In a coil, a current of 0.2 A increases at the rate of $0.4\, A\, s^{-1}$. If, there is power flow of $0.6\, J\, s^{-1}$ in the coil, its inductance is

7.5 H

The correct answer is Option (1) → 7.5 H

Given:

Current, $I = 0.2 \ \text{A}$

Rate of change of current, $\frac{dI}{dt} = 0.4 \ \text{A/s}$

Power, $P = 0.6 \ \text{J/s}$

Power in an inductor: $P = L I \frac{dI}{dt}$

Inductance: $L = \frac{P}{I \frac{dI}{dt}} = \frac{0.6}{0.2 \cdot 0.4} = \frac{0.6}{0.08} = 7.5 \ \text{H}$

Inductance, $L = 7.5 \ \text{H}$