Question

Two coils have mutual inductance $0.005H$. The current changes in the form coil according to equation, $I=I_0\sin \omega t.$ Where $I_0=10A.$ and $\omega =100\pi$ rads/s. The maximum value of emf in the second coil is :

• A. $12\pi$
• B. $8\pi$
• C. $5\pi$
• D. $2\pi$

Answer 1

Answer: (C)

$5\pi$

Mutual inductance between two coils

M = 0.005 H

Peak current $l_0=10A$

Angular frequency $\omega =100\pi$ rad/s

Current $l=l_0\sin \omega t$

$\frac{d}{dt}=\frac{d}{dt}\left(l\sin \omega t\right)$

$=l_0\cos \omega t.\omega$

$=10\times 1\times 100\pi$

$=1000\pi$

Hence, induced emf is given by

$E=M\times \frac{dl}{dt}$

$=0.005\times 1000\times \pi =5\pi V$