A change of current from 6.0 A to 3.0 A in 300 ms in a coil produces an induced emf of 0.5 V in the neighboring coil. The mutual inductance between the two coils would be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.05 H
Given:
- Initial current, $I_1 = 6.0 \, \text{A}$
- Final current, $I_2 = 3.0 \, \text{A}$
- Time interval, $\Delta t = 300 \, \text{ms} = 0.3 \, \text{s}$
- Induced emf, $E = 0.5 \, \text{V}$
We use the formula for mutual inductance:
$E = M \cdot \frac{\Delta I}{\Delta t}$
Rearranging to solve for $M$:
$M = \frac{E \cdot \Delta t}{\Delta I}$
$\Delta I = 6.0 - 3.0 = 3.0 \, \text{A}$
$M = \frac{0.5 \cdot 0.3}{3.0}$
$M = \frac{0.15}{3.0} = 0.05 \, \text{H}$
So, the mutual inductance is $0.05 \, \text{henry}$.