If charges flow along the surface of a conductor, why is resistance a function of cross-sectional area?

The skin effect dictates that charges tend to flow along the surface of a conductor. And yet resistance of a material is equal to resistivity multiplied by the cross-sectional area of the material divided by the length. Shouldn't it be based on the surface area?

• You are totally right. But skin effect is frequency dependent. The resistance at DC will be lower than the resistance at some frequency. If cases where the skin depth is larger than the cross section radius, then skin effect is not important. If skin depth is greater than the cross section radius, then you have to calculate the effective cross section using the skin depth. In some cases, pipes are used instead of cables for AC conductors. Why pay money for the center portion of the cable that carries no current? – mkeith Jan 7 '17 at 8:50

The skin effect is an effect of frequency.

At DC there is no skin effect so the resistance is a function of the cross section of the conductor.

As frequency rises, the current tends to decrease at the center of the conductor as you said. For the current to flow only at the surface of the conductor, the frequency of the current should be infinite. In reality there is always current flow with diverse density at different depths of the conductor, but there is never current "only on the surface".

The DC resistance is computed through the entire volume, using the cross sectional area.

For AC, the resistance rises, as current flows in less of the area, concentrating in the surface. As the AC frequency rises, the skin depth reduces, and the resistance increases.

At power line frequencies, 50-60Hz, the skin depth in copper is in the 1cm ballpark, so most practical conductors have their entire cross section used for current.

At 1MHz, the skin depth is less than 0.1mm, so even fine copper wires are starting to show an in creased resistance over DC. At 1GHz, the start of cellular frequencies, it's 2um, so even a thin plating of a different metal on the surface will dominate the resistance.