Question

Obtain the formula for the equivalent (effective) capacitance in the series / parallel
combination of capacitors.

Answer 1

In the parallel capacitors, the common voltage will be V = V1 = V2 and so on. And i1 = C1 dv/dt, i2 = C2 dv/dt and so on.

iT = i1+ i2 + i3 + so on

iT = C1 dv/dt + C2 dv/dt + C3 dv/dt and so on

iT = Ct dv/dt

Hence the capacitance will be Ct = C1 + C2 + C3 + so on.

In the series capacitors,

Qt = Q1 + Q2 + Q3 + so on

V = V1 + V2 + v3 + so on

QT/CT = QT/C1 + QT/ C2 + so on

Hence, 1/CT = 1/C1 + 1/C2 + 1/C3 + so on