Question

In an LC circuit, $C=4.00\mu \text{F}$, the maximum potential difference across the capacitor during the oscillations is $1.50\text{V}$ and the maximum current in the circuit is $50.0\text{mA}$. What is the value of inductance $L$?

• A. $2.4\text{mH}$
• B. $3.6\text{mH}$
• C. $4.8\text{mH}$
• D. $6.0\text{mH}$

Answer 1

The correct option is B $3.6\text{mH}$

According to conservation of energy principle, we can write,

Energy stored in fully charged capacitor $=$ Energy stored in inductor when capacitor is fully discharged

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

$\Rightarrow L=\frac{C{V}_0^2}{i_0^2}=\frac{4\times {10}^{-6}\times {1.5}^2}{(50\times {10}^{-3}{)}^2}$

$\Rightarrow L=3.6\times {10}^{-3}\text{H}=3.6\text{mH}$

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