A.C. resistance

If a conductor is carrying high alternating currents, the distribution of current is not
evenly disposed throughout the cross-section of the conductor. This is due to two
independent effects known as the 'skin effect' and the 'proximity effect'.
If the conductor is considered to be composed of a large number of concentric
circular elements, those at the centre of the conductor will be enveloped by a greater
magnetic flux than those on the outside. Consequently the self-induced back e.m.f, will
be greater towards the centre of the conductor, thus causing the current density to be
less at the centre than at the conductor surface. This extra concentration at the surface
is the skin effect and it results in an increase in the effective resistance of the conductor.
The magnitude of the skin effect is influenced by the frequency, the size of the
conductor, the amount of current flowing and the diameter of the conductor.
The proximity effect also increases the effective resistance and is associated with the
magnetic fields of two conductors which are close together. If each carries a current in
the same direction, the halves of the conductors in close proximity are cut by more
magnetic flux than the remote halves. Consequently, the current distribution is not even
throughout the cross-section, a greater proportion being carried by the remote halves. If
the currents are in opposite directions the halves in closer proximity carry the greater
density of current. In both cases the overall effect results in an increase in the effective
resistance of the conductor. The proximity effect decreases with increase in spacing
between cables.
Mathematical treatment of these effects is complicated because of the large number
of possible variations.
Skin and proximity effects may be ignored with small conductors carrying low
currents. They become increasingly significant with larger conductors and it is often
desirable for technical and economic reasons to design the conductors to minimise
them.

D.C. resistance

Factors affecting d.c. conductor resistance in terms of material resistivity and purity are
discussed elswhere The latter are associated with the fact that the prime path of the current is a helical one following the individual wires in the conductor. Hence if an attempt is made to calculate the
resistance of a length of stranded conductor a factor must be applied to cater for the
linear length of wire in the conductor to allow for extra length caused by the stranding
effect. In a multicore cable an additional factor must be applied to allow for the
additional length due to the lay of the cores.
The d.c. resistance is also dependent on temperature as given by
Rt --- R20[l + a20(t - 20)]
where Rt : conductor resistance at t°C (Ω)
R20 = conductor resistance at 20°C (Ω)
a20 = temperature coefficient of resistance of the conductor material at 20°C
t = conductor temperature (°C)