1. Find equivalent capacitance between A and B in the combination… - Vidyadip

Question

Find equivalent capacitance between A and B in the combination given below. Each capacitor is of 2 μF capacitance.

If a dc source of 7 V is connected across AB, how much charge is drawn from the source and what is the energy stored in the network?

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Answer

Capacitors $C_2$, $C_3$ $\text{and}$ $C_4 $$\ \ \text{are in parallel}$$\therefore C_{234}=C_2+C_3+C_4$
$\therefore C_{234}=6\mu F$
Capacitors $C_1$,$C_{234}$ $\text{and}$ $C_5$ are in series$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_{234}}+\frac{1}{C_5}=\frac{1}{2}+\frac{1}{6}+\frac{1}{2}$
$=\frac{7}{6}\mu F$
$C_{equivalent}=\frac{6}{7}\mu F$
Charge drawn from the source$Q=C_{eq}V,$
$=\frac{6}{7}\times7\mu C=6\mu C$
Energy stored $U=\frac{Q^2}{2C}$$=\frac{6\times6\times10^{-12}\times7}{2\times6\times10^{-6}}\text{J}$
$=21\mu \text{J}$.

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