A resistor of  $200\Omega$ and a capacitor of  $15.0\mu F$ are connected in series to a 220 V, 50Hz ac source. Calculate the current in the circuit.

Given,

$$\begin{gathered} R=200\Omega , C=15.0\mu F =15.0\times {10}^{-6}F \\ V=220V, v=50Hz \end{gathered}$$

a) In order to calculate the current, we need the impedance of the circuit. It is $Z=\sqrt{R^2+X_C^2}=\sqrt{R^2+{\left(2\pi vC\right)}^{-2}}$

$$\begin{gathered} \sqrt{{\left(200\Omega \right)}^2+{(2\times 3.14\times 50\times 15.0\times {10}^{-6}F)}^{-2}} \\ \sqrt{{\left(200\Omega \right)}^2+{\left(212.3\Omega \right)}^2} \\ =291.67\Omega \end{gathered}$$ 
Therefore, the current in the circuit is  $I=\frac{V}{Z}=\frac{220V}{291.5\Omega }=0.755A$