Editing Skin effect (section)

==== Resistance ====
The most important effect of skin effect on the impedance of a single wire is the increase of the wire's resistance, and consequent [[Copper loss|losses]]. The effective resistance due to a current confined near the surface of a large conductor (much thicker than {{mvar|δ}}) can be solved as if the current flowed uniformly through a layer of thickness {{mvar|δ}} based on the DC resistivity of that material. The effective cross-sectional area is approximately equal to {{mvar|δ}} times the conductor's circumference.
Thus a long cylindrical conductor such as a wire, having a diameter {{mvar|D}} large compared to {{mvar|δ}}, has a resistance ''approximately'' that of a hollow tube with wall thickness {{mvar|δ}} carrying direct current. The AC resistance of a wire of length {{mvar|ℓ}} and resistivity <math>\rho</math> is:
<math display="block">R\approx
{{\ell \rho} \over {\pi (D-\delta) \delta}}
\approx
{{\ell \rho} \over {\pi D \delta}}
 </math>

The final approximation above assumes <math>D \gg \delta</math>.

A convenient formula (attributed to [[Frederick Terman|F.E. Terman]]) for the diameter {{mvar|D}}{{sub|W}} of a wire of circular cross-section whose resistance will increase by 10% at frequency {{mvar|f}} is:<ref>{{harvnb|Terman|1943|p=??}}</ref>
<math display="block">D_\mathrm{W} = {\frac{200~\mathrm{mm}}{\sqrt{f/\mathrm{Hz}}}}</math>

This formula for the increase in AC resistance is accurate only for an isolated wire. For nearby wires, e.g. in a [[Electrical cable|cable]] or a coil, the AC resistance is also affected by [[proximity effect (electromagnetism)|proximity effect]], which can cause an additional increase in the AC resistance.
The ''internal'' [[Electrical impedance|impedance]] per unit length of a segment of round wire is given by:<ref name="Walter_Weeks"/>{{rp|p=40}}
<math display="block"> \mathbf{Z}_\text{int} =   \frac { k \rho } { 2 \pi R }      \frac {  J_0(k R) } { J_1(k R) }.</math>

This impedance is a [[complex number|complex]] quantity corresponding to a resistance (real) in series with the [[Electrical reactance|reactance]] (imaginary) due to the wire's internal self-[[inductance]], per unit length.