Question

Derive an expression for effective capacitance of three capacitors connected in parallel.

Answer 1

In the given figure, capacitors $C_1,C_{2}and{C}_3$are connected in parallel. The same potential is applied across all the three capacitors. Let $Q_1,Q_{2}and{Q}_3$are charges on the three plates of capacitors such that

$Q_1=C_{1}V$

$Q_2=C_{2}V$

$Q_3=C_{3}V$

The total charge stored is $Q=Q_1+Q_2+Q_3$ and equivalent capacitance is $C_{eq}=\frac{Q}{V}$

So,

$C_{eq}=\frac{Q_1+Q_2+Q_3}{V}$

$=\frac{Q_1}{V}+\frac{Q_2}{V}+\frac{Q_3}{V}$

$C_{eq}=C_1+C_2+C_3$