Question

The current flowing through a solenoid of self-inductance $1\text{H}$ is given by $i=5\sin \frac{\pi t}{4}.$ What will be the emf induced across the solenoid at time $t=2\text{s}.$

• A. $\frac{\pi }{4}\text{V}$
• B. $\frac{3\pi }{4}\text{V}$
• C. $\frac{5\pi }{4}\text{V}$
• D. $0\text{V}$

Answer 1

The correct option is D $0\text{V}$

Given:

$L=1\text{H};t=2\text{s}$

$i=5\sin \left(\frac{\pi t}{4}\right)$

We know that emf induced across the solenoid is given by:

$E=\begin{array}{c}|-L\frac{di}{dt}|\end{array}$

$=\left|\begin{array}{c}1\times \frac{d\left[5\sin \left(\frac{\pi t}{4}\right)\right]}{dt}\end{array}\right|$

$=\frac{5\pi }{4}\cos \left(\frac{\pi t}{4}\right)$

At $t=2\text{s}$

$E=\frac{5\pi }{4}\cos \left(\frac{\pi \times 2}{4}\right)=0\text{V}[\because \cos \left(\frac{\pi }{2}\right)=0]$

Hence, $\left(D\right)$ is the correct answer.