Skip to content
RFrftools.io
Motor

Winding Resistance vs Temperature

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

Loading calculator...

Formula

R(T)=R25×[1+α×(T−25°C)]R(T) = R₂₅ × [1 + α × (T − 25°C)]
α— Temperature coefficient (Cu: 0.00393) (/°C)
T— Operating temperature (°C)

How It Works

This calculator determines DC motor winding resistance and its effect on copper losses and speed regulation. Motor repair technicians, quality control engineers, and drive system designers use it to diagnose winding faults and predict performance variation with temperature. Winding resistance measurement is the primary diagnostic test for detecting shorted turns, open windings, and connection problems.

Per IEC 60034-4, armature resistance (R_a) includes conductor resistance plus brush contact resistance for brushed motors. Copper resistance follows the temperature coefficient equation: R(T) = R_25 × [1 + 0.00393 × (T - 25)], where 0.00393/°C is copper's resistance coefficient per IEC 60028. At typical operating temperature of 100°C, resistance increases 29.5% above the 25°C value.

Resistance directly impacts three performance metrics: (1) Copper losses P_Cu = I²×R_a, comprising 30-60% of total motor losses per IEEE 112; (2) Speed regulation—voltage drop I×R_a reduces back-EMF voltage and speed; (3) Maximum current at stall I_stall = V/R_a. A motor with 2Ω armature resistance on 24V supply draws 12A stall current—this determines fuse sizing and driver current capability. Per NEMA MG-1, winding resistance tolerance is ±10% from nameplate value at 25°C.

Worked Example

A 48V BLDC motor for an e-scooter has phase resistance 0.15Ω (line-to-line) at 25°C. Operating winding temperature reaches 110°C. Rated current is 30A continuous.

Step 1 — Calculate hot resistance: R_hot = R_25 × [1 + 0.00393 × (T - 25)] R_hot = 0.15 × [1 + 0.00393 × (110 - 25)] R_hot = 0.15 × [1 + 0.334] = 0.15 × 1.334 = 0.200Ω

Step 2 — Calculate copper losses at rated current: P_Cu_cold = I² × R = 30² × 0.15 = 135W P_Cu_hot = 30² × 0.200 = 180W Hot operation increases copper loss by 33%

Step 3 — Assess speed regulation impact: Voltage drop cold: I × R = 30 × 0.15 = 4.5V (9.4% of supply) Voltage drop hot: 30 × 0.200 = 6.0V (12.5% of supply) Speed reduction due to temperature: additional 3.1% at full load

Step 4 — Verify stall current capability: I_stall_hot = V / R = 48 / 0.200 = 240A Controller must handle 240A peak or implement current limiting

Result: At 110°C, winding resistance increases 33% from 0.15Ω to 0.20Ω. This raises copper losses from 135W to 180W and reduces loaded speed by an additional 3.1%. Design thermal management to limit temperature rise or derate continuous current.

Practical Tips

  • ✓Per IEEE 1415 motor diagnostics, resistance 10% below datasheet indicates shorted turns (lower impedance path); 10% above indicates high-resistance joints, broken strands, or brush wear
  • ✓Always normalize measurements to 25°C reference: R_25 = R_measured / [1 + 0.00393 × (T_measured - 25)] per IEC 60034-1 to compare with specifications
  • ✓For BLDC motors, measure line-to-line (phase-to-phase): star-wound motors read 2× single-phase resistance; delta-wound read 2/3× per phase—verify winding configuration before calculating

Common Mistakes

  • ✗Using standard multimeter for low resistance: Per IEC 60034-4, contact resistance and meter error introduce ±0.1-0.5Ω error; use 4-wire Kelvin measurement for resistances below 10Ω to achieve ±1% accuracy
  • ✗Ignoring brush resistance in brushed DC motors: Carbon brush contact adds 0.1-0.5Ω total (0.05-0.25Ω per brush per Mersen brush specifications)—this is part of effective armature circuit resistance
  • ✗Assuming cold and hot resistance are equal: At 100°C, copper resistance is 29.5% higher than at 25°C per IEC 60028; neglecting this causes 30% underestimate of hot copper losses and speed regulation

Frequently Asked Questions

Per IEEE 118 and IEC 60034-4: Use a 4-wire (Kelvin) low-resistance ohmmeter for values below 10Ω. For brushed DC motors, position the shaft to place two commutator segments in series (maximum reading position). Apply test current below 10% of rated to avoid heating. Temperature-correct to 25°C using copper coefficient 0.00393/°C. Measurement uncertainty should be ±1% for acceptance testing per NEMA MG-1.
Per Krishnan's 'Electric Motor Drives': Motor speed constant K_v (RPM/V) and torque constant K_t (N·m/A) are independent of winding resistance—they depend on magnet strength and winding turns. However, speed regulation (speed change with load) is directly proportional to R_a: higher resistance means more I×R_a drop and worse regulation. Select lower-resistance windings for applications requiring tight speed control without closed-loop feedback.
No—per IEC 60287, at VFD carrier frequencies (4-16 kHz), winding inductance dominates: Z = √(R² + (2πfL)²). At 8 kHz with 1 mH inductance, inductive reactance is 50Ω versus 0.5Ω DC resistance—100× higher. DC resistance only applies to DC copper loss calculation. Use AC impedance measured at operating frequency for current ripple and PWM filter design per IEEE 519.

Shop Components

As an Amazon Associate we earn from qualifying purchases.

NEMA 17 Stepper Motor

NEMA 17 bipolar stepper motors for precision motion control

Amazon →

Stepper Motor Driver (A4988)

A4988 stepper driver modules for microstepping control

Amazon →

DC Motor with Encoder

12 V DC motors with encoders for closed-loop drive applications

Amazon →

Related Calculators

Motor

Motor Heat

Calculate motor heat dissipation, temperature rise, and operating temperature from input power and efficiency.

Motor

Motor Efficiency

Calculate motor efficiency, power losses, and heat dissipation from electrical input and mechanical output measurements.

Motor

DC Motor

Calculate DC motor speed, torque, power, and efficiency from electrical parameters

Motor

Stepper Motor

Calculate stepper motor speed, step frequency, and travel per revolution