The thinner the wire, the bigger its resistance. You must use thick wire to carry a large current, or the wire gets too hot and melts (like a fuse). The relationship between resistance and thickness is not straightforward.Halving the thickness of a wire does not double the resistance. Compare this with the relationship between a wire's resistance and its length.he cross-sectional area is what you get when you cut through the wire, at right angles to its length, and look at the cut surface. If the wire is round, the cross-section is a flat circle and the area is πr2.