Capacitance In series

Capacitance In Series

The below given figure is series connection of capacitors.

When a cell is connected across the ends of the system, a charge Q is transferred from the one end of first plate to the last end of second plate.  The potential difference across the individual capacitors are therefore given by:

V₁ =Q/ C₁    V₂ =Q/ C₂   And  V₃ = Q/ C₃

Now

V  = V₁+ V₂+ V₃

     = Q/ C₁    + Q/ C₂   + Q/ C₃

     =Q(1/ C₁    + 1/ C₂   + 1/ C₃)

V/Q=1/ C₁    + 1/ C₂   + 1/ C₃

The resultant capacitance (C) of the system is the ratio of the charge stored to the applied voltage.

C = Q/V

So, 1/C = 1/ C₁    + 1/ C₂   + 1/ C₃

For n capacitor in series;

 1/C = 1/ C₁    + 1/ C₂   + 1/ C₃ +………..+ 1/C_n