Capacitors in Series and Parallel

Capacitors can be connected in either series or parallel configurations in a circuit.

Consider the capacitors connected in series to a battery; the plate connected to the battery's positive terminal develops a positive charge while the plate attached to the negative terminal is negatively charged.

An equal magnitude of the charge is induced on the other plates. However, the potential difference across each capacitor varies as the ratio of the charge to its capacitance.

Considering the capacitors as a single equivalent capacitor, the potential difference across it equals the sum of potentials across each capacitor.

Thus, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances.

Now, if the capacitors are connected in parallel, the potential difference of each capacitor equals the battery voltage. Therefore, the charge varies as the product of the capacitance of individual capacitors and the potential difference.

The total charge for the equivalent capacitor in a parallel connection is the sum of the charges of the individual capacitors. Therefore, the equivalent capacitance is additive.