Combination of Capacitors

 

Capacitors in Series

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If +Q units of charge are given to left plates of C₁, then by induction

-Q charge appears on the right plate. +Q appears on the left plate of capacitor C₂ and so on. Thus, same charge appears on each capacitor.

The potential difference across each capacitor however is different. Therefore,

V = V₁ + V₂ + V₃

On substituting,

OR

where C_S is the effective capacitance, when capacitors are connected in series.

This implies that when the capacitors are connected in series, the reciprocal of the equivalent capacitance equals to the reciprocals of the individual capacitance.

Capacitors in Parallel

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Here, the potential difference across each capacitor is the same but charges are different. Therefore,

Q = Q₁ + Q₂ + Q₃

C_PV = C₁ V + C₂V + C₃V

C_P = C₁ + C₂ + C₃

where C_p is the effective capacitance, when capacitors are connected in parallel.

This implies that when the capacitors are connected in parallel, the equivalent capacitance equals the sum of the individual capacitance.