Question

Compute the energy stored in the inductor at $t=2.00ms$

• A. $0.0094\mu J$
• B. $0.0940\mu J$
• C. $0.9400\mu J$
• D. $9.4000\mu J$

Answer 1

The correct option is A $0.0094\mu J$

Given : $L=3.3H$ $C=840\mu F$ $Q_i=105\mu C$
Charge stored on capacitor as a function of time $Q=Q_i\cos wt$
where $w=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{3.3\times 840\times {10}^{-6}}}=19$ rad/s
Current in the inductor $I=\frac{d}{dt}\left(Q_{i}coswt\right)=Q_{i}w\sin wt$
Charge stored at $t=2\times {10}^{-3}s$,
$Q=105\times {10}^{-6}\times 19\sin (19\times 2\times {10}^{-3})=105\times {10}^{-6}\times 19\times 0.038=7.6\times {10}^{-5}A$
Energy stored in inductor at that instant $U_L=\frac{L{I}^2}{2}$
$⟹U_L=\frac{\left(3.3\right)(7.6\times {10}^{-5}{)}^2}{2}=0.0094\mu J$