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

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