AC Resistance of wires - was 8 kHz Tesla Coil

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

Hi Jim and Bart,

The work that Dr Gary Johnson did for AC resistance seems to solve 
the Rac/Rdc problem for round wires (no proximitry effects).  The 
differential equation for the current density J(r) is:

d^2 J/dr^2  +dJ/rdr +T^2 J =0  (not sure what T is)

The solution is a Bessel function of the first kind zero order and 
the solution does involve an infinite series. The current density is 
complex and has real and imaginary parts that vary with radius from 
the wire center.  He carves up the wire into cylindrical shells and 
computes the average current density, cross sectional area, and 
current for each shell (still a complex number).  He then computes 
the power in each shell by multiplying the current by its complex 
conjugate to get the real portion of I^2 for each shell.  From this, 
the power in each shell is known.  He then sums up the shell powers 
to get total power and divides by Rdc*|I|^2.  Now for the good 
part.  He has created a table of Rac/Rdc for various ratios of 
wire_radius(wr)/flat_plane_skin_depth(sd).  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

Bart,  what I'm thinking is since you compute the sd and know the wr, 
you can just interpolate into the table and use the Rdc to compute the Rac.

Jim, how does Gary's table compare to the RDRE table???

Gerry R.