Two coils have a mutual inductance 0.005 H. The current changes i… - Vidyadip

MCQ

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 $\omega=100 \pi rad s ^{-1}$. The maximum value of emf in the second coil is

A
$12 \pi$
B
$2 \pi$
✓
$5 \pi$
D
$6 \pi$

✓

Answer

Correct option: C.

$5 \pi$

$\varepsilon=M \frac{d I}{d t}$
$=M \frac{d}{d t}\left[I_0 \sin \omega t\right]=M I_0 \omega \cos \omega t$
$E _{\max }=M I_0 \omega[\text { Max. value of } \cos \omega t=1]$
$=0.005 \times 10 \times 100 \pi=5 \pi V$

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