# Dependance of resistance on cross sectional area

I was wondering about a possibility......what if we take two conducting wires of the same material and the same length; both will have the same value of cross sectional area but one will be a hollow one and the other will be a completely filled one.......In such a situation will there be any difference in resistance shown by them if we apply the same potential difference across them and please assume that both of them obey ohm's law at room temperature......

• When you say they have the same cross sectional area, do you mean, eg a solid wire with radius 3 units vs a hollow wire with outer radius 5 units and inner radius 4 units, which both have an area of $9\pi$ square units? Sep 6, 2018 at 5:51
• yes that's what I wanted to ask Sep 7, 2018 at 2:36

For DC (ignoring secondary effects), the resistance would be about the same.

For AC, the resistance of the hollow conductor will be lower due to the skin effect, which causes the density of AC current to increase toward the surface of a conductor.

For a solid conductor, this would lead to the effective reduction of the active cross-section area and therefore, to the increased resistance. For a hollow conductor, this would not make as much difference.

As the frequency increases, the skin depth (the layer under the surface of a conductor where most of the current will concentrate) decreases, which further benefits the hollow conductor.

Of course both will have different resistance because here "A" is the area through which electrons flow, in case of hallow cylinder it is area of ring and in case solid cylinder it is area of circle

• I think you misunderstood my question. I have mentioned that the value of cross sectional area for both of them are same......area of the ring = area of the circle = A......in some way......so you can assume the hollow one to be larger than the filled one Sep 6, 2018 at 8:51

There can be difference in resistance, for example, if the hollow conductor has thin walls, as "It has been long known that the resistivity of a conductor increases sharply as its dimensions reduce to its electron mean free path" (http://stars.library.ucf.edu/cgi/viewcontent.cgi?article=4927&context=etd , see also E.H. Sondheimer (1952): The mean free path of electrons in metals, Advances in Physics, 1:1, 1-42)