The copper windings of a motor have a resistance of 50 Ω at 20° C when the motor is idle. After the motor has run for several hours the resistance rises to 58Ω. What is the temperature of the windings now? (Ignore changes in the dimensions of the windings).

The temperature of the windings are 60.61 °C

Explanation:

Step 1: Data given

Resistance = 50 Ω

Temperature = 20.0 °C

After the motor has run for several hours the resistance rises to 58Ω.

Step 2: Calculate the new temperature

Formula: R = Rref(1 + α(T-Tref))

⇒with α = temperature coëfficiënt of Cupper at 20 °C = 0.00394/°C

⇒with Tref = reference temperature = 20°C

⇒with T = end temperature = TO BE DETERMINED

⇒with R = resistance at end temperature = 58Ω

⇒with Rref = resistance at reference temperature =  50 Ω

==> T = (R/Rref - 1)/α + Tref  

T = (58/50) - 1 )/ 0.00394 + 20

   T = 60.61 °C

The temperature of the windings are 60.61 °C

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