Question

The self-induced emf of a coil is $15V$ . What would be the change in the energy of the inductance (in SI units), when the current in it is changed at a uniform rate from $5A$ to $25A$ in $2s\text{,}$

Answer 1

Answer: 450

$ϵ=15$ Volts
$I_1=5A$
$I_2=25A$
$t=2s$
$\Delta E=?$
$ϵ=L\frac{\Delta I}{\Delta t}$
$\Rightarrow 15=L\frac{(25-5)}{2}$
$\Rightarrow \frac{15}{10}=L\Rightarrow L=1.5H$
$\Delta E=\frac{1}{2}L\left(I_2^2-I_1^2\right)$
$=\frac{1}{2}\times \frac{3}{2}\left[25^2-5^2\right]$
$=\frac{3}{4}[25+5][25-5]$
$\therefore \Delta E=\frac{3}{4}[30][20]=450J$