Question

A capacitor is connected across an AC supply. The peak value of voltage and current in the circuit are $V_0$ and $I_0$ respectively. The magnitude of maximum charge on the plates of the capacitor is

• A. $\frac{2I_0}{\omega }$
• B. $\frac{I_0}{\sqrt{2}\omega }$
• C. $\frac{3I_0}{\sqrt{2}\omega }$
• D. $\frac{4I_0}{\omega }$

Answer 1

The correct option is B $\frac{I_0}{\sqrt{2}\omega }$

For a capacitor connected with an AC supply, the potential difference across the capacitor is

$V=I_{rms}\cdot X_C=\frac{I_{rms}}{\omega C}$

Also,

$V=\frac{q}{C}$

So,

$\frac{q}{C}=\frac{I_{rms}}{\omega C}$

$\therefore q=\frac{I_{rms}}{\omega }=\frac{I_0}{\sqrt{2}\omega }$

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