Temperature Coefficient of Resistance, Copper

Copper resistance follows R_T = R_20 [1 + α(T − 20)] with α = 0.00393 /K. Warm a winding from 20 °C to 75 °C and its resistance rises 21.6 %; run it to 130 °C class-H insulation temperature and it is up 43 %. This is why the same motor draws different current hot and cold, why voltage drop on a fully loaded feeder is worse than the cold calculation, and why the resistance method can infer average winding temperature without a sensor anywhere in the machine.

The reference temperature is part of the constant: quoted against 0 °C, copper's coefficient is 0.00427 /K, and the two are frequently confused. Aluminium's is 0.00403 /K at 20 °C, close enough that mixed installations behave similarly. Manganin and constantan exist precisely because their coefficients are near zero: that is what makes a precision shunt resistor stable. And note that the coefficient is unit-shaped like a thermal expansion coefficient (per kelvin) but describes something entirely different: it is the fractional change in resistance, not in length.