Two coils have mutual inductance 0.002 H. The current changes in … - Vidyadip

MCQ

Two coils have mutual inductance $0.002 \ \mathrm{H}$. The current changes in the first coil according to the relation $\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}$, where $\mathrm{i}_0=5 \mathrm{~A}$ and $\omega=50 \pi$ $\mathrm{rad} / \mathrm{s}$. The maximum value of $\mathrm{emf}$ in the second coil is $\frac{\pi}{\alpha} \mathrm{V}$. The value of $\alpha$ is_______.

A
$10$
B
$7$
✓
$2$
D
$73$

✓

Answer

Correct option: C.

$2$

c
$ \phi=\mathrm{Mi}=\mathrm{Mi}_0 \sin \omega \mathrm{t} $

$ \mathrm{EMF}=-\mathrm{M} \frac{\mathrm{di}}{\mathrm{dt}}=-0.002\left(\mathrm{i}_0 \omega \cos \omega \mathrm{t}\right) $

$ \mathrm{EMF}_{\max }=\mathrm{i}_0 \omega(0.002)=(5)(50 \pi)(0.002) $

$ \mathrm{EMF}_{\max }=\frac{\pi}{2} \mathrm{~V}$

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