Question:
A coil of inductance $2 \mathrm{H}$ having negligible resistance is connected to a source of supply whose voltage is given by $\mathrm{V}=3 \mathrm{t}$ volt. (where $t$ is in second). If the voltage is applied when $\mathrm{t}=0$, then the energy stored in the coil after $4 \mathrm{~s}$ is________ $\mathrm{J}$.
Solution:
$\varepsilon=\frac{\mathrm{LdI}}{\mathrm{dt}}$
$3 \int_{0}^{4} \mathrm{t} d \mathrm{t}=2 \int_{0}^{1} \mathrm{dI}$
$\frac{3}{2} \times 16=2 I$
$\mathrm{I}=12$
$\mathrm{V}=\frac{1}{2} \mathrm{LI}^{2}=\frac{1}{2} \times 2(12)^{2}=144 \mathrm{~J}$