Question

In the circuit shown, find $C$ if the effective capacitance of the whole circuit is to be $0.5\mu \text{F}$. All the values in the circuit are in $\mu \text{F}$.

• A. $\frac{6}{5}\mu \text{F}$
• B. $\frac{7}{11}\mu \text{F}$
• C. $4\mu \text{F}$
• D. $\frac{7}{10}\mu \text{F}$

Answer 1

The correct option is B $\frac{7}{11}\mu \text{F}$

The given circuit can be reduced as shown below


$\text{Given that,}{C}_{eq}=\frac{1}{2}\mu \text{F}$

For series combination

$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}$

$C_{eq}=\frac{C_1{C}_2}{C_1+C_2}$

$\Rightarrow \frac{\frac{7C}{3}}{\frac{7}{3}+C}=\frac{1}{2}$

$\Rightarrow 14C=7+3C$

$\Rightarrow C=\frac{7}{11}\mu \text{F}$

Hence, option $\left(A\right)$ is correct.