In the circuit shown, find $C$ if the effective capacitance of the whole circuit is to be $0.5\,\mu F.$ All values in the circuit are in $\mu F.$
JEE MAIN 2019, Diffcult
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$\mathrm{C}_{\mathrm{eq}}=0.5\, \mu \mathrm{F}=\frac{\left(1+\frac{4}{3}\right) \mathrm{C}}{\frac{7}{3}+\mathrm{C}}=\frac{7 \mathrm{C}}{\frac{7}{3}+\mathrm{C}}=\frac{1}{2}$
$\Rightarrow \quad \frac{14 \mathrm{C}}{3}=\mathrm{C}+\frac{7}{3}$
$C=\frac{7}{11}$
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