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Re: graphical analysis menagerie (was: Need Ideas)



On Sun, 2 Jan 2000, brian whatcott wrote:

At 15:34 1/2/00 -0500, John D wrote:

... If you take ordinary Allen-Bradley carbon resistors and cool them
down, the resistance depends on temperature. This makes them useful as
secondary thermometers in the range of roughly 77 Kelvin to maybe 10
milliKelvin. There is a large range where the resistance is
exponential in the square root of temperature to remarkably high
precision. ...

John's description possibly suggests the equation
Resistance = exp(k*sqrt(temperature))

Allen Bradley carbon composition resistors decrease in resistance with
temperature. So the scaling constant k is evidently negative.

Taking a sample A-B 0.27ohm resistor:
Temp (K) Res (ohms)
0.3 10^6
1 10^2
3 3
10 1
30 0.7
100 0.3 (from a graph of Rose-Innes's)

I don't have a curve fitting package here. Can someone else
fit this?

Make that Resistance = r*exp(k*sqrt(temperature))

Assuming that your data is good and that John's statement in true, then
your data does not all lie within the "large range" that John refers to.
I can get a tolerable, but far from excellent fit to no more than three of
these data points--not an impresssive feat for a two parameter fitting
function.

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm