An emf of 0.5 V is developed in the secondary coil, when current in primary coil changes from 5.0 A to 2.0 A in 300 ms. The mutual inductance of the two coils is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 50 mH
A changing current in the primary induces an emf in the secondary by mutual induction; the emf equals the mutual inductance times the rate of change of the primary current.
\( \displaystyle \varepsilon = M\,\frac{\Delta I}{\Delta t} \)
\( \Delta I = 5.0\,\mathrm{A} - 2.0\,\mathrm{A} = 3.0\,\mathrm{A} \)
\( \Delta t = 300\,\mathrm{ms} = 0.3\,\mathrm{s} \)
\( \displaystyle M = \frac{\varepsilon\,\Delta t}{\Delta I} \)
\( \displaystyle M = \frac{0.5\,\mathrm{V} \times 0.3\,\mathrm{s}}{3.0\,\mathrm{A}} \)
\( \displaystyle M = 0.05\,\mathrm{H} = 50\,\mathrm{mH} \)
Note: A similar question was also asked in CUET (UG) 2023 on 15-06-2023 (Slot 2).