Resistance due to temperature change

AI Thread Summary
The discussion focuses on calculating the resistance of a metal wire at -20°C, given its resistance at 20°C and 90°C. The initial calculations used the formula R = Ro[1 + a(T-To)] to find the temperature coefficient 'a' as 0.0041. However, the error occurred in the temperature difference calculation, where the correct value should have been negative, resulting in R = 8.70[1 + 0.0041(-40)]. This correction leads to the accurate resistance value at -20°C. The clarification emphasizes the importance of correctly applying temperature differences in resistance calculations.
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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
 
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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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