Q.
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 $\mu F$.
Solution:
From equs.
$\frac{\frac{7C}{3}}{\frac{7}{3}+C} \, = \, \frac{1}{2}$
$\Rightarrow \, \, 14 \, C \, = \, 7 \, + \, 3 \, C$
$\Rightarrow \, \, \, C \, = \, \frac{7}{11}$
