Question

Following figure shows a network of capacitors where the numbers indicate capacitance in $\mu F.$ The equivalent capacitance between points A and B is

• A. $\frac{28}{9}\mu F$
  
• B. $\frac{32}{9}\mu F$
  
• C. $4\mu F$
  
• D. $\frac{40}{9}\mu F$

Answer 1

The correct option is B

$\frac{32}{9}\mu F$

The series combination of 6 and 12 is equivalent to 4 and the parallel combination of 2 and 2 is equivalent to 4.
Hence the network can be simplified as shown in Fig.(a). The parallel combinations of 4 and 4 is equivalent to 8 and the series combination 8 and 4 is equivalent to 8/3.
The network further simplifies as shown in Fig.(b). The series combination of 1 and 8 gives 8/9, as shown in Fig.(c)
Now 8/3 and 8/9 are in parallel. Hence the net capacitance of the network is
$C=\frac{8}{3}+\frac{8}{9}=\frac{32}{9}\mu F$