Question

The value of the self inductance of a coil is $5\text{H}$. If the current in the coil changes as $i=2t^2+4t$, then the magnitude of induced emf $\left(\text{in Volt}\right)$ at $t=2\text{s}$ will be

Answer 1

Given:
$i=2t^2+4t,L=5\text{H},t=2\text{s}$

Self indcutance of a coil,

$E=-\frac{Ldi}{dt}$

$|E|=|-\frac{Ldi}{dt}|=5\frac{d}{dt}(2t^2+4t)=5(4t+4)$

$E(\text{at}t=2\text{s})=5(4\times 2+4)$

$\Rightarrow E=60\text{V}$