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Re: [TCML] Spark models, revisited

On 10/30/12 4:32 PM, Antonio Carlos M. de Queiroz wrote:

On 30/10/2012 10:07, Jim Lux wrote:


Using the formula from E.B. Rosa's 1907 NBS work... a 100 cm long wire
that is 0.04 cm in diameter has an inductance of 1.55 uH..

=2*(B9*LN((B9+SQRT(B9^2+C9^2))/C9)-SQRT(B9^2+C9^2)+B9/4+C9)
B9 is length
C9 is diameter
gives resulting inductance in cm (Yeah, back at the turn of the
century, they didn't always use MKS or SI units).. divide by 1000 to
get microhenries.

Using the formula implemented in the Inca program, tested by direct
solving of the numerical integral, I get 1.692 uH. Using then the speed
of light as propagation speed:
c = 1/sqrt(L*C)
C = 1/(c^2*L) = 1/(3e8^2*1.692e-6) = 6.57 pF
Quite close to the measurements.
A complication with this calculation is that the inductance of 1 m of
wire is not exactly the inductance per meter of the wire for small
lengths. But my calculation is not giving a constant L/m for small
lengths. Something to verify.
Rosa's equation doesn't either. For very long lengths (lengths of >10 meters and diameters <1 cm) it seems to converge.. that's because those length^2+diameter^2 terms get dominated by the length.)
BTW, Rosa has different equations for hollow tubes and solid bars (although there's not a huge difference, of course) 

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