Question

Find expressions for the equivalent capacitance of

(a) $N$identical capacitors $C$in parallel and

(b) $N$identical capacitors $C$in series.

Short answer

(a) In parallel, the expression for the equivalent capacitance is$NC$.

(b) In series, the expression for the equivalent capacitance is $\frac{N}{C}$.

Step-by-step solution

Part (a) step 1: Given Information

We have given that $N$identical capacitors $C$in parallel.

We need to find the expressions for equivalent capacitance.

Part (a) step 2: Explanation

The equivalent capacitance of capacitors capacitance $C_i$connected in parallel will be given as

$C_{eq}={\int }_i{C}_i$

As we have $N$capacitors of equal capacitance $C$. So, the capacitance will be

$C_{eq}=NC$

Part (b) step 1: Given information

We have given that the $N$identical capacitors $C$in series.

We need to find the expressions for the equivalent capacitance.

Part (b) step 2: Explanation

The equivalent capacitance of capacitors capacitance $C_i$connected in series will be given as

$\frac{1}{C_{eq}}={\int }_i\frac{1}{C_i}$

As we have $N$capacitors of equal capacitance $C$. So, the equivalent capacitance will be

$C_{eq}=\frac{N}{C}$