Question

If a number of capacitors of equal capacity C each are arranged as shown, the equivalent capacity is given by :

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

The capacitors in the each loop are in parallel and then they are also in parallel. The equivalent circuit is shown in figure below.
$C_{eq}=C+2C+3C+4C+.......+nC$
$C_{eq}=C(1+2+3+4+......+n)=C\left[\frac{n(n+1)}{2}\right]$