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Technology / Technical guide
Copper Winding Resistance & Temperature Approximation
Copper winding resistance changes with conductor temperature. Comparing values at different temperatures therefore requires a reference and an applicable material model. A temperature correction explains part of a resistance difference; it does not identify an insulation class or permissible machine temperature.
Keep the reference temperature in the equation.
A coefficient describes the local temperature sensitivity of resistance under stated conditions, not a universal operating rating.
01 / Two quantities
Separate material resistivity from winding resistance.
For a uniform conductor in a simple model, R = ρl/A, where resistivity ρ describes the material, l is length and A is cross-sectional area.
For a uniform conductor in a simple model, R = ρl/A, where resistivity ρ describes the material, l is length and A is cross-sectional area. Winding resistance also reflects the conductor geometry and the electrical path being represented.
A material name alone cannot determine a winding’s resistance. Turn arrangement, conductor dimensions and branch definition remain relevant. A resistance between line terminals may represent a combination of branches rather than one branch.
02 / Temperature effect
Explain why warmer copper usually resists more.
In the ordinary engineering-temperature region, increasing copper temperature increases scattering of conduction electrons and raises resistivity.
In the ordinary engineering-temperature region, increasing copper temperature increases scattering of conduction electrons and raises resistivity. OpenStax presents the approximate temperature dependence of metallic conductors.
This ordinary trend should not be extended without qualification to arbitrary temperature ranges or other materials. A near-reference linear approximation is a model, while an actual conductor can have material and geometric details beyond it.
03 / Linear correction
State the coefficient’s reference.
A common approximation is R(T) ≈ Rref[1 + αref(T − Tref)], with αref in inverse kelvins or inverse degrees Celsius.
A common approximation is R(T) ≈ Rref[1 + αref(T − Tref)], with αref in inverse kelvins or inverse degrees Celsius. Rref and αref belong to the same stated reference temperature and material assumption.
Differences of temperature in K and °C are numerically equal, although their absolute readings are not. Changing the reference temperature while retaining an unexplained coefficient can make a correction inconsistent. The coefficient is not a winding-temperature limit.
04 / Mathematical example
Illustrate the approximation without product values.
In an explicitly hypothetical model, Rref = 1 Ω, assumed αref = 0.004/K and a temperature increase of 50 K give R ≈ 1.20 Ω.
In an explicitly hypothetical model, Rref = 1 Ω, assumed αref = 0.004/K and a temperature increase of 50 K give R ≈ 1.20 Ω. These are illustrative assumptions, not a MARSTON measured resistance or a recommended material coefficient.
At an unchanged RMS current and using that resistance model, resistive loss I²R would increase by the same 20%. If current changes as well, the loss ratio changes. Temperature alone therefore does not establish the complete machine loss.
05 / Correction limits
Separate DC resistance from wider AC behaviour.
A DC resistance model does not capture every frequency-dependent winding effect.
A DC resistance model does not capture every frequency-dependent winding effect. Skin and proximity effects, inductive response and other machine losses can change the relationship between current, voltage and heating under AC conditions.
The impedance guide distinguishes resistance from reactance. A temperature-corrected resistance should not be labelled as the machine’s complete impedance, output-voltage drop or efficiency map.
06 / Material scope
Keep conductor facts apart from insulation classification.
A resistance change can be informative only within its stated model and path definition.
A resistance change can be informative only within its stated model and path definition. It does not certify a winding’s insulation system, establish a hot-spot temperature or explain every possible difference between two observations.
High-temperature copper winding wire is confirmed for the five current MARSTON models, but its exact grade and the machines’ actual winding resistances are unconfirmed. The thermal-class guide addresses that separate topic.
Continue the review with Generator Inductance, Reactance & Impedance.
Continue the review with Permanent-Magnet Temperature & Demagnetisation.
Continue the review with Semiconductor Conduction & Switching Loss Mechanisms.
General background: OpenStax: geometry, resistivity and local temperature approximation. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Resistivity | ρ in Ω·m | Material property under stated conditions. |
| Resistance | R in Ω | Also depends on conductor geometry and path. |
| Reference | Rref, Tref and αref | Use a consistent local approximation. |
| Temperature difference | ΔT in K or °C | Same numerical difference, different absolute scales. |
| Resistive loss | I²R in W | Current basis and resistance conditions matter. |
Engineering questions.
Does copper material alone determine winding resistance?
No. Geometry and the represented electrical path also matter.
Can the same coefficient be used at any reference temperature?
Not without a consistent model defining its reference.
Is the example coefficient a confirmed MARSTON value?
No. It is an explicit assumption for arithmetic illustration.
Does correction establish an insulation class?
No. Conductor resistance and insulation classification are different subjects.
Does DC resistance equal complete AC impedance?
No. Reactance and frequency-dependent effects require their own representation.
Does a warmer winding always imply the same percentage loss increase?
Only if the relevant current and resistance-model conditions are unchanged.
Technical enquiry
Discuss the technical question.
Copper winding resistance changes with conductor temperature. Share the model and applicable operating or design information for an engineering discussion.