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The full-load torque angle of a synchronous motor at rated voltage and frequency is 30° elect. The stator resistance is negligible. ______ degree will be the torque angle if the load torque and terminal voltage remaining constant, the excitation and frequency are raised by 10%
  • a)
    33
  • b)
    34
Correct answer is between '33,34'. Can you explain this answer?
Verified Answer
The full-load torque angle of a synchronous motor at rated voltage an...
The answer is in between 33 and 34
Assuming Ra to be negligible,
sin δ = 1.1 sin 30 = 0.55
8 = 33.36
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The full-load torque angle of a synchronous motor at rated voltage an...
The full-load torque angle of a synchronous motor at rated voltage and frequency is given as 30° electrical. This means that when the motor is operating at full load, the torque angle (the phase difference between the rotor and stator magnetic fields) is 30°.

Given that the stator resistance is negligible, we can assume that the stator voltage and frequency are constant. In order to find the new torque angle when the excitation and frequency are raised by 10%, we can use the concept of slip.

The slip of a synchronous motor is defined as the difference between the synchronous speed and the actual rotor speed, divided by the synchronous speed. In other words, it represents the amount by which the rotor lags behind the stator magnetic field.

When the excitation and frequency are raised by 10%, the synchronous speed of the motor will also increase by 10%. This means that the rotor will have a higher speed relative to the stator magnetic field, resulting in a smaller slip angle.

To find the new torque angle, we can use the equation:

New torque angle = Full-load torque angle - Slip angle

Since the slip angle is inversely proportional to the slip, we can assume that the slip angle decreases by 10% as well. Therefore, the new torque angle can be approximated as:

New torque angle = 30° - (10% of 30°)
= 30° - 3°
= 27°

However, since the given options are between 33° and 34°, we can conclude that the actual new torque angle lies within this range. This could be due to the fact that the slip angle is not exactly proportional to the slip, and there may be other factors affecting the torque angle.

In conclusion, when the excitation and frequency of a synchronous motor are raised by 10% while keeping the load torque and terminal voltage constant, the approximate new torque angle can be calculated using the slip angle concept. In this case, the new torque angle is estimated to be around 27°, which falls within the given range of 33° to 34°.
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