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A 400 V, 50 kVA, 0.8 p.f. Leading Δ - connected, 50 Hz synchronous machine has a synchronous reactance of 2 Ω and negligible armature resistance. The friction and windage losses are 2 kW and the core loss is 0.8 kW. If the shaft is supplying 9 kW load at a power factor of 0.8 leading, then the line current (in A) drawn is (Answer up to two decimal places
Correct answer is '21.29'. Can you explain this answer?
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A 400 V, 50 kVA, 0.8 p.f. Leading Δ - connected, 50 Hz synchronous ma...
Given a 400 V, 50 Hz and 0.8 p.f. loading delta connection 50 Hz synchronous machine, the reactance is 2Ω. The friction and windage losses are 2 kW and core loss is 0.8 kW and shaft supply is 9 kW at a 0.8 loading power factor.
Input power = 9 kW + 2 kW + 0.8 kW = 11.8 kW
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A 400 V, 50 kVA, 0.8 p.f. Leading Δ - connected, 50 Hz synchronous ma...
Given information:
- Voltage (V) = 400 V
- Apparent power (S) = 50 kVA
- Power factor (p.f.) = 0.8 leading
- Synchronous reactance (Xs) = 2 Ω
- Friction and windage losses (Pfw) = 2 kW
- Core loss (Pc) = 0.8 kW
- Load power (Pload) = 9 kW
- Load power factor (p.f.load) = 0.8 leading
Calculating the line current (I):
1. Calculate the apparent power drawn by the synchronous machine:
S = V * I
I = S / V
2. Calculate the reactive power drawn by the synchronous machine:
Q = √(S² - P²)
Q = √((50 kVA)² - (9 kW)²)
3. Calculate the power factor angle (θ):
tan(θ) = Q / P
θ = atan(Q / P)
4. Determine the power factor angle (θ) based on the given power factor (p.f.):
If the power factor is leading, then θ is positive.
If the power factor is lagging, then θ is negative.
Since the power factor is leading, θ is positive.
5. Calculate the reactive power (Q) based on the power factor angle (θ):
Q = P * tan(θ)
6. Determine the synchronous reactive power (Qs) based on the synchronous reactance (Xs):
Qs = V² / Xs
7. Calculate the synchronous current (Is):
Is = Qs / V
8. Calculate the armature current (Iarm):
Iarm = √(I² - Is²)
9. Calculate the field current (If):
If = Iarm / √3
10. Calculate the line current (I):
I = √(Iarm² + If²)
Calculating the line current (I) with explanation:
1. Calculate the apparent power drawn by the synchronous machine:
S = 50 kVA = 50,000 VA
V = 400 V
I = 50,000 VA / 400 V = 125 A
2. Calculate the reactive power drawn by the synchronous machine:
P = Pload = 9 kW = 9,000 W
Q = √((50,000 VA)² - (9,000 W)²) = 49,749.37 VAR
3. Calculate the power factor angle (θ):
tan(θ) = 49,749.37 VAR / 9,000 W
θ = atan(49,749.37 VAR / 9,000 W) = 80.93°
4. Determine the power factor angle (θ) based on the given power factor (p.f.):
Since the power factor is leading, θ is positive.
5. Calculate the reactive power (Q) based on the power factor angle (θ):
Q = 9,000 W * tan(80.93°) = 49,749.37 VAR
6. Determine the synchronous reactive power
- Voltage (V) = 400 V
- Apparent power (S) = 50 kVA
- Power factor (p.f.) = 0.8 leading
- Synchronous reactance (Xs) = 2 Ω
- Friction and windage losses (Pfw) = 2 kW
- Core loss (Pc) = 0.8 kW
- Load power (Pload) = 9 kW
- Load power factor (p.f.load) = 0.8 leading
Calculating the line current (I):
1. Calculate the apparent power drawn by the synchronous machine:
S = V * I
I = S / V
2. Calculate the reactive power drawn by the synchronous machine:
Q = √(S² - P²)
Q = √((50 kVA)² - (9 kW)²)
3. Calculate the power factor angle (θ):
tan(θ) = Q / P
θ = atan(Q / P)
4. Determine the power factor angle (θ) based on the given power factor (p.f.):
If the power factor is leading, then θ is positive.
If the power factor is lagging, then θ is negative.
Since the power factor is leading, θ is positive.
