Question

An LC circuit contains a 20 mH inductor and a 25 $\mu$ F capacitor with an initial charge of 5 mC. The total energy stored in the circuit initially is

• A. 5 J
• B. 0.5 J
• C. 50 J
• D. 500 J

Answer 1

The correct option is B 0.5 J

Here, $C=25\mu F=25\times {10}^{-6}F,$
$L=20mH=20\times {10}^{-3}H,q_0=5mC=5\times {10}^{-3}C$
$\therefore$ Total energy stored in the circuit initially is
$U=\frac{q_0^2}{2C}=\frac{(5\times {10}^{-3}{)}^2}{2\times 25\times {10}^{-6}}=\frac{25\times {10}^{-6}}{2\times 25\times {106}^{-6}}=\frac{1}{2}=0.5J$