Re: Primary and copper (fwd)

To: tesla-at-pupman-dot-com
Subject: Re: Primary and copper (fwd)
From: Tesla List <mod1-at-pupman-dot-com>
Date: Sat, 28 Mar 1998 22:23:56 -0700 (MST)
Approved: mod1-at-pupman-dot-com

---------- Forwarded message ----------
Date: Thu, 26 Mar 1998 21:32:30 -0800
From: "Antonio C. M. de Queiroz" <acmq-at-compuland-dot-com.br>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: Primary and copper

Erik Schulz wrote:

>      The following is a list of the 75% current depth in copper at different
> frequency.
> 
> kHz, mils         mil is 0.001 inches
> 1000, 2.6
> 900, 2.7...

Or: 
skin depth=sqrt(resistivity/(pi*frequency)/u0) meters
where u0=pi*4e-7.
For copper (resistivity=1.724e-8 Ohm-m):
skin depth=0.06608/sqrt(frequency) meters, or
skin depth=2602/sqrt(frequency) mils.

This value is valid for flat sheets. For round wires the usual approach
is to consider a sheet wrapped around the wire, what results in:
resistance=(length/diameter)*8.31e-8*sqrt(frequency) (any length unit).
This works if the skin depth is much smaller than diameter/2, but fails
totally for thinner wire or lower frequency.
Do someone know the expression for wire resistance as function of frequency
when the wire radius is not much greater than the skin depth? 

Antonio Carlos M. de Queiroz
http://www.coe.ufrj.br/~acmq