Re: AC Resistance of wires - was 8 kHz Tesla Coil

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Antonio Carlos M. de Queiroz" <acmdq@xxxxxxxxxx>

Tesla list wrote:

> Original poster: "Gerry  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>

> The work that Dr Gary Johnson did for AC resistance seems to solve 
> the Rac/Rdc problem for round wires (no proximitry effects).
>...
The following table shows
> this for wr/sd up to 8.
> wr/sd      Rac/Rdc
> ------------------
>   1            1.020
>   2            1.263
>   3            1.763
>   4            2.261
>   5            2.743
>   6            3.221
>   7            3.693
>   8            4.154

A simpler calculation, assuming that all the current is concentrated in
a ring with thickness equal to the skin depth and external radius equal
to the wire radius, results in:
Rac/Rdc = (wr/sd)^2/(2wr/sd-1)
The table above becomes:
wr/sd    Rac/Rdc  difference
1        1.000    -2.0%
2        1.333    +5.5%
3        1.800    +2.1%
4        2.286    +1.1%
5        2.778    +1.3%
6        3.273    +1.6%
7        3.769    +2.1%
8        4.267    +2.7%
The error is negligible in comparison with the more exact formula. So,
the basic skin depth formula can be used with round conductors quite
well.

Antonio Carlos M. de Queiroz