Question

$n$ equal capacitors are first connected in series and then in parallel. The ratio of capacitances in series and parallel arrangements will be :

• A. $n$
• B. $n^2$
• C. $\frac{1}{n}$
• D. $\frac{1}{n^2}$

Answer 1

Answer: (D)

$\frac{1}{n^2}$

When n capacitors are connected in series, the equivalent capacitance is $C_{series}=\frac{C}{n}$
and when n capacitors are connected in parallel, the equivalent capacitance is $C_{parallel}=nC$
$\frac{C_{series}}{C_{parallel}}=\frac{\frac{C}{n}}{nC}=\frac{1}{n^2}$