Question

$n$ identical capacitors each of capacitance $C$ when connected in parallel give the effective capacitance $ 90\,\mu F $ and when connected in series give $2.5\,\mu F $ . Then the values of $n$ and $C$ respectively are

• A. $ 6 $ and $ 15\,\mu F $
• B. $ 5 $ and $ 18\,\mu F $
• C. $ 15 $ and $ 6\,\mu ,F $
• D. $ 18 $ and $ 5\,\mu ,F $

Answer 1

Answer: (A)

If $n$ identical capacitors each having capacitances $C$ are connected in series with supply voltage $V$, then equivalent capacitance
$C_{e q}=\frac{C}{n}$
Here, $\frac{C}{n}=2.5\, \mu F$ ... (i)
If $n$ identical capacitors are connected in parallel equivalent capacitance
$C_{e q}=n C$
Here, $n C=90\, \mu F$ ... (ii)
$\Rightarrow n=6$ and $C=15\, \mu F$