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The rotor of a 3-phase induction motor has a resistance per phase of 0.04 ohm. This motor has a 0.2-ohm standstill reactance per phase. Neglect stator resistance. If the external resistance 0.02Ω is added to the circuit then what is the percentage improvement in p.f. during starting?
- a)5.67 %
- b)22.38 %
- c)26.25%
- d)46.60 %
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The rotor of a 3-phase induction motor has a resistance per phase of ...
Understanding Power Factor Improvement
To calculate the percentage improvement in power factor (p.f.) during the starting of a 3-phase induction motor when an external resistance is added, we first need to analyze the motor's equivalent circuit parameters.
Given Parameters:
- Rotor resistance per phase (R_r): 0.04 Ω
- Standstill reactance per phase (X): 0.2 Ω
- External resistance (R_ext): 0.02 Ω
Initial Impedance Calculation:
The initial impedance (Z_initial) without external resistance is given by:
- Z_initial = R_r + jX
- Z_initial = 0.04 + j0.2
The magnitude of Z_initial (|Z_initial|) is:
- |Z_initial| = √(R_r² + X²)
- |Z_initial| = √(0.04² + 0.2²) = √(0.0016 + 0.04) = √0.0416 ≈ 0.2039 Ω
Power Factor Calculation without External Resistance:
The power factor (p.f.) is given by:
- p.f. = R / |Z|
- p.f. (initial) = 0.04 / 0.2039 ≈ 0.196
New Impedance with External Resistance:
Now adding external resistance:
- Z_new = R_r + R_ext + jX
- Z_new = 0.04 + 0.02 + j0.2 = 0.06 + j0.2
Magnitude of Z_new (|Z_new|):
- |Z_new| = √(0.06² + 0.2²) = √(0.0036 + 0.04) = √0.0436 ≈ 0.2088 Ω
Power Factor Calculation with External Resistance:
- p.f. (new) = 0.06 / 0.2088 ≈ 0.287
Percentage Improvement in Power Factor:
To find the improvement:
- Percentage improvement = [(p.f. (new) - p.f. (initial)) / p.f. (initial)] × 100
- Percentage improvement = [(0.287 - 0.196) / 0.196] × 100 ≈ 46.60%
Thus, the percentage improvement in power factor during starting is approximately **46.60%**, matching option 'D'.
To calculate the percentage improvement in power factor (p.f.) during the starting of a 3-phase induction motor when an external resistance is added, we first need to analyze the motor's equivalent circuit parameters.
Given Parameters:
- Rotor resistance per phase (R_r): 0.04 Ω
- Standstill reactance per phase (X): 0.2 Ω
- External resistance (R_ext): 0.02 Ω
Initial Impedance Calculation:
The initial impedance (Z_initial) without external resistance is given by:
- Z_initial = R_r + jX
- Z_initial = 0.04 + j0.2
The magnitude of Z_initial (|Z_initial|) is:
- |Z_initial| = √(R_r² + X²)
- |Z_initial| = √(0.04² + 0.2²) = √(0.0016 + 0.04) = √0.0416 ≈ 0.2039 Ω
Power Factor Calculation without External Resistance:
The power factor (p.f.) is given by:
- p.f. = R / |Z|
- p.f. (initial) = 0.04 / 0.2039 ≈ 0.196
New Impedance with External Resistance:
Now adding external resistance:
- Z_new = R_r + R_ext + jX
- Z_new = 0.04 + 0.02 + j0.2 = 0.06 + j0.2
Magnitude of Z_new (|Z_new|):
- |Z_new| = √(0.06² + 0.2²) = √(0.0036 + 0.04) = √0.0436 ≈ 0.2088 Ω
Power Factor Calculation with External Resistance:
- p.f. (new) = 0.06 / 0.2088 ≈ 0.287
Percentage Improvement in Power Factor:
To find the improvement:
- Percentage improvement = [(p.f. (new) - p.f. (initial)) / p.f. (initial)] × 100
- Percentage improvement = [(0.287 - 0.196) / 0.196] × 100 ≈ 46.60%
Thus, the percentage improvement in power factor during starting is approximately **46.60%**, matching option 'D'.
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Community Answer
The rotor of a 3-phase induction motor has a resistance per phase of ...
Given: R2 = 0.04Ω
R2(external) = 0.02Ω, X2 = 0.2Ω
At starting power factor is given by, p.f. 
Without external resistance p.f.
with external resistance p.f. 
So, percentage improvement in p.f. 
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The rotor of a 3-phase induction motor has a resistance per phase of 0.04 ohm. This motor has a 0.2-ohm standstill reactance per phase. Neglect stator resistance. If the external resistance 0.02Ω is added to the circuit then what is the percentage improvement in p.f. during starting?a)5.67 %b)22.38 %c)26.25%d)46.60 %Correct answer is option 'D'. Can you explain this answer?
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The rotor of a 3-phase induction motor has a resistance per phase of 0.04 ohm. This motor has a 0.2-ohm standstill reactance per phase. Neglect stator resistance. If the external resistance 0.02Ω is added to the circuit then what is the percentage improvement in p.f. during starting?a)5.67 %b)22.38 %c)26.25%d)46.60 %Correct answer is option 'D'. 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 The rotor of a 3-phase induction motor has a resistance per phase of 0.04 ohm. This motor has a 0.2-ohm standstill reactance per phase. Neglect stator resistance. If the external resistance 0.02Ω is added to the circuit then what is the percentage improvement in p.f. during starting?a)5.67 %b)22.38 %c)26.25%d)46.60 %Correct answer is option 'D'. 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 The rotor of a 3-phase induction motor has a resistance per phase of 0.04 ohm. This motor has a 0.2-ohm standstill reactance per phase. Neglect stator resistance. If the external resistance 0.02Ω is added to the circuit then what is the percentage improvement in p.f. during starting?a)5.67 %b)22.38 %c)26.25%d)46.60 %Correct answer is option 'D'. Can you explain this answer?.
The rotor of a 3-phase induction motor has a resistance per phase of 0.04 ohm. This motor has a 0.2-ohm standstill reactance per phase. Neglect stator resistance. If the external resistance 0.02Ω is added to the circuit then what is the percentage improvement in p.f. during starting?a)5.67 %b)22.38 %c)26.25%d)46.60 %Correct answer is option 'D'. 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 The rotor of a 3-phase induction motor has a resistance per phase of 0.04 ohm. This motor has a 0.2-ohm standstill reactance per phase. Neglect stator resistance. If the external resistance 0.02Ω is added to the circuit then what is the percentage improvement in p.f. during starting?a)5.67 %b)22.38 %c)26.25%d)46.60 %Correct answer is option 'D'. 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 The rotor of a 3-phase induction motor has a resistance per phase of 0.04 ohm. This motor has a 0.2-ohm standstill reactance per phase. Neglect stator resistance. If the external resistance 0.02Ω is added to the circuit then what is the percentage improvement in p.f. during starting?a)5.67 %b)22.38 %c)26.25%d)46.60 %Correct answer is option 'D'. Can you explain this answer?.
Solutions for The rotor of a 3-phase induction motor has a resistance per phase of 0.04 ohm. This motor has a 0.2-ohm standstill reactance per phase. Neglect stator resistance. If the external resistance 0.02Ω is added to the circuit then what is the percentage improvement in p.f. during starting?a)5.67 %b)22.38 %c)26.25%d)46.60 %Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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