I am trying to find the resistance (in ohm/km) from 20 degrees Celsius of a metric conductor size of 10 mm^2 to 75 degrees Celsius resistance. By use of the equation temperature change:

R = Rref [( 1 + alpha ( T - Tref)]
alpha is a constant coefficient at 20 degrees Celsius for copper, aluminum, etc conductors.

If we want to know the resistance temperature change to 75, using 20 degrees Celsius coefficient, we get a certain value. Is the resistance the same if we used 75 degrees Celsius coefficient for alpha to find the 20 degrees Celsius resistance change?

How different would the coefficient values be using either 20 degrees and 75 degrees?

 

If alpha at 20C is different from alpha at 75C then linear extrapolation between those temperatures using both alpha values will give two different results.

How different would the coefficient values be using either 20 degrees and 75 degrees?

Check a resistance versus temperature graph and see.

 

Lots of info on the web

 

The precise method is to integrate it using alpha as a function of T over the range. Very similar to how you treat Cp, the heat capacity, in heat transfer problems (chemical engineering). But you can use numerical approximations. One point is not very good, averaging (interpolating) two points is "good enough" for many applications, going to 3 or 4 points probably drops the residual error below the precision of most real-world concerns. Integration gives you "infinite" points.

 

Most excellent gentlemen for the quick response. I have been researching this and trying to use the metric size converting over to imperial. Both using a different temperature resistance, imperial at 75 degrees and metric at 20 degrees. The difference between the two alphas for copper is only 0.001. Learning more from your responses, thats always perfect