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Motor

Winding Resistance vs Temperature

Calculate motor winding resistance at operating temperature using the copper temperature coefficient of resistance.

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Formula

R(T) = R₂₅ × [1 + α × (T − 25°C)]

α— Temperature coefficient (Cu: 0.00393) (/°C)
T— Operating temperature (°C)

How It Works

DC motor winding resistance (R_a) is the total resistance of the armature circuit, including the winding wire resistance and brush contact resistance. It determines copper losses (P_Cu = I² × R_a), affects motor speed regulation, and governs the maximum current at stall (I_stall = V / R_a). Winding resistance increases with temperature at a rate of approximately +0.393% per °C for copper: R(T) = R_25 × [1 + 0.00393 × (T − 25)]. Measuring cold resistance and comparing to the datasheet value quickly reveals shorted turns or brush wear.

Worked Example

A 12 V DC motor has a datasheet armature resistance of 1.5 Ω at 25 °C. During operation, winding temperature reaches 85 °C. Step 1 — Hot winding resistance: R_hot = R_cold × [1 + 0.00393 × (T − 25)] R_hot = 1.5 × [1 + 0.00393 × (85 − 25)] R_hot = 1.5 × [1 + 0.236] = 1.5 × 1.236 = 1.854 Ω Step 2 — Copper losses at rated current (4 A): P_Cu_cold = 4² × 1.5 = 24 W P_Cu_hot = 4² × 1.854 = 29.7 W (24% increase) Step 3 — No-load speed reduction due to increased winding resistance: V_backEMF at 4 A, cold: V_e = 12 − 4×1.5 = 6 V V_backEMF at 4 A, hot: V_e = 12 − 4×1.854 = 4.58 V Speed drop ≈ (6 − 4.58)/6 × 100 = 23.7% Result: At 85 °C, winding resistance rises 24%, increasing copper losses and noticeably reducing speed under load. Thermal management is critical for maintaining consistent motor performance.

Practical Tips

  • ✓Use winding resistance measurement as a quick diagnostic: a value significantly lower than the datasheet suggests shorted turns; significantly higher suggests broken strands or poor brush contact
  • ✓Always reference winding resistance to 25 °C when comparing measurements taken at different temperatures; this normalises the comparison and reveals real changes in the winding condition
  • ✓For BLDC motors, measure resistance phase-to-phase (twice the single-phase resistance for star windings) or consult the datasheet — the thermal correction formula is identical

Common Mistakes

  • ✗Measuring winding resistance with a standard multimeter — contact resistance and the meter's test current can introduce significant error; use a 4-wire (Kelvin) measurement for resistances below 5 Ω
  • ✗Ignoring brush resistance in brushed DC motors — contact resistance of carbon brushes (0.1–0.5 Ω total) is included in the effective armature resistance and should not be measured separately
  • ✗Assuming cold and hot resistance are the same — at 100 °C winding temperature, copper resistance is 29% higher than at 25 °C, which significantly affects torque-speed curve predictions

Frequently Asked Questions

Use a 4-wire (Kelvin) ohmmeter for resistances below 10 Ω. Connect the current-source leads and voltage-sense leads separately at the motor terminals. Slowly rotate the shaft to find the position giving the highest resistance reading (two commutator segments in series for brushed motors). Record this value as the reference resistance at the ambient temperature.
Lower winding resistance means less voltage drop and more voltage available for back-EMF at a given current, resulting in higher no-load speed and better speed regulation. The motor speed constant K_v (RPM/V) is independent of winding resistance, but the torque-speed slope (speed regulation) is directly proportional to R_a.
No — at VFD carrier frequencies (4–16 kHz), winding inductance dominates impedance. The AC impedance is Z = sqrt(R² + (2πfL)²), which is typically 5–20× higher than DC resistance at carrier frequency. Use DC resistance only for calculating DC copper losses and speed regulation under DC conditions.

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