Question

One volt induced emf is produced in the secondary coil when the current through the primary coil is changed from 3 A to 1 A in 100 milliseconds. The mutual inductance of the two coils is:

• A. 0.5 H
• B. 0.25 H
• C. 0.005 H
• D. 0.05 H

Hint:

The induced emf in a secondary coil is proportional to the rate of change of current in the primary coil. Use the formula \( \varepsilon = - M \frac{\Delta I}{\Delta t} \) to calculate mutual inductance.

Answer 1

The Correct Option is D

In this problem, we need to find the mutual inductance \( M \) between the two coils. The relationship between the induced emf \( \varepsilon \) in the secondary coil and the change in current \( \Delta I \) in the primary coil is given by the formula: \[ \varepsilon = - M \frac{\Delta I}{\Delta t} \] Where: - \( \varepsilon = 1 \, \text{V} \) is the induced emf in the secondary coil, - \( \Delta I = 3 \, \text{A} - 1 \, \text{A} = 2 \, \text{A} \) is the change in current through the primary coil, - \( \Delta t = 100 \, \text{ms} = 0.1 \, \text{s} \) is the time interval during which the current changes. Now, rearranging the formula to solve for \( M \): \[ M = \frac{\varepsilon \cdot \Delta t}{\Delta I} \] Substitute the known values: \[ M = \frac{1 \, \text{V} \times 0.1 \, \text{s}}{2 \, \text{A}} = \frac{0.1}{2} = 0.05 \, \text{H} \] Thus, the mutual inductance of the two coils is \( 0.05 \, \text{H} \). Therefore, the correct answer is Option (D): \( 0.05 \, \text{H} \).