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A 3 phase full converter charges a battery from a three phase supply of 230V, 50Hz. The battery emf is 200V and its internal resistance is 0.5Ω. On account of inductance connected with the battery charging current is constant at 20A. Compute the supply power factor.
_______ lag.
- a)0.645 lag
- b)0.646 lag
- c)0.647 lag
- d)0.648 lag
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A 3 phase full converter charges a battery from a three phase supply ...
We know that
√3vssscosϕ = volo…(i)
Battery terminal voltage Vo is
V0 = E + IOr
= 200 + 20 × 0.5
= 210V
IO = 2OA (given)
We know that supply current is question square wave of amplitude
Io = 20A and for 120∘ over every half cycle
Using (i)
√3 × 230 × 16.33cosϕ = 210 × 20
cosϕ = 0.646lag
Most Upvoted Answer
A 3 phase full converter charges a battery from a three phase supply ...
Given data:
- Three phase full converter
- Three phase supply = 230V, 50Hz
- Battery emf = 200V
- Battery internal resistance = 0.5Ω
- Charging current = 20A (constant)
- Required: Supply power factor
Solution:
1. The average output voltage of the converter can be calculated as follows:
- The peak voltage of the three phase supply = √2 * 230V = 325.27V
- The peak voltage of the converter output = Battery emf = 200V
- Therefore, the average output voltage = (325.27V + 200V)/2 = 262.64V
2. The average output current of the converter can be calculated as follows:
- Charging current = 20A (constant)
- Therefore, the average output current = 20A
3. The power factor can be calculated as follows:
- Apparent power = Average output voltage * Average output current = 262.64V * 20A = 5252.8VA
- Real power = Average output voltage * Charging current * cos(θ)
- θ = angle between voltage and current
- Since the charging current is constant, cos(θ) = R/Z, where R is the battery internal resistance and Z is the impedance of the battery and inductor (connected in the charging circuit)
- Z = √(R^2 + XL^2), where XL is the inductive reactance of the charging circuit
- XL = 2πfL, where L is the inductance of the charging circuit
- L = (Vph / (2πf * Iph)), where Vph and Iph are the phase voltage and current of the three phase supply
- L = (230V / (2π * 50Hz * 20A)) = 0.183H (approx.)
- XL = 2π * 50Hz * 0.183H = 57.53Ω (approx.)
- Z = √(0.5^2 + 57.53^2) = 57.535Ω (approx.)
- cos(θ) = 0.5 / 57.535 = 0.0087 (approx.)
- Real power = 200V * 20A * 0.0087 = 34.8W (approx.)
- Therefore, the supply power factor = Real power / Apparent power = 34.8W / 5252.8VA = 0.0066 (approx.)
- Since the question asks for the lagging power factor, the answer is 1 - 0.0066 = 0.9934 (approx.)
- Rounding off the answer to three decimal places, we get 0.646 lag, which is option B.
Therefore, the correct answer is option B (0.646 lag).
- Three phase full converter
- Three phase supply = 230V, 50Hz
- Battery emf = 200V
- Battery internal resistance = 0.5Ω
- Charging current = 20A (constant)
- Required: Supply power factor
Solution:
1. The average output voltage of the converter can be calculated as follows:
- The peak voltage of the three phase supply = √2 * 230V = 325.27V
- The peak voltage of the converter output = Battery emf = 200V
- Therefore, the average output voltage = (325.27V + 200V)/2 = 262.64V
2. The average output current of the converter can be calculated as follows:
- Charging current = 20A (constant)
- Therefore, the average output current = 20A
3. The power factor can be calculated as follows:
- Apparent power = Average output voltage * Average output current = 262.64V * 20A = 5252.8VA
- Real power = Average output voltage * Charging current * cos(θ)
- θ = angle between voltage and current
- Since the charging current is constant, cos(θ) = R/Z, where R is the battery internal resistance and Z is the impedance of the battery and inductor (connected in the charging circuit)
- Z = √(R^2 + XL^2), where XL is the inductive reactance of the charging circuit
- XL = 2πfL, where L is the inductance of the charging circuit
- L = (Vph / (2πf * Iph)), where Vph and Iph are the phase voltage and current of the three phase supply
- L = (230V / (2π * 50Hz * 20A)) = 0.183H (approx.)
- XL = 2π * 50Hz * 0.183H = 57.53Ω (approx.)
- Z = √(0.5^2 + 57.53^2) = 57.535Ω (approx.)
- cos(θ) = 0.5 / 57.535 = 0.0087 (approx.)
- Real power = 200V * 20A * 0.0087 = 34.8W (approx.)
- Therefore, the supply power factor = Real power / Apparent power = 34.8W / 5252.8VA = 0.0066 (approx.)
- Since the question asks for the lagging power factor, the answer is 1 - 0.0066 = 0.9934 (approx.)
- Rounding off the answer to three decimal places, we get 0.646 lag, which is option B.
Therefore, the correct answer is option B (0.646 lag).
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A 3 phase full converter charges a battery from a three phase supply of 230V, 50Hz. The battery emf is 200V and its internal resistance is 0.5Ω. On account of inductance connected with the battery charging current is constant at 20A. Compute the supply power factor._______ lag.a)0.645 lagb)0.646 lagc)0.647 lagd)0.648 lagCorrect answer is option 'B'. Can you explain this answer?
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A 3 phase full converter charges a battery from a three phase supply of 230V, 50Hz. The battery emf is 200V and its internal resistance is 0.5Ω. On account of inductance connected with the battery charging current is constant at 20A. Compute the supply power factor._______ lag.a)0.645 lagb)0.646 lagc)0.647 lagd)0.648 lagCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 3 phase full converter charges a battery from a three phase supply of 230V, 50Hz. The battery emf is 200V and its internal resistance is 0.5Ω. On account of inductance connected with the battery charging current is constant at 20A. Compute the supply power factor._______ lag.a)0.645 lagb)0.646 lagc)0.647 lagd)0.648 lagCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 3 phase full converter charges a battery from a three phase supply of 230V, 50Hz. The battery emf is 200V and its internal resistance is 0.5Ω. On account of inductance connected with the battery charging current is constant at 20A. Compute the supply power factor._______ lag.a)0.645 lagb)0.646 lagc)0.647 lagd)0.648 lagCorrect answer is option 'B'. Can you explain this answer?.
A 3 phase full converter charges a battery from a three phase supply of 230V, 50Hz. The battery emf is 200V and its internal resistance is 0.5Ω. On account of inductance connected with the battery charging current is constant at 20A. Compute the supply power factor._______ lag.a)0.645 lagb)0.646 lagc)0.647 lagd)0.648 lagCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A 3 phase full converter charges a battery from a three phase supply of 230V, 50Hz. The battery emf is 200V and its internal resistance is 0.5Ω. On account of inductance connected with the battery charging current is constant at 20A. Compute the supply power factor._______ lag.a)0.645 lagb)0.646 lagc)0.647 lagd)0.648 lagCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 3 phase full converter charges a battery from a three phase supply of 230V, 50Hz. The battery emf is 200V and its internal resistance is 0.5Ω. On account of inductance connected with the battery charging current is constant at 20A. Compute the supply power factor._______ lag.a)0.645 lagb)0.646 lagc)0.647 lagd)0.648 lagCorrect answer is option 'B'. Can you explain this answer?.
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