Question

Compute the energy stored in the capacitor at $t=2.00ms$.

• A. $9.5531\mu J$
• B. $6.5531\mu J$
• C. $3.5531\mu J$
• D. $2.5531\mu J$

Answer 1

The correct option is B $6.5531\mu J$

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
Charge stored at $t=2\times {10}^{-3}s$,
$Q=105\times {10}^{-6}\cos (19\times 2\times {10}^{-3})=105\times {10}^{-6}\times 0.999=104.9\times {10}^{-6}C$
Energy stored in capacitor at that instant $U_C=\frac{Q^2}{2C}$
$⟹U_C=\frac{(104.9\times {10}^{-6}{)}^2}{2\times 840\times {10}^{-6}}=6.5531\mu J$