Difficulty: Medium
Correct Answer: When the two wattmeters read equal and opposite values, the power factor is zero
Explanation:
Introduction / Context:The two-wattmeter method is a standard technique for measuring total three-phase power in 3-wire systems. It works for both star and delta connections. Relationships between wattmeter readings and load power factor are well-known and provide diagnostic insight into system conditions.
Given Data / Assumptions:
Concept / Approach:At unity power factor (φ = 0°), W1 = W2 = V_L I_L cos 30° (both positive and equal). At φ = 60° (power factor 0.5), one reading becomes zero: cos(30° + 60°) = cos 90° = 0. At φ = 90° (purely reactive; power factor zero), readings are equal in magnitude and opposite in sign because cos(120°) = −cos(60°) = −0.5 and cos(−60°) = 0.5. Hence the only correct statement among the choices is that equal and opposite readings indicate pf = 0.
Step-by-Step Solution:
Unity pf: φ = 0° ⇒ W1 = W2 > 0 (not zero).pf = 0.5: φ = 60° ⇒ one wattmeter = 0.pf = 0: φ = 90° ⇒ W1 = −W2.Verification / Alternative check:
Sum P = W1 + W2 gives zero when readings are equal and opposite, matching reactive load with zero real power.Why Other Options Are Wrong:
Method is not limited to star loads; and equal readings do not imply pf = 0.5; at pf = 1 no wattmeter reads zero.Common Pitfalls:
Mixing the φ = 60° condition (one zero reading) with φ = 0° (equal positive readings).Final Answer:
When the two wattmeters read equal and opposite values, the power factor is zero
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