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 $
$\Rightarrow \frac{32}{9} \times C =\frac{32}{9}+ C$
$\Rightarrow C \left(\frac{32-9}{9}\right)=\frac{32}{9}$
$C =\frac{32}{23}\, \mu F$