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
$C_{eq}=\frac{C}{n}$
Here, $\frac{C}{n}=2.5\mu F$ ... (i)
If $n$ identical capacitors are connected in parallel equivalent capacitance
$C_{eq}=nC$
Here, $nC=90\mu F$ ... (ii)
$\Rightarrow n=6$ and $C=15\mu F$