Question

The equivalent capacitance between points $X$ and $Y$ in figure shown is :

• A. $\frac{6}{5}\mu F$
• B. $4\mu F$
• C. $\frac{18}{5}\mu F$
• D. none of these

Answer 1

The correct option is C $\frac{18}{5}\mu F$

As the structure is balanced Wheatstone bridge, so $5\mu F$ capacitor will draw no charge from battery and may be removed. Now the circuit is a simple circuit.
$4\mu F$ and $6\mu F$ are in series, then $C_1=\left(\frac{4\times 6}{6+4}\right)$
$3\mu F$ and $2\mu F$ are also in series, therefore $C_2=\left(\frac{3\times 2}{3+2}\right)$
Now $C_1$ and $C_2$ are in parallel
$C_{eq}=\left(\frac{4\times 6}{6+4}\right)+\left(\frac{3\times 2}{3+2}\right)=\frac{18}{5}\mu F$