Question

A network of four $10\, \mu F$ capacitors is connected to a $500\, V$ supply as shown in figure. Determine the equivalent capacitance of the network.

• A. $12\, \mu F$
• B. $13.3\, \mu F$
• C. $11.5\, \mu F$
• D. $14\, \mu F$

Answer 1

Answer: (B)

In the given network, $C_{1}, C_{2}$ and $C_{3}$ are connected in series.
The effective capacitance $C^{\prime}$ of these capacitors is given by
$\frac{1}{C^{\prime}}-\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}$
For $C_{1}=C_{2}=C_{3}=10\, \mu F , C^{\prime}=(10 / 3) \mu F$
The network has $C^{\prime}$ and $C_{4}$ connected in parallel.
Thus, the equivalent capacitance $C$ of the network is
$C=C^{\prime}+C_{4}=\left(\frac{10}{3}+10\right)=13.3\, \mu F$