Question

Write down the definition of coefficient of self-induction and coefficient of mutual induction. Current of 5 A decreases to zero in 0.1 s in a coil of 5 H self-inductance. Find out induced e.m.f. produced in the coil.

Hint:

The induced e.m.f. in a coil is proportional to the rate of change of current and the self-inductance of the coil, as given by Faraday’s law of induction.

Answer 1

Step 1: Coefficient of Self-Induction.
The coefficient of self-induction \( L \) of a coil is a measure of the coil’s ability to induce an electromotive force (e.m.f.) in itself when the current passing through it changes. It is defined by the relation: \[ L = \frac{\text{Induced e.m.f.}}{\text{Rate of change of current}} \] where \( L \) is the self-inductance of the coil.
Step 2: Coefficient of Mutual Induction.
The coefficient of mutual induction \( M \) of two coils is a measure of the ability of one coil to induce an e.m.f. in the other coil when the current in the first coil changes. It is defined by: \[ M = \frac{\text{Induced e.m.f. in coil 2}}{\text{Rate of change of current in coil 1}} \]
Step 3: Induced e.m.f. in the Coil.
The induced e.m.f. in a coil due to a change in current is given by Faraday's law of induction: \[ \mathcal{E} = - L \frac{\Delta I}{\Delta t} \] where: - \( L = 5 \, \text{H} \) is the self-inductance, - \( \Delta I = 5 \, \text{A} \) (current decreases from 5 A to 0), - \( \Delta t = 0.1 \, \text{s} \). Substituting the values: \[ \mathcal{E} = - 5 \times \frac{5}{0.1} = - 250 \, \text{V} \] Thus, the induced e.m.f. is 250 V (negative sign indicates the direction of the induced e.m.f. opposing the change in current).