A coil of inductance 2 H having negligible resistance
Question:

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by $\mathrm{V}=3 \mathrm{t}$ volt. (where $\mathrm{t}$ is in second). If the voltage is applied when $\mathrm{t}=0$, then the energy stored in the coil after $4 \mathrm{~s}$ is J.

Solution:

(144)

$L \frac{d i}{d t}=\varepsilon$

$=3 t$

$L \int d \mathrm{i}=3 \int \mathrm{td} \mathrm{t}$

$\mathrm{Li}=\frac{3 t^{2}}{2}$

$i=\frac{3 t^{2}}{2 L}$

energy, $\mathrm{E}=\frac{1}{2} \mathrm{Li}^{2}$

$=\frac{1}{2} \mathrm{~L}\left(\frac{3 t^{2}}{2 \mathrm{~L}}\right)^{2}$

$=\frac{1}{2} \times \frac{9 t^{4}}{4 \mathrm{~L}}$

$=\frac{9}{8} \times \frac{(4)^{4}}{4 \times 2}=144 \mathrm{~J}$