The power in a 3phase circuit is measured with the help of 2 wattmeters. The reading of one of wattmeters is positive and that of the others is negative. The magnitude of readings is different. It can be concluded that the power factor of the circuit is 

Explanation:

Power Measurement in a 3-Phase Circuit Using Two Wattmeters

Definition: The two-wattmeter method is a commonly used technique for measuring power in a 3-phase circuit. This method requires two wattmeters to be connected to two of the three lines in a 3-phase system. The readings of these wattmeters give the total power in the circuit. The method is especially useful for both balanced and unbalanced loads.

Working Principle: In a 3-phase circuit, the total power can be calculated as the algebraic sum of the readings of the two wattmeters:

Total Power (P) = W₁ + W₂

Where W₁ and W₂ are the readings of the two wattmeters. Depending on the power factor of the circuit, the readings of the wattmeters can be positive, negative, or even zero. The phase angle (φ) between the line voltage and current determines the power factor, and this in turn affects the wattmeter readings.

Given Condition:

In the question, one of the wattmeter readings is positive, and the other is negative. The magnitudes of the readings are different. This condition indicates that the power factor of the circuit is less than 0.5 (lagging).

Analysis:

Let’s analyze the readings of the two wattmeters for various power factors:

• For a power factor of 1 (unity), both wattmeter readings will be positive and equal, as the angle between voltage and current is 0°.
• For a power factor between 0.5 and 1 (lagging), both wattmeter readings will still be positive but unequal. The difference in their magnitudes increases as the power factor decreases.
• For a power factor of 0.5 (lagging), one wattmeter reading becomes zero. This happens because the phase angle φ is 60°, leading to the wattmeter connected to a specific phase showing zero reading.
• For a power factor less than 0.5 (lagging), one wattmeter reading becomes negative. The negative reading occurs because the phase angle φ exceeds 60°, causing the current direction relative to the voltage to result in a negative product in one wattmeter.

In the given scenario, one wattmeter shows a positive reading, and the other shows a negative reading, with different magnitudes. This is a clear indication that the power factor of the circuit is less than 0.5 (lagging).

Conclusion:

The correct answer is:

Option 4: Less than 0.5 (lagging)

This conclusion is based on the characteristic behavior of wattmeters in the two-wattmeter method when the power factor of the circuit is less than 0.5. The negative reading of one wattmeter, combined with the positive reading of the other, confirms this condition.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Unity

If the power factor were unity, both wattmeter readings would be positive and equal. This does not match the given condition where one wattmeter reading is negative, and the magnitudes are different.

Option 2: 2 (lagging)

A power factor of 2 (lagging) is not possible in any electrical circuit, as power factor is defined as the cosine of the phase angle (cos φ), which always lies between -1 and 1. Hence, this option is invalid.

Option 3: 5 (lagging)

Similar to Option 2, a power factor of 5 (lagging) is not physically possible, as power factor values cannot exceed 1. Therefore, this option is also invalid.

Option 4: Less than 0.5 (lagging)

This is the correct answer, as explained above. The negative reading of one wattmeter and the positive reading of the other, with different magnitudes, indicate a power factor less than 0.5 (lagging).

Conclusion:

Understanding the behavior of wattmeters in the two-wattmeter method is essential for determining the power factor of a 3-phase circuit. The key takeaway is that when one wattmeter reading is negative and the other is positive, with different magnitudes, the power factor is less than 0.5 (lagging). This knowledge is crucial for accurately analyzing and diagnosing power systems in electrical engineering applications.