Question

In an LC oscillator circuit, $L=10\text{mH},C=40\mu \text{F}$. At $t=0$, the capacitor is fully charged with $q_0=4\mu \text{C}$. Find the current in the circuit, when the capacitor and inductor share energies equally.

• A. $0.2\text{mA}$
• B. $4.5\text{mA}$
• C. $0.3\text{mA}$
• D. $2.2\text{mA}$

Answer 1

The correct option is B $4.5\text{mA}$

Given:
$L=10\text{mH}$
$C=40\mu \text{F}$
$q_0=4\mu \text{C}$

So, total energy stored in the capacitor,

$U_T=\frac{q_0^2}{2C}=\frac{(4\times {10}^{-6}{)}^2}{2\times 40\times {10}^{-6}}=2\times {10}^{-7}\text{J}$

When the capacitor and inductor share energies equally, energy stored in the inductor,

$U_L=\frac{U_T}{2}=\frac{2\times {10}^{-7}}{2}=1\times {10}^{-7}\text{J}$

$\Rightarrow \frac{1}{2}L{i}^2=1\times {10}^{-7}$

$\Rightarrow \frac{1}{2}\times 10\times {10}^{-3}\times i^2={10}^{-7}$

$\Rightarrow i\approx 4.5\times {10}^{-3}\text{A}=4.5\text{mA}$

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