Question

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

• A. $\pi$ 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, $e_B=-M\frac{d{l}_A}{dt}$
where, $e_B=$ emf in coil $B$
$e_B=-2\times 10^{-2}\frac{d}{dt}[5\sin 10\pi t]$
$[\because i=5\sin 10\pi t]$
$e_B=-2\times 5\times 10^{-2}\times 10\pi [\cos 10\pi t]$
$e_B=-\pi [\cos 10\pi t]$
The maximum value of emf induced in coil $B=\pi V$