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The armature resistance of a 6-pole lap wound d.c. machine is 0.05 Ω. If the armature is rewound as a wave-winding, what is the armature resistance?

The armature resistance of a 6-pole lap wound d.c. machine is 0.05 Ω. If the armature is rewound as a wave-winding, what is the armature resistance? Correct Answer 0.45 <span style="">Ω</span>

Concept:

The armature winding of the DC machine is classified into two types:

1) Lap winding: 

  • A = P
  • (Ia)L =  A(IP)

2) Wave winding: 

  • A = 2
  • (Ia)w = 2(IP)

where A= No. of parallel paths

P= No. of poles

A= No. of parallel paths

(Ia)L  = Armature current in Lap winding

(Ia)w = Armature current in Wave winding

 IP = Current in parallel path

 Calculation:

Given, For Lap winding : 

  • A = P = 6 
  • (Ia)L =  A(IP)

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Given, For Wave winding : 

  • A = 2
  • (Ia)w = 2(IP)

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By the power conservation theorem, total power remains constant irrespective of the connection type of the armature resistance.

 (P)L = (P)W

(Ia)2L (Ra)L = (Ia)2w  (Ra)w

(6IP)2 (0.05) = (2IP)2 (Ra)w

(Ra)w = 9 × 0.05

(Ra)w = 0.45Ω

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