Question

Two coaxial coils are very close to each other and their mutual inductance is $3\text{H}.$ If a current $i_1=2\sin 30t\text{A}$ is passing through the first coil, then find the peak value of induced emf in the second coil.

• A. $0\text{V}$
• B. $90\text{V}$
• C. $\frac{180}{\sqrt{2}}\text{V}$
• D. $180\text{V}$

Answer 1

The correct option is D $180\text{V}$

Given, $i_1=2\sin 30t\text{A};M=3\text{H}$

Flux linked with the second coil due to the field produced by current in the first coil is,

${\varphi }_2=M{i}_1$

$\therefore$ The emf induced in the second coil is,

$\left|\begin{array}{c}{E}_2\end{array}\right|=\frac{d{\varphi }_2}{dt}=M\left(\frac{d{i}_1}{dt}\right)$

$=3\times \frac{d}{dt}\left(2\sin 30t\right)=3\times \left(30\right)\times 2\cos 30t$

$\left|\begin{array}{c}{E}_2\end{array}\right|=\left(180\cos 30t\right)\text{V}.....\left(1\right)$

We have,

$E=\left(E_0\cos 30t\right)\text{V}.....\left(2\right)$

On comparing (1) and (2) we get,

The peak value of induced emf in the second coil is $180\text{V}$.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.