In a coil, a current of 0.2 A increases at the rate of \( 0.4\,\mathrm{A\,s^{-1}} \). If, there is power flow of \( 0.6\,\mathrm{J\,s^{-1}} \) in the coil, its inductance is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 7.5\,\mathrm{H} \)
A growing current induces a back emf \( \varepsilon = L\,di/dt \) in the coil. The source must push the current against it, so the power flowing into the coil (stored in its magnetic field) is
\( \displaystyle P = \varepsilon\,i = L\,i\,\frac{di}{dt} \)
\( i = 0.2\,\mathrm{A} \)
\( di/dt = 0.4\,\mathrm{A\,s^{-1}} \)
\( P = 0.6\,\mathrm{J\,s^{-1}} = 0.6\,\mathrm{W} \)
\( \displaystyle L = \frac{P}{i\,(di/dt)} = \frac{0.6}{0.2 \times 0.4} = \frac{0.6}{0.08} = 7.5\,\mathrm{H} \)