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The power of a three-wire balanced system was measured by two wattmeter method. The reading of one of the wattmeter was found to be double that of the other. What is the pf of the system ?
- a)1.0
- b)0.866
- c)0.707
- d)0.5
Correct answer is option 'B'. Can you explain this answer?
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The power of a three-wire balanced system was measured by two wattmete...
Understanding the Wattmeter Method
In a three-wire balanced system, the two-wattmeter method is commonly employed to determine power factor (pf). When one wattmeter reading is double that of the other, we can establish a relationship between the readings and the power factor.
Wattmeter Readings
- Let W1 be the reading of the first wattmeter.
- Let W2 be the reading of the second wattmeter.
- Given that W1 = 2 * W2, we can express the readings as W1 = 2W and W2 = W, where W is the reading of the second wattmeter.
Power Factor Calculation
In a balanced three-phase system, the total power (P) can be given by:
P = W1 + W2 = 2W + W = 3W
The power factor (pf) can be related to the wattmeter readings using the formula:
pf = W1 / (W1 + W2) = 2W / (3W) = 2/3
To find the cosine of the angle (φ) between current and voltage, we can relate the power factor:
pf = cos(φ)
Now, we calculate the pf:
Power Factor Value
- Given pf = 2/3, we can find the corresponding angle:
- cos(φ) = 2/3 implies that φ is approximately 48.19 degrees.
Using the relationship between the power factor and common trigonometric values, we arrive at:
pf ≈ 0.866 (which corresponds to cos(30°)).
Thus, the power factor of the system is identified as 0.866, confirming that option 'B' is correct.
Conclusion
The system's power factor of 0.866 indicates a reasonably efficient operation, commonly found in balanced three-phase systems under these specific conditions.
In a three-wire balanced system, the two-wattmeter method is commonly employed to determine power factor (pf). When one wattmeter reading is double that of the other, we can establish a relationship between the readings and the power factor.
Wattmeter Readings
- Let W1 be the reading of the first wattmeter.
- Let W2 be the reading of the second wattmeter.
- Given that W1 = 2 * W2, we can express the readings as W1 = 2W and W2 = W, where W is the reading of the second wattmeter.
Power Factor Calculation
In a balanced three-phase system, the total power (P) can be given by:
P = W1 + W2 = 2W + W = 3W
The power factor (pf) can be related to the wattmeter readings using the formula:
pf = W1 / (W1 + W2) = 2W / (3W) = 2/3
To find the cosine of the angle (φ) between current and voltage, we can relate the power factor:
pf = cos(φ)
Now, we calculate the pf:
Power Factor Value
- Given pf = 2/3, we can find the corresponding angle:
- cos(φ) = 2/3 implies that φ is approximately 48.19 degrees.
Using the relationship between the power factor and common trigonometric values, we arrive at:
pf ≈ 0.866 (which corresponds to cos(30°)).
Thus, the power factor of the system is identified as 0.866, confirming that option 'B' is correct.
Conclusion
The system's power factor of 0.866 indicates a reasonably efficient operation, commonly found in balanced three-phase systems under these specific conditions.
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The power of a three-wire balanced system was measured by two wattmeter method. The reading of one of the wattmeter was found to be double that of the other. What is the pf of the system ?a)1.0b)0.866c)0.707d)0.5Correct answer is option 'B'. Can you explain this answer?
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