Question

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

• A. $3$
• B. $2.5$
• C. $2$
• D. $\frac{1}{2}$

Answer 1

The correct option is C $2$

Given, $V_{AB}={10}^3\text{V}$ and $Q_{AB}=0.75\text{mC}$
Effective capacitance $C_{AB}=\frac{1\times (C+1)}{1+(C+1)}$
$Q_{AB}=C_{AB}{V}_{AB}$
$\Rightarrow 0.75\times {10}^{-3}=\frac{(C+1)1}{C+1+1}\times {10}^3$
$\Rightarrow \frac{3}{4}\times {10}^{-6}=\frac{C+1}{C+2}$
$\therefore C=2\mu F$