5. Calculate the reactive power (Q) based on the power factor angle (θ):
Q = P * tan(θ)
6. Determine the synchronous reactive power (Qs) based on the synchronous reactance (Xs):
Qs = V² / Xs
7. Calculate the synchronous current (Is):
Is = Qs / V
8. Calculate the armature current (Iarm):
Iarm = √(I² - Is²)
9. Calculate the field current (If):
If = Iarm / √3
10. Calculate the line current (I):
I = √(Iarm² + If²)
Calculating the line current (I) with explanation:
1. Calculate the apparent power drawn by the synchronous machine:
S = 50 kVA = 50,000 VA
V = 400 V
I = 50,000 VA / 400 V = 125 A
2. Calculate the reactive power drawn by the synchronous machine:
P = Pload = 9 kW = 9,000 W
Q = √((50,000 VA)² - (9,000 W)²) = 49,749.37 VAR
3. Calculate the power factor angle (θ):
tan(θ) = 49,749.37 VAR / 9,000 W
θ = atan(49,749.37 VAR / 9,000 W) = 80.93°
4. Determine the power factor angle (θ) based on the given power factor (p.f.):
Since the power factor is leading, θ is positive.
5. Calculate the reactive power (Q) based on the power factor angle (θ):
Q = 9,000 W * tan(80.93°) = 49,749.37 VAR
6. Determine the synchronous reactive power
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A 400 V, 50 kVA, 0.8 p.f. Leading Δ - connected, 50 Hz synchronous machine has a synchronous reactance of 2 Ω and negligible armature resistance. The friction and windage losses are 2 kW and the core loss is 0.8 kW. If the shaft is supplying 9 kW load at a power factor of 0.8 leading, then the line current (in A) drawn is (Answer up to two decimal placesCorrect answer is '21.29'. Can you explain this answer?
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A 400 V, 50 kVA, 0.8 p.f. Leading Δ - connected, 50 Hz synchronous machine has a synchronous reactance of 2 Ω and negligible armature resistance. The friction and windage losses are 2 kW and the core loss is 0.8 kW. If the shaft is supplying 9 kW load at a power factor of 0.8 leading, then the line current (in A) drawn is (Answer up to two decimal placesCorrect answer is '21.29'. 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 400 V, 50 kVA, 0.8 p.f. Leading Δ - connected, 50 Hz synchronous machine has a synchronous reactance of 2 Ω and negligible armature resistance. The friction and windage losses are 2 kW and the core loss is 0.8 kW. If the shaft is supplying 9 kW load at a power factor of 0.8 leading, then the line current (in A) drawn is (Answer up to two decimal placesCorrect answer is '21.29'. 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 400 V, 50 kVA, 0.8 p.f. Leading Δ - connected, 50 Hz synchronous machine has a synchronous reactance of 2 Ω and negligible armature resistance. The friction and windage losses are 2 kW and the core loss is 0.8 kW. If the shaft is supplying 9 kW load at a power factor of 0.8 leading, then the line current (in A) drawn is (Answer up to two decimal placesCorrect answer is '21.29'. Can you explain this answer?.
A 400 V, 50 kVA, 0.8 p.f. Leading Δ - connected, 50 Hz synchronous machine has a synchronous reactance of 2 Ω and negligible armature resistance. The friction and windage losses are 2 kW and the core loss is 0.8 kW. If the shaft is supplying 9 kW load at a power factor of 0.8 leading, then the line current (in A) drawn is (Answer up to two decimal placesCorrect answer is '21.29'. 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 400 V, 50 kVA, 0.8 p.f. Leading Δ - connected, 50 Hz synchronous machine has a synchronous reactance of 2 Ω and negligible armature resistance. The friction and windage losses are 2 kW and the core loss is 0.8 kW. If the shaft is supplying 9 kW load at a power factor of 0.8 leading, then the line current (in A) drawn is (Answer up to two decimal placesCorrect answer is '21.29'. 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 400 V, 50 kVA, 0.8 p.f. Leading Δ - connected, 50 Hz synchronous machine has a synchronous reactance of 2 Ω and negligible armature resistance. The friction and windage losses are 2 kW and the core loss is 0.8 kW. If the shaft is supplying 9 kW load at a power factor of 0.8 leading, then the line current (in A) drawn is (Answer up to two decimal placesCorrect answer is '21.29'. Can you explain this answer?.
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