Question

A capacitor of capacitance, $C=25\mu \text{F}$ is fully charged and then connected with an inductor of inductance, $L=10\text{mH}$. The ratio of magnitude of maximum charge on the capacitor to the maximum current through the circuit, is -

Assume ideal conditions.

• A. $1:2000$
• B. $2000:1$
• C. $1:1000$
• D. $1000:1$

Answer 1

The correct option is A $1:2000$

Given:

$C=25\mu \text{F}=25\times {10}^{-6}\text{F}$
$L=10\text{mH}=10\times {10}^{-3}\text{H}$

The total energy in the ideal LC circuit is constant.

$\Rightarrow \frac{1}{2}\frac{q_0^2}{C}=\frac{1}{2}L{i}_0^2$

$\Rightarrow \frac{q_0^2}{i_0^2}=LC$

$\Rightarrow \frac{q_0}{i_0}=\sqrt{LC}$

$\Rightarrow \frac{q_0}{i_0}=\sqrt{10\times {10}^{-3}\times 25\times {10}^{-6}}=\frac{1}{2000}=1:2000$

Hence, option $\left(A\right)$ is the correct answer.