electricity

The resistance of a wire R = ρ l/A
where ρ - resistivity of the wire(its constant for a material)
            l - Length of the wire
            A - area of the crossection

Now A = πr² where r - radius of the cross section. If d is the diameter then  
r = d/2

Hence A = 1/4πd²

This implies R  1/A  R1/d²

i.e. if the diameter is doubled the resistance reduces to 1/4 of the original value.