Question

Derive an expression for equivalent capacitance of two capacitors connected in parallel.

Answer 1

Here, \(Q = Q_1 + Q_2\) ------- (1)

The charge on the first capacitor is given by \( Q_1 = C_1V, Q_2 = C_2 V\)

Equation (1) become

\(Q = C_1 V + C_2 V\)

\(Q = V [C_1+C_2] \).........(2)

If Cp is the effective capacitance of the combination

\(Q=Cp \,V\)---- (3)

From equation (2) and (3) we get,

\(Cp \,V = V [C_1 + C_2]\)

\(Cp = C_1 + C_2\)