Question

When a potential difference of $10^3 V$ is applied between $A$ and $B$ , a charge of $0.75 \, mC$ is stored in the system of capacitors as shown.The value of $C$ is $(in\, \mu F)$

• A. $1/2$
• B. $2$
• C. $2.5$
• D. $3$

Answer 1

Answer: (B)

In the given circuit, $2 \mu F$ and $2 \mu F$ capacitors are in series
$C_{S}=\frac{2 \times 2}{2+2}=1 \,\mu F$
equivalent circuit will be

Now $C \mu F$ and $1\, \mu F$ are in parallel which is in series with $1 \mu F$
$ \therefore C_{\text {eff }}=\frac{(C+1) \times 1}{(C+1)+1}=\frac{C+1}{C+2}$
Given, $q=0.75 \times 10^{-3}\, C =750 \times 10^{-6} \,C ,\, V=10^{3} \,V$
So, $C_{\text {eff }}=\frac{q}{V}$
$\Rightarrow \frac{C+1}{C+2}=\frac{750 \times 10^{-6}}{10^{3}}$
$=750 \times 10^{-3}\, F =0.75\, \mu F$
$\Rightarrow 0.75=\frac{C+1}{C+2}$
$\Rightarrow \frac{3}{4}=\frac{C+1}{C+2}$
$\Rightarrow 3 C+6=4 C+4 $
$\Rightarrow C=2 \,\mu F$