25.4 : Equivalent Capacitance

Multiple capacitors can be connected in a circuit in series or parallel configuration. When the capacitor combination is connected to a battery, the potential drop across each capacitor and the magnitude of charge stored in the individual capacitor depends on the type of the connection. The capacitor combination is replaced by a single equivalent capacitor that stores the same amount of charge as the combination for a given potential difference.

The following strategies are adopted to calculate the net capacitance for a capacitor network:

1. The capacitor network is grouped into capacitors connected in series and parallel in the network.
2. A series combination's equivalent capacitor has the same charge magnitude as the individual capacitors. The potential difference across the series combination is the sum of potential differences across the individual capacitors. Finally, the sum of reciprocals of individual capacitances gives the reciprocal of the equivalent capacitance in a series circuit.
3. The equivalent capacitor for a parallel combination has the same potential difference as the individual capacitor. The sum of the charges of the individual capacitors equals the charge of the equivalent capacitor. The equivalent capacitance equals the sum of all individual capacitances in the network.
4. For series combinations, the magnitude of equivalent capacitance is smaller than any of the individual capacitances. On the contrary, the equivalent capacitance value is greater for the capacitors connected in parallel than any of the individual capacitances.
5. All the series or parallel groups in the network are replaced with the equivalent capacitance in multiple steps till the net capacitance is obtained.