Question

Find equivalent capacitance between $A$ and $B$

• A. $\frac{25}{32}\,\mu F$
• B. $\frac{32}{25}\,\mu F$
• C. $\frac{32}{9}\,\mu F$
• D. $\frac{9}{32}\,\mu F$

Answer 1

Answer: (B)

Capacitors, $2$ and $3$ are in series, their equivalent capacitance $C'$ is given by
$\frac{1}{C'}=\frac{1}{1\mu F}+\frac{1}{8\mu F}=\frac{9}{8}\mu F$
or $C'=\frac{8}{9} \mu F $
Capacitors 5 and 4 are in series, their equivalent capacitance $C''$ is given by
$\frac{1}{C''}=\frac{1}{8 \mu\,F}+\frac{1}{4\mu\,F}=\frac{3}{8} \mu \,F$
or $C''=\frac{8}{3}\mu F$
Now, the capacitance $C$' and $C$'' are in parallel [Figure 1 ] their equivalent capacitance $C$''' will be

$C''' = \frac{8}{9} \mu F+\frac{8}{3} \mu F =\frac{32}{9}\mu F$
Now capacitance $C$''' and capacitor 1 are in series [Figure 2], hence the equivalent capacitance between A and B is given by

$\frac{1}{C_{eqi}}=\frac{1}{C^{m}}+\frac{1}{2\mu F}$
$=\frac{9}{32 \mu F}+\frac{1}{2\,\mu F}=\frac{25}{32} \mu F $
or $C_{eqi} =\frac{32}{25}\mu F$