Question

Three uncharged capacitors of capacitance C1, C2, and C3 are connected as

Answer 1

Taking into account the relation between the capacitance, voltage, and charge of a capacitor, we can write the following equations for the three capacitors: φA – φ0 = q1/c1, φB – φ0 = q2/c2 and φD – φ0 = q3/c3 where c1, c2, and c3 are considered as the capacitances of respective capacitors. On the other hand, q1, q2, and q3 are considered as the charges on the plates.

According to conservation law of charge, we can write q1 + q2 + q3 = 0, and therefore the potential of a common point O is φ0 = ( φA  . c1 +   φB c2  + φD . c3)/ (c1 + c2 +c3).