delta I}{\Delta t} \] Where: - \( \text{Induced emf} = 2 \, \mu V = 2 \times 10^{-6} \, \text{V} \), - \( \Delta I = 5 \, A - 3 \, A = 2 \, A \), - \( \Delta t = 0.2 \, \text{s} \). Now, solve for \( L \): \[ 2 \times 10^{-6} = L \cdot \frac{2}{0.2} \] \[ L = \frac{2 \times 10^{-6} \times 0.2}{2} \] \[ L = 0.2 \times 10^{-6} \, \text{H} = 0.2 \, \mu \text{H} \]
Thus, the self-inductance of the coil is \( 0.2 \, \mu \text{H} \).