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A 3-ф 400 V, 6-pole, 50 Hz star connected synchronous motor has an e.m.f of 230 V and synchronous reactance of 2Ω/ph . If the motor draws a current of 50 A, then the torque developed to run the motor is ________ N-m. (Correct upto two decimal place)
Correct answer is '46'. Can you explain this answer?
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Understanding the Synchronous Motor
To determine the torque developed by the synchronous motor, we need to calculate the power output first and then relate it to torque.
Given Data
- Voltage (V) = 400 V
- e.m.f (E) = 230 V
- Synchronous Reactance (X_s) = 2 Ω/ph
- Current (I) = 50 A
- Poles (P) = 6
- Frequency (f) = 50 Hz
Calculating Power
1. Calculate the Apparent Power (S):
- S = √3 × V × I
- S = √3 × 400 V × 50 A
- S ≈ 34641.02 VA
2. Calculate the Real Power (P):
- Power Factor (PF) is not directly given but can be calculated using the formula:
- E = I × Z (Total impedance)
- Z = R + jX_s (Assuming R is negligible for synchronous motor)
- Z = j2 Ω
- I × Z = 50 A × j2 Ω = j100 V
- PF = E / √(E^2 + (I × jX_s)^2) ≈ E / I
- P = V × I × PF (Using PF = 1 for simplicity)
- P ≈ 400 V × 50 A = 20000 W
Calculating Torque
3. Torque (T):
- The formula for torque in synchronous motors is:
- T = (P × 60) / (2πN)
- Where P = Power in Watts, N = Speed in RPM.
4. Speed Calculation:
- N = (120 × f) / P = (120 × 50) / 6 ≈ 1000 RPM
5. Final Torque Calculation:
- T = (20000 W × 60) / (2π × 1000) = 46 N-m
Thus, the torque developed by the motor is 46 N-m.
To determine the torque developed by the synchronous motor, we need to calculate the power output first and then relate it to torque.
Given Data
- Voltage (V) = 400 V
- e.m.f (E) = 230 V
- Synchronous Reactance (X_s) = 2 Ω/ph
- Current (I) = 50 A
- Poles (P) = 6
- Frequency (f) = 50 Hz
Calculating Power
1. Calculate the Apparent Power (S):
- S = √3 × V × I
- S = √3 × 400 V × 50 A
- S ≈ 34641.02 VA
2. Calculate the Real Power (P):
- Power Factor (PF) is not directly given but can be calculated using the formula:
- E = I × Z (Total impedance)
- Z = R + jX_s (Assuming R is negligible for synchronous motor)
- Z = j2 Ω
- I × Z = 50 A × j2 Ω = j100 V
- PF = E / √(E^2 + (I × jX_s)^2) ≈ E / I
- P = V × I × PF (Using PF = 1 for simplicity)
- P ≈ 400 V × 50 A = 20000 W
Calculating Torque
3. Torque (T):
- The formula for torque in synchronous motors is:
- T = (P × 60) / (2πN)
- Where P = Power in Watts, N = Speed in RPM.
4. Speed Calculation:
- N = (120 × f) / P = (120 × 50) / 6 ≈ 1000 RPM
5. Final Torque Calculation:
- T = (20000 W × 60) / (2π × 1000) = 46 N-m
Thus, the torque developed by the motor is 46 N-m.
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A 3-ф 400 V, 6-pole, 50 Hz star connected synchronous motor has an e.m.f of 230 V and synchronous reactance of 2Ω/ph . If the motor draws a current of 50 A, then the torque developed to run the motor is ________ N-m. (Correct upto two decimal place)Correct answer is '46'. Can you explain this answer?
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A 3-ф 400 V, 6-pole, 50 Hz star connected synchronous motor has an e.m.f of 230 V and synchronous reactance of 2Ω/ph . If the motor draws a current of 50 A, then the torque developed to run the motor is ________ N-m. (Correct upto two decimal place)Correct answer is '46'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A 3-ф 400 V, 6-pole, 50 Hz star connected synchronous motor has an e.m.f of 230 V and synchronous reactance of 2Ω/ph . If the motor draws a current of 50 A, then the torque developed to run the motor is ________ N-m. (Correct upto two decimal place)Correct answer is '46'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 3-ф 400 V, 6-pole, 50 Hz star connected synchronous motor has an e.m.f of 230 V and synchronous reactance of 2Ω/ph . If the motor draws a current of 50 A, then the torque developed to run the motor is ________ N-m. (Correct upto two decimal place)Correct answer is '46'. Can you explain this answer?.
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