Question

The current through an inductor of $1\text{H}$ is given by $I=3t\sin t$. The voltage across the inductor of $1\text{H}$ is

• A. $3\sin t+3\cos t$
• B. $3\sin t+3t\cos t$
• C. $3\cos t+t\sin t$
• D. $3t\cos t+\sin t$

Answer 1

The correct option is B $3\sin t+3t\cos t$

Given, $L=1\text{H}$

The potential drop across an inductor is,

$|V|=L\frac{dI}{dt}$

$|V|=\left(1\right)\frac{d}{dt}\left(3t\sin t\right)$

$|V|=3(\sin t+t\cos t)$

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