Question

Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance $C$ if the equivalent capacitance between point $A$ and $B$ is to be $1\mu F$ is :

• A. $\frac{31}{23}\mu F$
• B. $\frac{32}{23}\mu F$
• C. $\frac{33}{23}\mu F$
• D. $\frac{34}{23}\mu F$

Answer 1

Answer: (B)

$\frac{8\times 12}{18}=4\mu F$
$4\mu F+4\mu F=8\mu F$
$\frac{8\times 1}{8+1}=\frac{8}{9}\mu F$
$\frac{8\times 4}{8+4}=\frac{32}{12}=\frac{8}{3}\mu F$
$\frac{8}{3}+\frac{8}{9}=\frac{24+8}{9}=\frac{32}{9}\mu C$
$\frac{\frac{32}{9}\times C}{\frac{32}{9}+C}=1$
$\Rightarrow \frac{32}{9}\times C=\frac{32}{9}+C$
$\Rightarrow C\left(\frac{32-9}{9}\right)=\frac{32}{9}$
$C=\frac{32}{23}\mu F$