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Conductor Resistance Temperature Correction

Also known as temperature coefficient of resistance

R2=R1[1+α(T2−T1)]R_{2} = R_{1} \left[ 1 + \alpha (T_{2} - T_{1}) \right]

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Metals conduct worse when hot: heat jostles the lattice and scatters the electrons. Copper's coefficient is about 0.00393 per kelvin referenced to 20 °C, aluminium's about 0.00403, so a 10 Ω copper winding at 20 °C measures 10 × (1 + 0.00393 × 55) = 12.16 Ω at 75 °C — a 22% rise. Because a kelvin and a Celsius degree are the same size, only the temperature difference matters; if your α is quoted per °F, choose that unit and the solver handles it.

This relation is quietly one of the most useful in the trade. It turns a winding's cold and hot resistance into a motor's average winding temperature, the basis of the standard heat-run test — no thermocouple can reach the middle of a coil, but its resistance always can. It is also why cable ampacity tables assume a conductor temperature, why voltage-drop constants differ between 20 °C and 75 °C, and why platinum's clean, repeatable version of this curve makes the RTD the workhorse of industrial temperature measurement.

Conductor Resistance Temperature Correction
R2=R1[1+α(T2−T1)]R_{2} = R_{1} \left[ 1 + \alpha (T_{2} - T_{1}) \right]
Where
  • R2R_{2}= Resistance at T₂
  • R1R_{1}= Resistance at T₁
  • α\alpha= Temperature coefficient
  • T2T_{2}= New temperature
  • T1T_{1}= Reference temperature
Missing one of these? Work it out first, then come back
Part of this formula set

Voltage drop

4 formulasSingle-phase and three-phase voltage drop, percent drop and conductor resistance at temperature — sizing a conductor for a long run.