Question

Take $C_1=4·0\mu \mathrm{F}\mathrm{and}{C}_2=6·0\mu \mathrm{F}$ in figure (31-E3). Calculate the equivalent capacitance of the combination between the points indicated.

Answer 1

(a)


For the combination of capacitors given in figure (a), the pairs of capacitors C₁ and C₂ are in parallel.
The equivalent capacitance of each parallel combination of capacitors is given by
C₁ + C₂ = 4 + 6 = 10 μF
The equivalent circuit can be drawn as:



The equivalent capacitance for the above series circuit is given by
$$\begin{gathered} \frac{1}{C_{\mathrm{eq}}}=\frac{1}{C_1+C_2}+\frac{1}{C_1+C_2}=\frac{1}{10}+\frac{1}{10}=\frac{2}{10} \\ \Rightarrow C_{\mathrm{eq}}=5\mathrm{\mu F} \end{gathered}$$

(b)


For the combination of capacitors given in figure (b), the pairs of capacitors C₁ and C₂ are in parallel.
The equivalent capacitance of each parallel combination of capacitors is given by
C₁ + C₂ = 4 + 6 = 10 μF

The equivalent circuit can be drawn as:


In the above circuit, it can be seen that C_A and C_B are in series and are in parallel to the series combination of C_C and C_B.

The equivalent capacitance for the series combination of C_A and C_B is given by
$$\begin{gathered} \frac{1}{C_{\mathrm{eq}}}=\frac{1}{C_{\mathrm{A}}}+\frac{1}{C_{\mathrm{B}}}=\frac{1}{C_1+C_2}+\frac{1}{C_1+C_2}=\frac{1}{10}+\frac{1}{10}=\frac{1}{5} \\ \Rightarrow C_{\mathrm{eq}}=5\mathrm{\mu F} \end{gathered}$$
Similarly, the equivalent capacitance of the series combination of C_C and C_D is 5 μF.

∴ Net equivalent capacitance = 5 + 5 = 10 μF