Question

A number of identical condensers are first connected in parallel and then in series. The equivalent capacitance are found to be in the ratio $9:1$. The number of condensers used is :

• A. $9$
• B. $81$
• C. $3$
• D. $100$

Answer 1

The correct option is C $3$

In series
$\frac{1}{C_{eff}}=\frac{1}{C}+\frac{1}{C}+\frac{1}{C}+$ upto n terms
$C_{e}ff=\frac{C}{n}$

In parallel
$C_{e}ff=C+C+$ upto n terms

$C_{e}ff=nC$

$\frac{C_P}{C_S}=\frac{9}{1}$

$\frac{nC}{\frac{C}{n}}=\frac{9}{1}$

$n^2=9$

$n=3$