Question

The equivalent capacitance in between points A and B in the following combination is $5x\mu F$. Find the value of $x$.

Answer 1

The equivalent circuit for the given network is shown in figure below.
For the parallel branch the total capacitance $C_p=10+5+15=30\mu F$
$\therefore C_{AB}=\frac{30C_p}{30+C_p}=\frac{30\times 30}{30+30}=15\mu F$

As given, $5x=15$

$x=3$