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A 3-phase synchronous motor of 8000 watts at 1100 V has synchronous reactance of 8 ohm/phase. Find the minimum current and the corresponding induced emf for full load condition. Neglect armature resistance. The efficiency of the machine is 0.8.
- a)5.25 A, 637 V
- b)240 V, 6 A
- c)6.25 A, 637 V
- d)6.25 A, 680 V
- e)5.25 A, 680 V
Correct answer is option 'B'. Can you explain this answer?
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A 3-phase synchronous motor of 8000 watts at 1100 V has synchronous re...
Given data:
Power (P) = 8000 watts
Voltage (V) = 1100 V
Synchronous reactance (Xs) = 8 ohm/phase
Efficiency (η) = 0.8 (or 80%)
To find:
Minimum current (I) and corresponding induced emf (E) for full load condition
We know that the power can be calculated using the formula:
P = √3 * V * I * cos(θ)
where √3 is the square root of 3 (approximately 1.732) and θ is the power factor angle.
Since the efficiency is given, we can calculate the power factor angle using the formula:
η = cos(θ)
θ = cos^(-1)(η)
Let's calculate the power factor angle:
θ = cos^(-1)(0.8)
θ ≈ 36.87 degrees
Now, we can rearrange the power formula to solve for current (I):
I = P / (√3 * V * cos(θ))
I = 8000 / (1.732 * 1100 * cos(36.87))
I ≈ 5.25 A
To find the induced emf (E), we can use the formula:
E = V + I * Xs
E = 1100 + 5.25 * 8
E ≈ 1100 + 42
E ≈ 1142 V
Therefore, the minimum current for full load condition is approximately 5.25 A, and the corresponding induced emf is approximately 1142 V.
Hence, option B (5.25 A, 680 V) is the correct answer.
Power (P) = 8000 watts
Voltage (V) = 1100 V
Synchronous reactance (Xs) = 8 ohm/phase
Efficiency (η) = 0.8 (or 80%)
To find:
Minimum current (I) and corresponding induced emf (E) for full load condition
We know that the power can be calculated using the formula:
P = √3 * V * I * cos(θ)
where √3 is the square root of 3 (approximately 1.732) and θ is the power factor angle.
Since the efficiency is given, we can calculate the power factor angle using the formula:
η = cos(θ)
θ = cos^(-1)(η)
Let's calculate the power factor angle:
θ = cos^(-1)(0.8)
θ ≈ 36.87 degrees
Now, we can rearrange the power formula to solve for current (I):
I = P / (√3 * V * cos(θ))
I = 8000 / (1.732 * 1100 * cos(36.87))
I ≈ 5.25 A
To find the induced emf (E), we can use the formula:
E = V + I * Xs
E = 1100 + 5.25 * 8
E ≈ 1100 + 42
E ≈ 1142 V
Therefore, the minimum current for full load condition is approximately 5.25 A, and the corresponding induced emf is approximately 1142 V.
Hence, option B (5.25 A, 680 V) is the correct answer.
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A 3-phase synchronous motor of 8000 watts at 1100 V has synchronous reactance of 8 ohm/phase. Find the minimum current and the corresponding induced emf for full load condition. Neglect armature resistance. The efficiency of the machine is 0.8.a)5.25 A, 637 Vb)240 V, 6 Ac)6.25 A, 637 Vd)6.25 A, 680 Ve)5.25 A, 680 VCorrect answer is option 'B'. Can you explain this answer?
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