Question

When a potential difference of $10^{3}V$ is applied between $A$ and $B$ , a charge of $0.75mC$ 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, $C_{\text{eff }}=\frac{q}{V}$
$\Rightarrow \frac{C+1}{C+2}=\frac{750\times 10^{-6}}{10^3}$
$=750\times 10^{-3}F=0.75\mu F$
$\Rightarrow 0.75=\frac{C+1}{C+2}$
$\Rightarrow \frac{3}{4}=\frac{C+1}{C+2}$
$\Rightarrow 3C+6=4C+4$
$\Rightarrow C=2\mu F$