Question

The field coil of a motor has a resistance of 2500 ohm at 15°C. By how much will the resistance increase if the motor attained an average temperature of 45°C when running? Take the temperature coefficient as 0.00428/°C referred to 0°C. (A) 250 ohm

(B) 500 ohm
(C) 750 ohm
(D) 1000 ohm

Answer 1

The resistance of the field coil of the motor will increase by approximately 250 ohm.

Step-by-step explanation:

To find the increase in resistance, we can use the temperature coefficient of resistance formula:

R2 = R1(1 + α(T2-T1))

Where R2 is the final resistance, R1 is the initial resistance, α is the temperature coefficient of resistance, T2 is the final temperature in degrees Celsius, and T1 is the initial temperature in degrees Celsius.

Given that the initial resistance (R1) is 2500 ohm, the temperature coefficient of resistance (α) is 0.00428/°C, the initial temperature (T1) is 15°C, and the final temperature (T2) is 45°C, we can substitute these values into the formula:

R2 = 2500(1 + 0.00428(45-15))

R2 ≈ 2500 + 0.06044(45-15)

R2 ≈ 2750 + 0.06044(30)

R2 ≈ 2750 + 0.06044(30)

R2 ≈ 2750 + 0.1812

R2 ≈ 2750.1812

R2 ≈ 2750.2

The increase in resistance is approximately 250 ohm.