A coil has a self inductance of 10 mH. The magnitude of the maximum induced emf in the coil when a current $I=0.1 \sin 200 t$ A flows through it at a time t will be:

0.2 V

The correct answer is Option (2) → 0.2 V

The magnitude of the max. induced emf (ε) is the coil, is -

$ε=-L\frac{dI}{dt}$

$I(t)=0.1\sin(200t)A$

$\frac{dI}{dt}=0.1200\cos(200t)=20\cot(200t)A/s$

$\left|\frac{dI}{dt}\right|_{max}=20A/s$ [$\cos(200t)_{max}=1$]

$ε_{max}=L\left(\frac{dI}{dt}\right)_{max}$

$=(10×10^{-3})×20=0.2V$