Question

Two coils have a mutual inductance of $0.01H$. The current in the first coil changes according to equation, $l=5sin200\pi t$. The maximum value of $emf$ induced in the second coil is

• A. $10\pi V$
• B. $0.1\pi V$
• C. $\pi V$
• D. $0.01\pi V$

Answer 1

Answer: (A)

Given, mutual inductance in the coil, $M=0.01H$
and current in coil, $I=5\sin 200\pi t$.
Emf induced in secondary coil is given,
$e=M\frac{dl}{dt}$
putting the value in above relation,
$\theta =0.01\times \frac{d}{dt}(5\sin 200\pi t)$
$=0.01\times 5\times 200\pi \cos 200\pi t=10\pi \cos 200\pi t$
Compairing the above equation with the general equation of induced emf, which is represented as,
$\theta ={\theta }_0\cos \omega t$
where, ${\theta }_0$ is the maximum value of the emf.
$\therefore$ In the question, the maximum value of emf induced in the coil is; ${\theta }_0=10\pi V$.