A capacitor of $C=10\times 10^{-6}\text{ F}$ is connected to an AC source of $V_{\text{rms}}=220\text{ V}$ and $f=50\text{ Hz}$. The rms current in the circuit is approximately:

Solution

1. Angular frequency $$\begin{array}{rl}\omega & =2\pi f\\ & =2\times 3.14\times 50\\ & =314\text{ rad/s}\end{array}$$.
2. Capacitive reactance $$\begin{array}{rl}{X}_C& =1/(\omega C)\\ & =1/(314\times 10\times 10^{-6})\\ & =1/0.00314\approx 318.5\Omega \end{array}$$.
3. RMS current $$\begin{array}{rl}{I}_{\text{rms}}& =V_{\text{rms}}/X_C\\ & =220/318.5\approx 0.69\text{ A}\end{array}$$.
4. Hence the answer is (A).