A coil has a self inductance of 10 mH. The magnitude of the maximum induced emf in the coil when a current \( I = 0.1\sin 200t \) A flows through it at a time t will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.2 V
A changing current in a coil induces an emf in the coil itself (self-induction), proportional to the rate of change of current.
\( \displaystyle e = -L\,\frac{dI}{dt} \)
\( \displaystyle \frac{dI}{dt} = \frac{d}{dt}\left(0.1\sin 200t\right) = 0.1 \times 200\cos 200t = 20\cos 200t\,\mathrm{A\,s^{-1}} \)
The magnitude is largest when \( \cos 200t = 1 \).
\( L = 10\,\mathrm{mH} = 10^{-2}\,\mathrm{H} \)
\( e_{\max} = 10^{-2} \times 20 = 0.2\,\mathrm{V} \)