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The temperature rise of a motor under constant load follows

  • A.a straight line rising indefinitely with the time for which it runs
  • B.a sinusoidal variation about the ambient temperature of the room
  • C.a step change to its final value at the instant of switching on
  • D.an exponential approach to a final value

Answer: D

The lumped model gives \( \theta = \theta_f(1 - e^{-t/\tau}) \), so the rise is quick at first and then slows as the losses begin to escape as fast as they are generated. Around four time constants brings it within two per cent of the final value.

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