Question

In the circuit shown, the effective capacitance between points $X$ and $Y$ is :

• A. $3.33\mu F$
• B. $1\mu F$
• C. $0.44\mu F$
• D. none of these

Answer 1

The correct option is B $1\mu F$

Dotted circuit makes balanced Wheatstone bridge and we can remove the $3\mu F$ capacitance from the circuit.

The circuit can be simplified as shown in the figure.

The net capacitance for Wheatstone bridge part is $C_{eq}=\frac{1\times 2}{1+2}+\frac{1\times 2}{1+2}=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}\mu F$

Now, $\frac{1}{C_{XY}}=\frac{1}{8}+\frac{3}{4}+\frac{1}{8}=\frac{1}{4}+\frac{3}{4}=1$

$⟹C_{XY}=1\mu F$