Find the potential difference `V_(A)- V_(B)` between points A and B of the circuit shown in figure.

Explanation

First of all, make the charge distribution , as shown in figure.

In the loop 12341 , using `SigmaDeltaV =0`
`- (q_(1))/(C_(1)) + epsilon_(1) -(q_(1)-q_(2))/(C_(3))=0` ....(i)
Similarly, in the loop 61456 , using `SigmaDeltaV=0`
`-(q_(2))/(C_(2))- (q_(2)-q_(1))/(C_(3))+epsilon_(2)=0` ....(ii)
From equations (i) and (ii) we have
`q_(2) - q_(1)= (epsilon_(2)C_(2) - epsilon_(1) C_(1))/((C_(2))/(C_(3))+(C_(1))/(C_(3))+1)`
Hence, `V_(A)-V_(a)= (q_(2)-q_(1))/(C_(3))= (epsilon_(2)C_(2)-epsilon_(1)C_(1))/(C_(1)+C_(2)+C_(3))`