![[rlc-series-example.png]]


Lets find out the total impedance and current of this circuit:

$$
\begin{flalign}
&I = \frac{V}{Z}&\\\
&Z = R^2 + (X_C-X_C)^2&\\
&X_C = \frac{1}{\omega C} &\\
&X_L = \omega C &\\
\end{flalign}
$$
Lets put in some numbers

$$
\begin{flalign}
&X_C = \frac{1}{2\pi*50*0.0001} \approx 31.830\ohm &\\\
&X_L = 2\pi*50*0.15 \approx 47.123\ohm&\\
&Z = \sqrt{12^2+(31.830-47.123)^2} \approx 19.4\ohm\\
&I = \frac{100}{19.439} \approx 5.14A
\end{flalign}
$$

Now lets finally calculate the voltage drops across all the components

$$
\begin{flalign}
V_R = 5.14*12 &\approx 61.68V&\\\
V_L = 5.14*47.13 &\approx 242.24V\\
V_C = 5.14*31.83 & \approx 163.6V\\
\end{flalign}
$$