Skin effect with AC and DC current

Skin effect is the tendency of alternating current to flow mostly near the outer surface ("skin") of a conductor, instead of being spread evenly over its cross-section.

With DC

• The current is steady, so there is no changing flux and no induced emf inside the conductor.
• The current divides according to resistance only. Every filament has the same resistance, so the current density is uniform over the whole area.
• The full area is used, and the resistance is $R_{dc} = \rho l/A$.

With AC

• The changing current produces alternating flux inside the conductor. A filament at the centre is linked by more flux (internal plus external) than a filament at the surface.
• So the central filaments have higher inductance and reactance, and larger back-emf. The current is pushed towards the surface, where the impedance is lower.
• The effective conducting area is reduced, so $R_{ac} > R_{dc}$. The effect grows with frequency, diameter and permeability. The skin depth is $\delta = \sqrt{2\rho/(\omega\mu)}$, about 9.3 mm for copper at 50 Hz.

 DC (uniform J)          AC (J higher near surface)
   .-------.               .-------.
  / ::::::: \             / ####### \
 | ::::::::: |           | ##.....## |
 | ::::::::: |           | #.......# |
  \ ::::::: /             \ ####### /
   '-------'               '-------'

Effects and remedies: higher losses and lower efficiency. It is reduced by using stranded, ACSR (current flows mainly in the outer aluminium strands), hollow or bundled conductors.