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A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting): Zm = (12.50 + j15.75)Ω (main winding), Za = (24.50 + j12.75)Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.
Correct answer is between '95,100'. Can you explain this answer?
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A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has ...
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Given information:
- Power of the motor, P = 375 W
- Voltage, V = 230 V
- Frequency, f = 50 Hz
- Main winding impedance, Zm = 12.50 + j15.75
- Auxiliary winding impedance, Za = 24.50 + j12.75
Calculating the current:
The power, voltage, and current are related by the formula: P = VI
Convert power to kilowatts:
P = 375 W = 0.375 kW
Calculate the current:
V = 230 V
I = P / V = 0.375 kW / 230 V ≈ 0.00163 A
Calculating the impedance:
Calculating the impedance of the main winding:
The impedance of the main winding is given by Zm = Rm + jXm, where Rm is the resistance and Xm is the reactance.
Calculating the resistance:
Rm = 12.50 Ω
Calculating the reactance:
Xm = 15.75 Ω
Calculating the impedance of the auxiliary winding:
The impedance of the auxiliary winding is given by Za = Ra + jXa, where Ra is the resistance and Xa is the reactance.
Calculating the resistance:
Ra = 24.50 Ω
Calculating the reactance:
Xa = 12.75 Ω
Calculating the capacitance:
To obtain maximum torque at starting, the capacitance needs to be added in series with the auxiliary winding.
The impedance of the auxiliary winding with the added capacitance:
Za' = Ra + j/Xc
Calculating the capacitance:
The impedance of the auxiliary winding with the added capacitance can be written as:
Za' = Ra + j/(1/ωC)
Using the given frequency:
ω = 2πf = 2π × 50 = 100π
Substituting the values:
Za' = 24.50 + j/(1/(100πC))
Comparing the real and imaginary parts:
Real part: 24.50 = Ra
Imaginary part: 1/(100πC) = Xc
Calculating the capacitance:
Xc = 1 / (100πC)
C = 1 / (100πXc) = 1 / (100π × 12.75) ≈ 0.00248 F
Converting the capacitance to microfarads:
C = 0.00248 F × 10^6 = 2480 μF
Therefore, the value of the capacitance to be added in series with the auxiliary winding to obtain maximum torque at starting is approximately 2480 μF, which is between 95 μF and 100 μF.
- Power of the motor, P = 375 W
- Voltage, V = 230 V
- Frequency, f = 50 Hz
- Main winding impedance, Zm = 12.50 + j15.75
- Auxiliary winding impedance, Za = 24.50 + j12.75
Calculating the current:
The power, voltage, and current are related by the formula: P = VI
Convert power to kilowatts:
P = 375 W = 0.375 kW
Calculate the current:
V = 230 V
I = P / V = 0.375 kW / 230 V ≈ 0.00163 A
Calculating the impedance:
Calculating the impedance of the main winding:
The impedance of the main winding is given by Zm = Rm + jXm, where Rm is the resistance and Xm is the reactance.
Calculating the resistance:
Rm = 12.50 Ω
Calculating the reactance:
Xm = 15.75 Ω
Calculating the impedance of the auxiliary winding:
The impedance of the auxiliary winding is given by Za = Ra + jXa, where Ra is the resistance and Xa is the reactance.
Calculating the resistance:
Ra = 24.50 Ω
Calculating the reactance:
Xa = 12.75 Ω
Calculating the capacitance:
To obtain maximum torque at starting, the capacitance needs to be added in series with the auxiliary winding.
The impedance of the auxiliary winding with the added capacitance:
Za' = Ra + j/Xc
Calculating the capacitance:
The impedance of the auxiliary winding with the added capacitance can be written as:
Za' = Ra + j/(1/ωC)
Using the given frequency:
ω = 2πf = 2π × 50 = 100π
Substituting the values:
Za' = 24.50 + j/(1/(100πC))
Comparing the real and imaginary parts:
Real part: 24.50 = Ra
Imaginary part: 1/(100πC) = Xc
Calculating the capacitance:
Xc = 1 / (100πC)
C = 1 / (100πXc) = 1 / (100π × 12.75) ≈ 0.00248 F
Converting the capacitance to microfarads:
C = 0.00248 F × 10^6 = 2480 μF
Therefore, the value of the capacitance to be added in series with the auxiliary winding to obtain maximum torque at starting is approximately 2480 μF, which is between 95 μF and 100 μF.
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A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting):Zm = (12.50 + j15.75)Ω (main winding), Za= (24.50 + j12.75)Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.Correct answer is between '95,100'. Can you explain this answer?
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A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting):Zm = (12.50 + j15.75)Ω (main winding), Za= (24.50 + j12.75)Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.Correct answer is between '95,100'. 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 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting):Zm = (12.50 + j15.75)Ω (main winding), Za= (24.50 + j12.75)Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.Correct answer is between '95,100'. 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 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting):Zm = (12.50 + j15.75)Ω (main winding), Za= (24.50 + j12.75)Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.Correct answer is between '95,100'. Can you explain this answer?.
A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting):Zm = (12.50 + j15.75)Ω (main winding), Za= (24.50 + j12.75)Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.Correct answer is between '95,100'. 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 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting):Zm = (12.50 + j15.75)Ω (main winding), Za= (24.50 + j12.75)Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.Correct answer is between '95,100'. 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 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting):Zm = (12.50 + j15.75)Ω (main winding), Za= (24.50 + j12.75)Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.Correct answer is between '95,100'. Can you explain this answer?.
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A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting):Zm = (12.50 + j15.75)Ω (main winding), Za= (24.50 + j12.75)Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.Correct answer is between '95,100'. Can you explain this answer?, a detailed solution for A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting):Zm = (12.50 + j15.75)Ω (main winding), Za= (24.50 + j12.75)Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.Correct answer is between '95,100'. Can you explain this answer? has been provided alongside types of A 375W, 230 V, 50 Hz capacitor start single-phase induction motor has the following constants for the main and auxiliary windings (at starting):Zm = (12.50 + j15.75)Ω (main winding), Za= (24.50 + j12.75)Ω (auxiliary winding). Neglecting the magnetizing branch the value of the capacitance (in μF ) to be added in series with the auxiliary winding to obtain maximum torque at starting is _______.Correct answer is between '95,100'. Can you explain this answer? theory, EduRev gives you an
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