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Electrical resistance vs temperature

Electrical resistance vs temperature

Electrical resistance vs temperature

(OP)
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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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

RE: Electrical resistance vs temperature

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

RE: Electrical resistance vs temperature

(OP)
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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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

RE: Electrical resistance vs temperature

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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RE: Electrical resistance vs temperature

(OP)
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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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

RE: Electrical resistance vs temperature

(OP)
This link gives the same equation but stipulates that R0 and T0 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 T0. But I can work it out from what I have assuming dR/dT is constant.

http://www.utc.edu/Faculty/Tatiana-Allen/Temp.html

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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

RE: Electrical resistance vs temperature

(OP)
Since my alpha of .00393 is specified at 20 C and I'm looking for R0 @ 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.

R0 = R1 / (1+alpha(T1-T0))

R0 = 6.54 ohms (at 20 C)

That comes back to 5 ohms at -40 C.

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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

RE: Electrical resistance vs temperature

(OP)
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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The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

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