Or, qC_{1} â€“ q_{1}C_{1 }+ qC_{3} = E_{1}C_{1}C_{3}

Or, q(C_{1} + C_{3}) â€“ q_{1}C_{1} = E_{1}C_{1}C_{3} ——-(i)

Using KVL for the loop BQRAB we get (V_{B} â€“ V_{Q}) + (V_{Q} â€“ V_{R}) + (V_{R} â€“ V_{A}) + (V_{A} â€“ V_{B}) = 0

Or, – E_{2} + 0 + Â – Â = 0

Or, q_{1}C_{3} â€“ qC_{2} + q_{1}C_{2} = E_{2}C_{2}C_{3}

Or, â€“ qC_{2} + q_{1}(C_{2} + C_{3}) = E_{2}C_{2}C_{3} ——-(ii)

Subtracting equation (i) from equation (ii) we get, q(C_{1} + C_{2} + C_{3}) – q_{1}(C_{1} + C_{2} + C_{3}) = E_{1}C_{1}C_{3} – E_{2}C_{2}C_{3}

Or, q – q_{1} = .

Therefore V_{A} â€“ V_{B} = – Â = .

Nodal analysis of capacitive circuit:

(i) At first identify different nodes and write their potential in the circuit.

(ii) Identify the isolated systems in the capacitive circuit and make equations using conservation of charge.

(iii) Solve the equations to get the values of potential at different points.

Find the potential difference between the points A and B using this concept: