Question

Two coils $A$ and $B$ have mutual inductance $2 \times 10^{-2}$ henry. If the current in the primary is $i = 5\, sin\, (10π \,t)$ then the maximum value of e.m.f. induced in coil $B$ is

• A. $π$ volt
• B. $\frac{\pi}{2}$ volt
• C. $\frac{\pi}{3}$ volt
• D. $\frac{\pi}{4}$ volt

Answer 1

Answer: (A)

$M=2 \times 10^{-2} H$ and $i=5 \sin 10 \pi t$
Induced emf, $e_{B}=-M \frac{d l_{A}}{d t}$
where, $e_{B}=$ emf in coil $B$
$e_{B}=-2 \times 10^{-2} \frac{d}{d t}[5 \sin 10 \pi t]$
${[\because i=5 \sin 10 \pi t]} $
$e_{B}=-2 \times 5 \times 10^{-2} \times 10 \pi[\cos 10 \pi t]$
$e_{B}=-\pi[\cos 10 \pi t]$
The maximum value of emf induced in coil $B=\pi V$