How do you calculate capacitors in series and parallel

This post answers the question “How do you calculate capacitors in series and parallel?”.

Let’s consider first the series combinaton of two capacitors like on the figure below.

The charge these two capacitors are storing is $q (t) = C_{1} v_{1} (t) = C_{2} v_{2} (t)$ . At the same time $v (t) = v_{1} (t) + v_{2} (t)$ , then $\frac{1}{C} = \frac{1}{C_{1}} + \frac{1}{C_{2}}$ or $C = \frac{C_{1} C_{2}}{C_{1} + C_{2}}$ .

For the parallel connection of capacitors like on the figure below, we can conclude that $q_{1} = C_{1} v (t)$ and $q_{2} = C_{2} v (t)$ .

Then $v (t) = \frac{q_{1} (t)}{C_{1}}, v (t) = \frac{q_{2} (t)}{C_{2}}$ . And $q (t) = q_{1} (t) + q_{2} (t)$ . Then $C = C_{1} + C_{2}$ .

More educational content can be found at Reddit community r/ElectronicsEasy.