Question

A network of four capacitors each of 15 $\mu F$ capacitance is connected to a 500 V supply as shown in the figure. Determine
(i) equivalent capacitance of the network.
(ii) charge of each capacitor.

Answer 1

Given : $C_1=C_2=C_3=C_4=C=15\mu F$

Since $C_1,C_2$ and $C_3$ are in series and this combination is connected in parallel to $C_4$.

So, equivalent capacitance of $C_1,C_2$ and $C_3$, $C_s=\frac{C}{3}=\frac{15}{3}=5\mu F$

Equivalent capacitance of $C_s$ and $C_4$, $C_{eq}=C_s+C_4=5+15=20\mu F$

Voltage across $C_4,$ $V=500volts$

So, charge on $C_4$ $Q_4=C_{4}V=15\times {10}^{-6}\times 500=7.5mC$

Charge each on $C_1$, $C_2$ and $C_3$, $Q=5\times {10}^{-6}\times 500=2.5mC$