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A,2300V, 3 - ϕ , star connected synchronous motor has a resistance of 0.2Ω per phase and synchronous reactance of 2.2Ω per phase. The motor is operating at 0.5 power factor leading with a line current of 200A. The value of the generated emf per phase in volts is _____. (Correct upto nearest integer)
Correct answer is '1708'. Can you explain this answer?
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To find the value of the generated emf per phase in a synchronous motor, we need to consider the power factor and the electrical parameters of the motor.
Given data:
- Voltage (V) = 2300V
- Resistance (R) = 0.2Ω per phase
- Synchronous reactance (Xs) = 2.2Ω per phase
- Line current (I) = 200A
- Power factor (PF) = 0.5 leading
We know that the power factor (PF) is the ratio of the real power (P) to the apparent power (S). In a synchronous motor, the real power is given by the product of the line current (I), the voltage (V), and the power factor (PF). The apparent power is given by the product of the line current (I) and the voltage (V).
Real Power (P) = I * V * PF
Apparent Power (S) = I * V
To find the reactive power (Q), we can use the following formula:
Reactive Power (Q) = sqrt(Apparent Power^2 - Real Power^2)
The generated emf per phase (E) can be calculated using the following formula:
E = sqrt(V^2 - (I * R)^2) + j * sqrt((I * R)^2 - (I * Xs)^2)
Now let's calculate the values:
Real Power (P) = 200A * 2300V * 0.5 = 230,000W
Apparent Power (S) = 200A * 2300V = 460,000VA
Reactive Power (Q) = sqrt(460,000^2 - 230,000^2) ≈ 398,131.84VAR
Now we can calculate the generated emf per phase (E):
E = sqrt(2300^2 - (200A * 0.2Ω)^2) + j * sqrt((200A * 0.2Ω)^2 - (200A * 2.2Ω)^2)
E = sqrt(5,290,000 - 800)^2) + j * sqrt((800)^2 - (4400)^2)
E ≈ sqrt(5,289,200) + j * sqrt(6400 - 19,360,000)
E ≈ 2298.03 + j * 0.07
Since the question asks for the value of the generated emf per phase up to the nearest integer, the answer is approximately 2298V.
However, the given correct answer is '1708', which appears to be a discrepancy. It is possible that there is an error in the provided answer or in the calculations above.
Given data:
- Voltage (V) = 2300V
- Resistance (R) = 0.2Ω per phase
- Synchronous reactance (Xs) = 2.2Ω per phase
- Line current (I) = 200A
- Power factor (PF) = 0.5 leading
We know that the power factor (PF) is the ratio of the real power (P) to the apparent power (S). In a synchronous motor, the real power is given by the product of the line current (I), the voltage (V), and the power factor (PF). The apparent power is given by the product of the line current (I) and the voltage (V).
Real Power (P) = I * V * PF
Apparent Power (S) = I * V
To find the reactive power (Q), we can use the following formula:
Reactive Power (Q) = sqrt(Apparent Power^2 - Real Power^2)
The generated emf per phase (E) can be calculated using the following formula:
E = sqrt(V^2 - (I * R)^2) + j * sqrt((I * R)^2 - (I * Xs)^2)
Now let's calculate the values:
Real Power (P) = 200A * 2300V * 0.5 = 230,000W
Apparent Power (S) = 200A * 2300V = 460,000VA
Reactive Power (Q) = sqrt(460,000^2 - 230,000^2) ≈ 398,131.84VAR
Now we can calculate the generated emf per phase (E):
E = sqrt(2300^2 - (200A * 0.2Ω)^2) + j * sqrt((200A * 0.2Ω)^2 - (200A * 2.2Ω)^2)
E = sqrt(5,290,000 - 800)^2) + j * sqrt((800)^2 - (4400)^2)
E ≈ sqrt(5,289,200) + j * sqrt(6400 - 19,360,000)
E ≈ 2298.03 + j * 0.07
Since the question asks for the value of the generated emf per phase up to the nearest integer, the answer is approximately 2298V.
However, the given correct answer is '1708', which appears to be a discrepancy. It is possible that there is an error in the provided answer or in the calculations above.
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A,2300V, 3 - ϕ , star connected synchronous motor has a resistance of 0.2Ω per phase and synchronous reactance of 2.2Ω per phase. The motor is operating at 0.5 power factor leading with a line current of 200A. The value of the generated emf per phase in volts is _____. (Correct upto nearest integer)Correct answer is '1708'. Can you explain this answer?
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