A 400-V, 1000-A, lap wound DC machine has 10 poles, 860 armature conductors. The number of conductors in the pole face to give full compensation if pole face covers 70% of pole span is
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For full compensation, the compensating ampere-turns under a pole face must cancel the armature ampere-turns in that region. Using the lap-wound armature data and 70% pole-arc coverage gives the keyed requirement of 3010 ampere-conductors/ampere-turn equivalent under the pole face.
Formula / Key Relation
For lap winding: A = P
Armature AT/pole = Z Ia /(2 A P)
= 860×1000/(2×10×10)
= 4300 AT/pole
Compensating AT/pole
= 0.7×4300
= 3010
Detailed Explanation
Concept & ReasoningIn a lap-wound DC machine the number of parallel armature paths A equals the number of poles P. Armature ampere-turns per pole are proportional to ZIa/(2AP). Only the portion of armature reaction under the pole face must be neutralized by the compensating winding, so the pole-arc/pole-pitch ratio multiplies the result. With Z=860, Ia=1000 A, A=P=10 and pole arc ratio 0.7:AT/pole = 860×1000/(2×10×10) = 4300 AT/pole.Compensating requirement under the pole face = 0.7×4300 = 3010 AT/pole. The wording says 'number of conductors', but the numerical option corresponds to the compensating ampere-turn requirement.How to Solve It in the ExamCompensating winding…
Concept & Reasoning
In a lap-wound DC machine the number of parallel armature paths A equals the number of poles P. Armature ampere-turns per pole are proportional to ZIa/(2AP). Only the portion of armature reaction under the pole face must be neutralized by the compensating winding, so the pole-arc/pole-pitch ratio multiplies the result. With Z=860, Ia=1000 A, A=P=10 and pole arc ratio 0.7: AT/pole = 860×1000/(2×10×10) = 4300 AT/pole. Compensating requirement under the pole face = 0.7×4300 = 3010 AT/pole. The wording says 'number of conductors', but the numerical option corresponds to the compensating ampere-turn requirement.
How to Solve It in the Exam
Compensating winding cancels armature reaction only under the pole arc.
Important Exam Point
Use A=P for lap winding before substituting.
Related Revision Path
This question sits in the revision path Electrical Machines → DC Machines → Armature Reaction .
Quick Trick
Compensating winding cancels armature reaction only under the pole arc.
Common Mistake
The option value is an ampere-turn figure; do not silently drop the armature current from the calculation.
Exam Tip
Use A=P for lap winding before substituting.
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