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A field coil of a shunt motor has a resistance of 45 Ω at 20° C. Find the average temperature of the winding at the end of the run when the resistance is increased to 48 Ω. The temperature coefficient of resistance is 0.004/°C.

A field coil of a shunt motor has a resistance of 45 Ω at 20° C. Find the average temperature of the winding at the end of the run when the resistance is increased to 48 Ω. The temperature coefficient of resistance is 0.004/°C. Correct Answer 38° C

Concept:

Resistance at a temperature t is given by

Rt = R0(1 + α Δt)

Where Rt = resistance at final temperature

R0 = resistance at initial temperature

α = temperature coefficient

Δt = change in temperature

Calculation:

Given Rt = 48 ohm

R0 = 45 ohm

α = 0.004/° C

48 = 45 (1 + 0.004 × Δt)

⇒ Δt = 16.67°

Δt = T2 - T1

Final temperature, T2 = 20 + 16.67 = 36.67° ≈ 38°

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