From: "Tesla list" <tesla@xxxxxxxxxx>
To: tesla@xxxxxxxxxx
Subject: Re: AC Resistance of wires - was 8 kHz Tesla Coil
Date: Sun, 02 Oct 2005 22:34:22 -0600
Original poster: "Gerry Reynolds" <gerryreynolds@xxxxxxxxxxxxx>
Hi Antonio,
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