Combination of Capacitors

Ask a Question, Get an Answer!

Type your question here

Hundreds of tutors are online and ready to help you right now!

Grouping of Capacitors

In many electrical circuits, capacitors are to be grouped suitably to obtain the desired capacitance. The two most common modes are:

1. Capacitors in series

2. Capacitors in parallel

Capacitors in Series

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

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.