Question

Two coils have a mutual inductance of $0.01\, H$. The current in the first coil changes according to equation, $l = 5\, sin\, 200\pi t$. 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, $M=0.01 H$
and current in coil, $I=5 \sin 200 \pi t$.
Emf induced in secondary coil is given,
$e =M \frac{d l}{d t}$
putting the value in above relation,
$\theta =0.01 \times \frac{d}{d t}(5 \sin 200 \pi t)$
$=0.01 \times 5 \times 200 \pi \cos 200 \pi t=10 \pi \cos 200 \pi t$
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; $\theta_{0}=10 \pi V$.