The capacitance between the points $A$ and $B$ in the following figure.

• A

  $\frac{3}{8} \mu F$
• Correct answer
  B

  $\frac{9}{4} \mu \mathrm{F}$
• C

  $\frac{4}{5} \mu \mathrm{F}$
• D

  $2 \mu F$

Solution

The given circuit diagram can be represented as
Since,$\frac{C_1}{C_2}=\frac{C_3}{C_4}=\frac{1}{3}$ Hence, given circuit follows the condition of balance wheatstone bridge. Hence, capacitor $C_5$ is ineffective. Now, the circuit diagram is redrawn as
$C_{A B}=\frac{C_1 C_2}{C_1+C_2}+\frac{C_3 C_4}{C_3+C_4}=\frac{1 \times 3}{1+3}+\frac{2 \times 6}{2+6}$ $=\frac{3}{4}+\frac{12}{8}=\frac{9}{4} \mu \mathrm{F}$

Hence, the correct answer is option: 'B'.