Question

In the circuit shown $k_1$ is closed for a long time. Then $k_1$ is opened and $k_2$ is closed simultaneously. If $R=20\Omega ,L=30mH$ and $C=12\mu F$, then maximum charge on the capacitor will be

• A. $3\times {10}^{-3}C$
• B. $5\times {10}^{-3}C$
• C. $10\times {10}^{-3}C$
• D. $12\times {10}^{-3}C$

Answer 1

The correct option is A $3\times {10}^{-3}C$

$\epsilon =iR\Rightarrow 100=i_0\times 20$
So, $i_0=5A$

By Conservation of Energy,
$\frac{1}{2}L{i}_0^2=\frac{Q^2}{2C}$
$\Rightarrow Q=i_0\sqrt{LC}$
$Q=5\times \sqrt{30\times {10}^{-3}\times 12\times {10}^{-6}}=3\times {10}^{-3}C$