Question

A number of capacitors, each of equal capacitance $C$, are arranged as shown in the figure. The equivalent capacitance between $A$ and $B$ is :

• A. $n^{2}C$
• B. $(2n+1)C$
• C. $\frac{(n-1)n}{2}C$
• D. $\frac{(n+1)n}{2}C$

Answer 1

The correct option is D $\frac{(n+1)n}{2}C$

There are n groups
$C_1=C$ $C_2=2C$ $C_3=3C$
Likewise $C_n=nC$
$C_{eq}=C_1+C_2+C_3+......+C_n$
$C_{eq}=C+2C+3C+............nC=\frac{n(n+1)C}{2}$