Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to the equation \( I=I_0\sin\omega t \), where \( I_0=10\,\mathrm{A} \), and \( \omega=100\pi\,\mathrm{rad/s} \). The maximum value of emf in the second coil is (in V):
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 5\pi \)
By Faraday’s law a changing current in one coil induces an emf in the other, \( |\varepsilon_2| = M\left|\frac{dI}{dt}\right| \), where \( M \) is the mutual inductance.
\( \displaystyle \frac{dI}{dt} = I_0\omega\cos\omega t \)
The emf is largest when \( |\cos\omega t| = 1 \):
\( \varepsilon_{\max} = M I_0\omega = 0.005\,\mathrm{H}\times10\,\mathrm{A}\times100\pi\,\mathrm{rad\,s^{-1}} = 5\pi\,\mathrm{V} \)
Note: The same question was also asked in CUET (UG) 2022 on 05-08-2022 (Slot 2).