A coil of inductance 2 H having negligible resistance is connected to a source of supply whose volta

Question

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

Professor PC Thomas Classes · Answer

(144) : $L=2 \mathrm{H}, V=3 t, t=4 \mathrm{~s}$\ $V=L \frac{d i}{d t}$ or $3 t=L \frac{d i}{d t}, L \int d i=\int 3 t d t$\ $L i=\frac{3 t^{2}}{2} \Rightarrow i=\frac{3 t^{2}}{2 L}$\ $E=\frac{1}{2} L i^{2}=\frac{1}{2} 	imes L 	imes \frac{\left(3 t^{2}ight)^{2}}{4 L^{2}}=\frac{9}{8 L} 	imes t^{4}$\ $	herefore \quad E=\frac{9}{8 	imes 2} 	imes(4)^{4}=144 \mathrm{~J}$\