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# Skin effect

The skin effect is the tendency of a high-frequency electric current to distribute itself in a conductor so that the current density near the surface of the conductor is greater than that at its core. It causes the effective resistance of the conductor to increase with the frequency of the current.

The effect was first explained by Lord Kelvin in 1887.

The change in resistance due to the skin effect is quantified by calculating the skin depth σ. The conductor behaves as if the material below the skin depth σ does not exist, and the surface layer of the conductor has the same resistance as it does for direct current.

$\sigma={{\left({{2\rho}\over{\omega \mu}}\right)}^{1/2}}$

where

ρ = resistivity[?] of conductor
ω = angular frequency of current
μ = magnetic permeability of conductor

Having calculated σ, the effective resistance of the conductor can then be obtained by geometry. For example, for a cylindrical conductor such as a round wire, the resistance is:

$R={{\rho \over \sigma}\left({L\over{\pi D}}\right)}$

where

L = length of conductor
D = diameter of conductor

A type of cable called litz wire (from the German Litzendraht, woven wire) is used to mitigate the skin effect. It consists of a number of insulated wire strands woven together in a carefully designed pattern, so that the overall magnetic field acts equally on all the wires and causes the total current to be distributed equally among them.

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