Electromagnetic Induction - Result Question 27

27. Two coils have a mutual inductance $0.005 H$. The current changes in the first coil according to equation $I=I_0 \sin \omega t$, where $I_0=10 A$ and $\omega=100 \pi radian / sec$. The maximum value of e.m.f. in the second coil is

[1998]]

(a) $2 p$

(b) $5 p$

(c) $p$

(d) $4 p$

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Answer:

Correct Answer: 27. (b)

Solution:

(b) $e=-M \frac{d i}{d t}=-0.005 \times \frac{d(i_0 \sin \omega t)}{dt}$

$ =-0.005 \times i_0 \times(\omega \cos \omega t) $

$e _{\text{max }}=0.005 \times i_0 \times \omega($ when $\cos \omega t=-1)$

$ =0.005 \times 10 \times 100 \pi=5 \pi V $