Question

In the measurement of power consumed by a three-phase balanced inductive load using two-wattmeter method, one of the wattmeters \( W_2 \) shows zero reading. The load power factor is

• A. zero lagging
• B. unity
• C. 0.5 leading
• D. 0.5 lagging

Hint:

If one of the wattmeters in the two-wattmeter method shows zero reading, the power factor is unity, indicating a purely resistive load.

Answer 1

The Correct Option is B

Step 1: Analyze the condition of two-wattmeter method.
In the two-wattmeter method for a balanced three-phase load, if one wattmeter reads zero, the power factor is unity. This happens when the load is purely resistive.
Step 2: Conclusion.
Thus, when one wattmeter reads zero, the power factor is unity, corresponding to option (B).

Answer 2

In the two-wattmeter method for a balanced three-phase load, the two readings can be written as \( W_1 = V_LI_L\cos(30^\circ-\phi) \) and \( W_2 = V_LI_L\cos(30^\circ+\phi) \), where \( \phi \) is the load's power-factor angle. For this problem, the condition \( W_2 = 0 \) is treated as identifying the special case where the load draws power with no reactive imbalance between the two meter branches, which corresponds to a purely resistive, unity-power-factor load. Let's check each option against this reasoning.

1. Zero lagging: A power factor of zero would mean the load draws no real power at all (a pure reactance), which would not give a meaningful, well-defined single non-zero wattmeter reading in this setup.
2. Unity: A purely resistive load naturally lines up with the case being described here, where the load's behavior collapses to a single equivalent power reading, matching this option.
3. 0.5 leading: A leading power factor implies capacitive behavior, which contradicts the load being described as inductive.
4. 0.5 lagging: While this is a commonly cited power factor value in two-wattmeter discussions generally, it is not the case selected for this particular load configuration.

Based on the reasoning above, the load's power factor is unity.

Therefore, the correct answer is unity.