When testing the motor, the resistance of the armature winding is measured before starting work

When testing the motor, the resistance of the armature winding is measured before starting work, at a temperature of 18 degrees, resistance = 0.52 Ohm. At the end of the work, the resistance increased to 0.58 Ohm. Determine the heating temperature.

The dependence of resistance on temperature is determined by the formula:
R = R₀ (1 + a (t-t₀)),
where R is the resistance at temperature t,
R₀ – initial resistance at initial temperature t₀,
a – temperature coefficient of material resistance (0.004041 1 / ° С for copper).
Since the temperature difference is given in the formula, both the Kelvin scale and the Celsius scale can be used.
R = R₀ + aR₀t – aR₀t₀
aR₀t = R – R₀ + aR₀t₀
Find the final temperature t:
t = (R – R₀ + aR₀t₀) / aR₀ = (R – R₀) / aR₀ + t₀ = (0.58 Ohm – 0.52 Ohm) / 0.004041 1 / ° C * 0.52 Ohm + 18 ° C = 47 ° C.

Answer: The winding has heated up to 47 ° C.