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The synchronizing reactance of a 500V 50 KVA alternator having an effective resistance of 0.2W, if an excitation current of 10 A produces 200A armature current on short circuit and an emf of 450 volts on open circuit is
- a)2.6W
- b)5.2W
- c)2.24W
- d)4.5W
Correct answer is option 'C'. Can you explain this answer?
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Question:
The synchronizing reactance of a 500V 50 KVA alternator having an effective resistance of 0.2W, if an excitation current of 10 A produces 200A armature current on short circuit and an emf of 450 volts on open circuit is
a) 2.6W
b) 5.2W
c) 2.24W
d) 4.5W
Answer:
Given data:
Voltage rating = 500V
Power rating = 50 KVA
Effective resistance = 0.2W
Excitation current = 10A
Armature current = 200A
Open circuit emf = 450V
To find:
Synchronizing reactance
Solution:
From the given data, we can find the impedance of the alternator on short circuit and open circuit as follows:
On short circuit:
Zsc = V/Isc
= 500/200
= 2.5W
On open circuit:
Zoc = Voc/Iexc
= 450/10
= 45W
The synchronous reactance can be calculated using the following formula:
Xs = sqrt(Zoc^2 - Re^2)
= sqrt(45^2 - 0.2^2)
= 44.997W
= 2.24W (approx)
Therefore, the synchronizing reactance of the alternator is 2.24W (option c).
Explanation:
The synchronizing reactance is a parameter used to determine the stability of the synchronous machine. It is the imaginary part of the synchronous impedance and is calculated by subtracting the effective resistance from the impedance of the machine on open circuit. The synchronizing reactance is a function of the machine's physical characteristics and the excitation current.
In this question, we are given the voltage rating, power rating, effective resistance, excitation current, armature current, and open circuit emf of the alternator. Using this data, we can calculate the impedance of the machine on short circuit and open circuit. The synchronizing reactance is then calculated using the formula mentioned above.
The correct answer is option c (2.24W).
The synchronizing reactance of a 500V 50 KVA alternator having an effective resistance of 0.2W, if an excitation current of 10 A produces 200A armature current on short circuit and an emf of 450 volts on open circuit is
a) 2.6W
b) 5.2W
c) 2.24W
d) 4.5W
Answer:
Given data:
Voltage rating = 500V
Power rating = 50 KVA
Effective resistance = 0.2W
Excitation current = 10A
Armature current = 200A
Open circuit emf = 450V
To find:
Synchronizing reactance
Solution:
From the given data, we can find the impedance of the alternator on short circuit and open circuit as follows:
On short circuit:
Zsc = V/Isc
= 500/200
= 2.5W
On open circuit:
Zoc = Voc/Iexc
= 450/10
= 45W
The synchronous reactance can be calculated using the following formula:
Xs = sqrt(Zoc^2 - Re^2)
= sqrt(45^2 - 0.2^2)
= 44.997W
= 2.24W (approx)
Therefore, the synchronizing reactance of the alternator is 2.24W (option c).
Explanation:
The synchronizing reactance is a parameter used to determine the stability of the synchronous machine. It is the imaginary part of the synchronous impedance and is calculated by subtracting the effective resistance from the impedance of the machine on open circuit. The synchronizing reactance is a function of the machine's physical characteristics and the excitation current.
In this question, we are given the voltage rating, power rating, effective resistance, excitation current, armature current, and open circuit emf of the alternator. Using this data, we can calculate the impedance of the machine on short circuit and open circuit. The synchronizing reactance is then calculated using the formula mentioned above.
The correct answer is option c (2.24W).
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The synchronizing reactance of a 500V 50 KVA alternator having an effective resistance of 0.2W, if an excitation current of 10 A produces 200A armature current on short circuit and an emf of 450 volts on open circuit isa)2.6Wb)5.2Wc)2.24Wd)4.5WCorrect answer is option 'C'. Can you explain this answer?
Question Description
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