Question

Describe the relationship between the effective capacitance for a series and parallel combination to the individual capacitance of each capacitor. Derive the equations.

Answer 1

Let the capacitors be: C',C'',C''' and so on

now, if they are all mutually connected in parallel:

V is the voltage on each capacitor which will be the same since voltages in a parallel connection are the same. The charges however, are not the same.

so,

=>

therefore, the capacitance values gets summed if they are connected in parallel.

If they are all connected in series, the charge on them is the same however, the voltages are distributed

=>

=> .

the equivalent capacitance will be given by this form when they are connected in series.