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) → \( 0.05\,\mathrm{H} \)
The emf induced in one coil by a changing current in the neighbouring coil is given by the mutual inductance \( M \). Its magnitude is, with \( dI/dt \) the rate of change of current,
\( \displaystyle |\varepsilon| = M\,\left|\frac{dI}{dt}\right| \)
\( \Delta I = 6.0 - 3.0 = 3.0\,\mathrm{A} \)
\( \Delta t = 300\,\mathrm{ms} = 0.3\,\mathrm{s} \)
\( \displaystyle \frac{dI}{dt} = \frac{3.0}{0.3} = 10\,\mathrm{A\,s^{-1}} \)
\( \displaystyle M = \frac{|\varepsilon|}{|dI/dt|} = \frac{0.5}{10} = 0.05\,\mathrm{H} \)