Lets take two capacitors having unequal potentials. Connect them through a conducting material such as a copper wire.Then the charge will flow from the conductor having larger amount of charge towards the conductor having less amount of charge. The flow of charge between these conductors will remain in continuity until and unless their potentials are not equal. After some time when the charge will stop flowing after coming to a particular potential. That potential is known as Common Potential.
We have taken two capacitors. Let one capacitor be C1 and other capacitor C2. Both having the different potentials .Lets say V1 and V 2 respectively.
So total charge will be :
C1V1 +C2V2
Lets suppose that the potential is same i.e. V
So = C1V +C2V.
Taking V common from the above equation
(C1+C2)V
There is no net loss of any kind of charge across the whole circuit.
So (C1+C2)V= C1V1 +C2V2
V= C1V1 +C2V2 / (C1+C2) ———2.19
Common potential is equal to the total charge on a body to the ratio of the total capacity.
So
So using the above equation 2.19
C1V1 + C2V2= C1V+C2V
Or
C1V1 – C1V= C2V2 – C2V
The result shows that the charge wasted or lost by one capacitor in the circuit will be taken by the other capacitor.
But it cant be true in any case .The reason behind this is , the capacities of the different capacitors are different . So, in case of potentials of the capacitors it is not true.
