Resistance due to temperature change

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SUMMARY

The discussion focuses on calculating the resistance of a metal wire at -20°C, given its resistance at 20°C (8.70 ohms) and at 90°C (11.20 ohms). The formula used is R = Ro[1 + a(T-To)], where the temperature coefficient of resistance (a) was calculated as 0.0041. The error identified in the calculation was the incorrect application of the temperature difference, which should have been (-20-20) instead of (40), leading to the correct resistance calculation at -20°C.

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xxkylexx
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A metal wire has a resistance of 8.70 ohms at a temperature of 20°C. If the same wire has a resistance of 11.20 ohms at 90°C, what is the resistance of the wire when its temperature is -20°C?
R = Ro[1 + a(T-To)]
Basically what I did was found a first by using the 2 given resistances and temperatures:
11.20 = 8.70[1 + a(90-20)], and I got a = .0041 .

Then I used this a = .0041 to find the R we were looking for (that was the temperature of -20°C):
R = 8.70[1 + .0041(40)], and I get R = 10.12 ohms -- which is wrong.

I'm not sure what I am doing wrong here.

Any help is appreciated.

Thanks,
Kyle
 
Last edited:
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I think you missed a negative sign. Your (T-To) should be (-20-20), giving -40 instead of +40 in your equation.
 

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