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 $I_0=10 A$, and $\omega=100 \pi rad/s$. The maximum value of emf in the second coil is (in V):

$5 \pi$

The correct answer is Option (2) → $5 \pi$

According to faraday law,

$ε=M\frac{dI}{dt}$

M = Mutual inductance = 0.005 H

$I(t)=I_0\sin(ωt)$  [given]

$I_0=10A$

$ω=100\pi\,rad/s$

$\frac{dI}{dt}=I_0ω\cos(ωt)$

$ε_{max}=M.I_0.ω$ [Max. Current occurs when $\cos/ωt=1$]

$ε_{max}=0.005×10×100\pi$

$=5\pi V$