For a balanced three-phase load, W₁+W₂=P=10 kW and tanφ=√3(W₁−W₂)/(W₁+W₂). With cosφ=0.9, φ≈25.84°; solving gives W₁≈6.40 kW and W₂≈3.60 kW, nearest to 6350 W and 3650 W.
Formula / Key Relation
P = W₁ + W₂ = 10,000 W
φ = cos⁻¹(0.9)
tanφ ≈ 0.4843
tanφ = √3(W₁−W₂)/(W₁+W₂)
W₁−W₂ = P tanφ/√3
≈ 10,000×0.4843/1.732
≈ 2796 W
W₁ ≈ (10,000+2796)/2 ≈ 6398 W
W₂ ≈ (10,000−2796)/2 ≈ 3602 W
Nearest option: 6350 W, 3650 W
Detailed Explanation
Concept & ReasoningThe two-wattmeter method measures total three-phase real power in a 3-wire system. Power factor determines the difference between readings. At unity power factor both readings are equal; as lag angle increases, one reading rises and the other falls. Here the relatively high 0.9 pf gives two positive readings with a modest difference.How to Solve It in the ExamUse sum for total power, difference for power factor.Important Exam PointCheck that W₁+W₂ is approximately 10 kW for any candidate.Related Revision PathThis question sits in the revision path Electrical Measurements → Three-Phase Circuits → Two-Wattmeter Method .
Concept & Reasoning
The two-wattmeter method measures total three-phase real power in a 3-wire system. Power factor determines the difference between readings. At unity power factor both readings are equal; as lag angle increases, one reading rises and the other falls. Here the relatively high 0.9 pf gives two positive readings with a modest difference.
How to Solve It in the Exam
Use sum for total power, difference for power factor.
Important Exam Point
Check that W₁+W₂ is approximately 10 kW for any candidate.
Related Revision Path
This question sits in the revision path Electrical Measurements → Three-Phase Circuits → Two-Wattmeter Method .
Quick Trick
Use sum for total power, difference for power factor.
Common Mistake
Choosing 5 kW,5 kW; equal readings imply unity power factor, not 0.9.
Exam Tip
Check that W₁+W₂ is approximately 10 kW for any candidate.
SEO + Knowledge GraphRelated PYQs & Exam ContextExam path, knowledge path and deeper practice links.
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