I think the problem lies in this assumption: ========================= Since L and r both are the units of length……one can be expressed in terms of the other i.e. r = nL ======================== I will show why it is flawed. See, for a wire of given cross-section, the area of cross-section is constant, hence its radius is also constant. Length has NOTHING to do with the cross-section. So no matter by how much you change the length, cross-section is same and hence the radius is constant. It cannot be related with the length. You cannot generalise a concept just by looking at a given piece of a wire.