The arrangement shows a part of complete circuit . The potentials at points A and B are `V_(1)` and `V_(2)` respectively . Find the potential at point P .

Strategy `:` The two capacitors `C_(1)` and `C_(2)` are connected in series . Therefore the charge on both of the capacitors is same. Let the potential at P is V.

Explanation

`:.` Potential difference across `C_(1)` is `V_(1)-V` and across `C_(2)` is `V-V_(2)`.
Let charge on `C_(1)` is Q, such that , `Q = C_(1) ( V_(1) - V)`
Also, charge on `C_(2)` is Q, such that , `Q = C_(2) ( V-V_(2))`
`implies C_(1)(V_(1)- V)= C_(2)(V-V_(2))`
`implies V= ( C_(1)V_(1)+C_(2)V_(2))/(C_(1)+C_(2))`