Resistance due to temperature change

[xxkylexx]

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

 

[hage567]

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

 

[m2003]

Hello Kyle,

Thank you for sharing your work and thought process. Your approach is correct, but I believe there is a small error in your calculation. When finding the value of "a", you used the temperatures in Kelvin instead of Celsius. The formula for temperature coefficient of resistance is a = (R2-R1)/(R1(T2-T1)), where T is in Kelvin. So, in this case, it would be a = (11.20-8.70)/(8.70(363-293)) = 0.0039.

Using this value of a, we can find the resistance at -20°C as:
R = 8.70[1 + 0.0039(-40)] = 8.31 ohms.

I hope this helps clarify the issue. Keep up the good work!
Best,