If the current through an inductor increases from 2 A to 3 A, the magnetic energy stored in the inductor…
If the current through an inductor increases from 2 A to 3 A, the magnetic energy stored in the inductor increases by
$125 \%$
$225 \%$
$50 \%$
$75 \%$
Solution
Magnetic energy stored in the inductor is
$\mathrm{U}=\frac{1}{2} \mathrm{LI}^2 \Rightarrow \mathrm{U} \propto \mathrm{I}^2$
$\therefore \frac{\mathrm{U}_2}{\mathrm{U}_1}=\frac{\mathrm{I}_2}{\mathrm{I}_1}=\left(\frac{3}{2}\right)^2 \Rightarrow \mathrm{U}_2=\frac{9}{4} \mathrm{U}_1$
$\therefore \quad \%$ increase in energy stored is
$\begin{aligned} & \Delta U \%=\left(\frac{U_2-U_1}{U_1} \times 100\right) \% \\ & =\frac{\frac{9}{4} U_1-U_1}{U_1} \times 100=125 \%\end{aligned}$