Question

For the circuit shown in the figure, find the instantaneous current through the capacitor.

• A. $V_0\omega C\sin \omega t$
• B. $V_0\omega C\cos \omega t$
• C. $V_0\omega C$
• D. None

Answer 1

The correct option is B $V_0\omega C\cos \omega t$

Since, the resistor, the capacitor and the inductor are connected in parallel, the voltage across all three will be same as source voltage.

Therefore, the voltage across the capacitor is

$V_C=V_0\sin \omega t$

In capacitor current leads voltage by $\frac{\pi }{2}$.

$\therefore i_C=\frac{V_0}{X_C}\sin (\omega t+\frac{\pi }{2})$

Also, $X_C=\frac{1}{\omega C}$

$\Rightarrow i_C=V_0\omega C\cos \omega t$

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