Electrical resistance vs temperature

[dgallup]

I'm trying to do a simple calculation to find the electrical resistance of a copper coil at a different temperature. I thought I knew the equation but to check I took my results an worked it backwards and got a different result than I started with. I did a web search and found several online calculators and which give the exact same result.

Here's what I've got:
copper coef. of resistivity alpha = 0.00393 /deg C
T1 -40 deg C
R1 5 ohms
T2 20 deg C

R2 = R1[1+alpha(T2-T1)] = 6.179 ohms

But when you back solve it
T1 20 deg C
R1 6.179 ohms
T2 -40 deg C

R2 comes out 4.715 ohms, not the 5 ohms I started with.

I can see what is going on here, in the first case the [1+alpha(T2-T1)] factor is 1.236, in the second case it is 0.764, multiply them together and you get 0.944 which is not equal to 1.000 so I don't come back to where I started. But it should. So what am I doing wrong?



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[hamsuplo]

You mixed up T1 and T2? You should use the same for each.

R2 = R1[1+alpha(T2-T1)] = 6.179 ohms

R1 = R2/[1+alpha(T2-T1)] = 6.179/[1+0.0039(20--40)]=5.007293

 

[IRstuff]

You need to show your equation. R1 is simply R2 divided by the 1.2358. Your 0.764 is not correct. Just invert 1.2358, you should get 0.8092

TTFN
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[dgallup]

But which condition is 1 and which is 2 is completely arbitrary. And in the online calculators the same equation is used, you can not invert it.

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[IRstuff]

So, don't use the online calculator. It's not a very complicated problem:

That said, the equation CANNOT be used with arbitrary temperature differences. The alpha is for a POSITIVE temperature coefficient. Therefore, the only way to do it in whatever calculator you're using is to use a different temperature coefficient, 0.00318/ºC

TTFN
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[dgallup]

Well, if the equation can not be used with arbitrary temperature variations then it can't be used at all. Never the less, it's the only equation I've found doing numerous searches.

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[dgallup]

This link gives the same equation but stipulates that R[sub]0[/sub] and T[sub]0[/sub] can only be the values at which alpha is specified, not an arbitrary value. Unfortunately, that makes this equation unusable to me as I don't have the resistance at T[sub]0[/sub]. But I can work it out from what I have assuming dR/dT is constant.

[URL unfurl="true"]http://www.utc.edu/Faculty/Tatiana-Allen/Temp.html[/url]

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[dgallup]

Since my alpha of .00393 is specified at 20 C and I'm looking for R[sub]0[/sub] @ 20 C then it works out that my first equation in the original post was the one that was wrong and needed to be inverted.

R[sub]0[/sub] = R[sub]1[/sub] / (1+alpha(T[sub]1[/sub]-T[sub]0[/sub]))

R[sub]0[/sub] = 6.54 ohms (at 20 C)

That comes back to 5 ohms at -40 C.


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[IRstuff]

Which is what I suggested to you in my original posting.

TTFN
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[dgallup]

No, it's not. The first equation was the one that had to be inverted. That makes the resistance at 20 C 6.54 ohms and the factor is 1.308 which is the reciprocal of the .764 factor in the second equation. So you actually had it backward.

We can close this now all is right in the world.

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[IRstuff]

I'll just refer you to one of the many sites on the web:

http://spiff.rit.edu/classes/phys273/manual/temp_coeff.html

TTFN
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