Question

Two coils have a mutual inductance $0.005H$. The current changes in the first coil according to the equation $i=i_m\sin \omega t$ where $i_m=10A$ and $\omega =100\pi rad{s}^{-1}$. The maximum value of the emf induced in the second coil is

• A. $2\pi$
• B. $5\pi$
• C. $\pi$
• D. $4\pi$

Answer 1

Answer: (B)

$5\pi$

Given : $L=0.005H$

Variation of current in first coil $i=i_m\sin wt$

$\therefore$ $\frac{di}{dt}=i_{m}w\cos wt$

Emf induced $E=-L\frac{di}{dt}=-i_{m}wL\cos wt$

Thus maximum emf induced $E_{max}=i_{m}wL$ when $\cos wt=-1$

$\therefore$ $E_{max}=10\times 100\pi \times 0.005=5\pi$ volts