25.3: Capacitors in Series and Parallel
Multiple capacitors connected serve as electrical components in various applications. These multiple capacitors behave as a single equivalent capacitor, and its total capacitance depends on the capacitance of individual capacitors and the type of connections. Capacitors can be arranged in two - orientations, either in series or parallel connections.
Suppose the capacitors are connected one after the other such that the negative terminal of the first connects to the positive terminal of the second. In that case, it is called a series connection. Each capacitor acquires an equal magnitude of charge Q, when this series combination is connected to a battery with voltage V. The charge on the plate attached to the battery's positive terminal is +Q, and the charge on the plate connected to the negative terminal is −Q. Charges are then induced on the other plates so that the sum of the charges on all plates, and the sum of charges on any pair of capacitor plates, is zero.
However, the potential drop on each capacitor varies as the ratio of the charge to its capacitance. The sum of the potential drop across each capacitor equals the total battery voltage. The reciprocal of equivalent capacitance in a series circuit is the sum of reciprocals of individual capacitances. Thus, the capacitor combination resembles a single equivalent capacitor with a capacitance value smaller than the smallest capacitances in a series combination.
When the multiple capacitors are connected such that the positive terminals of all the capacitors are connected to the battery's positive terminal, and negative terminals are connected to the battery's negative terminal, it's called a parallel connection. The voltage drop across each capacitor is the same, but the charge stored varies. The total charge stored by the network is the sum of the charge stored in each capacitor. The equivalent capacitance in a parallel circuit equals the sum of all individual capacitances in the network. Thus, the capacitor combination resembles a single equivalent capacitor with higher capacitance.
