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

Original poster: "D.C. Cox" <resonance@xxxxxxxxxx>




What does the "wr" (wire radius?) and the "sd" stand for in this equation?

Dr. Resonance

Your formula is the same as the one I originally quoted but reduced somewhat. ie:
Rac/Rdc = pi*wr^2/ (pi*wr^2 - pi*[wr-sd]^2) = (wr/sd)^2 / (2wr/sd - 1)
The equation for sd that the web site gave seems to predict a little larger sd than what JAVATC calculated. If this also predicts a little larger sd than what you used, then that would bring the positive errors down some. This approach seems fine to me, but some want something more accurate and doing interpolation on a table lookup is also fine with me. Once the program adds the routine, we dont have to worry about it anymore :-)))
Gerry R.

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