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Temperature rise of machine field winding

Short answer

Find R0 = R20/(1+α0×20) = 147.33 Ω. Hot temperature t from R_hot = R0(1+α0 t) gives t = 59.46°C. Temperature rise = 59.46−20 = 39.46°C ≈ 39.5°C.

The temperature rise of the machine field winding was determined by the measurement of the winding resistance at 20°C the field winding resistance was 160 Ohm(Ω). After running the machine for some hours at full load the resistance is 185 Ω. If the temperature coefficient of resistance of the copper winding is 4.3 × 10⁻³/°C at 0°C. Determine the temperature rise of the machine.

Copper resistance rises with temperature, so the rise can be found from the resistance values.

Data

R₂₀ = 160 Ω, R_hot = 185 Ω, α₀ = 4.3 × 10⁻³ per °C at 0°C

Step 1: Resistance at 0°C

R₂₀ = R₀ (1 + α₀ × 20) 160 = R₀ (1 + 0.086) = 1.086 R₀ R₀ = 147.33 Ω

Step 2: Hot temperature

R_t = R₀ (1 + α₀ t) 185 = 147.33 (1 + 0.0043 t) 1 + 0.0043 t = 1.2557 t = 59.46°C

Step 3: Temperature rise

Rise = 59.46 − 20 = 39.46°C

Answer: Temperature rise ≈ 39.5°C (final temperature ≈ 59.5°C)

✓ Answer checked by Claude Opus 5.5 (high effort)

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