Capacitors in series and parallel

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Physics Electromagnetism Capacitors in series and parallel

Capacitance:

The ability to store charge in a capacitor is called as its capacitance and is given by the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between them. Mathematically the capacitance (C) of a capacitor can be written as:

C = Q / ∆V

The capacitance is always a positive quantity. And the potential difference used here is also a positive quantity. Since the potential difference increases linearly with the stored charge, the ratio Q/ΔV is constant for a given capacitor. Thus, the capacitance is a measure of a capacitor’s ability to store charge and electric potential energy.

Capacitors in series and parallel

In a parallel combination, the individual potential differences across capacitors are all the same and are equal to the potential difference applied across the combination. The total charge on capacitors connected in parallel is the sum of the charges on the individual capacitors. Then the resultant capacitance of the combination of capacitors in parallel is the sum of the individual capacitance in the combination:

In a series combination the total potential difference across any number of capacitors is the sum of the potential differences across the individual capacitors. And the charges on the capacitors connected in series are the same. Then the resultant capacitance of the combination of a set of capacitors will be as follows: