Correct AnswerD. Both operate at same power factor
Quick Explanation
If two transformers have different impedance magnitudes but identical X/R ratios, their impedance angles are equal. They may share unequal magnitudes of load, but the load-current phase angles are the same, so both operate at the same power factor.
Concept & ReasoningFor transformers in parallel with equal voltage ratios, circulating-current issues aside, load division is inversely proportional to their complex impedances. If ZA and ZB have the same X/R ratio, they have the same impedance angle. Multiplying the common load current by complex division changes magnitude according to |Z| but does not introduce a different phase angle between each transformer's current and the common terminal voltage. Hence both transformer currents have the same power factor, although their kVA sharing may be unequal.How to Solve It in the ExamSame X/R ratio ⇒ same impedance angle ⇒ same load-current power factor.Important…
Concept & Reasoning
For transformers in parallel with equal voltage ratios, circulating-current issues aside, load division is inversely proportional to their complex impedances. If ZA and ZB have the same X/R ratio, they have the same impedance angle. Multiplying the common load current by complex division changes magnitude according to |Z| but does not introduce a different phase angle between each transformer's current and the common terminal voltage. Hence both transformer currents have the same power factor, although their kVA sharing may be unequal.
How to Solve It in the Exam
Same X/R ratio ⇒ same impedance angle ⇒ same load-current power factor.
Important Exam Point
Separate load-sharing magnitude from power-factor angle.
Related Revision Path
This question sits in the revision path Electrical Machines → Transformers → Parallel Operation .
Quick Trick
Same X/R ratio ⇒ same impedance angle ⇒ same load-current power factor.
Common Mistake
Different percentage impedance does not automatically mean different power factor if impedance angles are identical.
Exam Tip
Separate load-sharing magnitude from power-factor angle.
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