Question

Derive an expression for the effective capacitance when capacitors are connected
in (a) series and (b) parallel

Answer 1

Series Combination of Capacitors:
V1V2V3VC1C2C3In series combination,
i)Charge is same in each capacitor
ii)Potential is distributed in inverse proportion to capacitancesi.e.V = V1+ V2+ V3ButqV1= C1V2= C2qV3= C3q,andqV= C,(where C is the equivalent capacitance or effective capacitance or net capacitance or total capacitance)q= C1+C2q+C3qqCorThe reciprocal of the effective ¢

In parallel combination,
i) Potential is same across each capacitor
ii) Charge is distributed in direct proportion to capacitances i.e.
But q = q1 + q2+ q3 q1 = C1 V , q2 = C2 V C V = C1V + C2V + C3V , q3 = C3 V (where C is the equivalent capacitance) or C = C1+ C2+ C3 C = The effective capacitance is the sum of the indiv