In the circuit shown,


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

  1. (1) $\frac{7}{11} \mu \mathrm{F}$

  2. (2) $\frac{6}{5} \mu \mathrm{F}$

  3. (3) $4 \mu \mathrm{F}$

  4. (4) $\frac{7}{10} \mu \mathrm{F}$

Correct Option: 1


For series combination


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

$\Rightarrow 14 \mathrm{C}=7+3 \mathrm{C}$

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

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