In the shown arrangement of the experiment of the meter bridge if A...

At null point $\frac{R_{1}}{R_{2}}=\frac{R_{3}}{R_{4}}=\frac{x}{100-x}$ If radius of the wire is doubled, then the resistance of $A C$ will change and also the resistance of $C B$ will change. But since $\frac{R_{1}}{R_{2}}$ does not change so, $\frac{R_{3}}{R_{4}}$ should also not change at null point. Therefore the point $C$ does not change.