In the shown arrangement of a meter bridge, if AC corresponding to null deflection of galvanometer is x, what would be its value if the radius of the wire AB is doubled? 

At null point, $R_1/R_2=R_3/R_4=x(100-x).$ If radius of the wire is doubled, then the resistance of AC will change and the resistance of CB will also change. But since $R_1/R_2$ does not change, so $R_3/R_4$ should also not change at null point. Therefore, point C does not change.