Capacitance in Series and Parallel:

Capacitors in Series

Let,      C₁, C₂, C₃ = capacitance of each capacitor,

              V₁, V₂, V₃ = voltage gradient across each capacitor, and

                             C = equivalent capacitance.

In this case, charge on each of the capacitor is same but potential difference is different.

Figure: Capacitors in Series

V = V₁ + V₂ + V₃            (as capacitors are in series)

or         Q/C =  Q/C₁  +  Q/C₂ +  Q/C₃  ⇒ 1 /C =  1/C₁  +  1/C₂ +  1/C₃ 

⇒         C = C₁C₂C₃ / (C₁ C₂ + C₂ C₃+ C₃ C₁)

Capacitors in Parallel

In this case, potential difference is same but charge is different on each capacitor

∴          Q = Q₁  + Q₂  + Q₃

or         CV  = C₁ V + C₂ V + C₃ V

or         C = C₁  + C₂  + C₃ 

Figure: Parallel Capacitors