The field winding of d.c. motor connected across 230 V supply takes 1.15 A at room temp. of 20°C. After working for some hours the current falls to 0.26 A, the supply voltage remaining constant. Calculate the final working temperature of field winding. Resistance temperature coefficient of cop�per at 20°C is 1/254.5.
Answers
Answer:
across 230 V supply takes 1.15 A at room temp. of 20°C. After working for some hours the current falls to 0.26 A, the supply voltage remaining constant. Calculate the final working temperature of field winding. Resistance temperature coefficient of cop�per at 20°C is 1/254.5.
Explanation:
across 230 V supply takes 1.15 A at room temp. of 20°C. After working for some hours the current falls to 0.26 A, the supply voltage remaining constant. Calculate the final working temperature of field winding. Resistance temperature coefficient of cop�per at 20°C is 1/254.5.
Answer:
To calculate the final working temperature of the field winding, we need to use the temperature coefficient of copper to find the change in resistance of the field winding.
Explanation:
To calculate the final working temperature of the field winding, we can use the formula:
R2 = R1 [1 + α(T2 - T1)]
Where R1 is the initial resistance of the field winding, R2 is the final resistance of the field winding, α is the temperature coefficient of copper at 20°C, T1 is the initial temperature of the field winding (20°C), and T2 is the final temperature of the field winding (unknown).
To find R1, we can use Ohm's law:
R1 = V/I1 = 230/1.15 = 200 ohms
To find R2, we can use Ohm's law again:
R2 = V/I2 = 230/0.26 = 884.6 ohms
Plugging in the values we have:
884.6 = 200 [1 + (1/254.5)(T2 - 20)]
Simplifying the equation:
T2 = ((884.6/200) - 1) / (1/254.5) + 20
T2 = 468.3°C
Therefore, the final working temperature of the field winding is 468.3°C.
This calculation shows the importance of understanding the relationship between temperature and resistance in electrical systems. As the temperature of a component increases, its resistance will also generally increase. This can lead to changes in the performance and behaviour of the system, which is why it is important to account for temperature effects in design and analysis. In this case, the change in current in the field winding is a sign that its temperature has increased, which can affect the motor's overall performance. By calculating the final temperature of the winding, we can gain a better understanding of how this change may impact the motor's operation.
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