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Long shunt compound generator speed

Short answer

Load current 40 A, Ish = 1 A, Ia = 41 A, E = 260.25 V. For lap winding, speed N = 60 A E / (P Φ Z) = 1041 rpm.

A 4 pole, 250 V long shunt dc compound generator supplies a load of 10 kW at the rated voltage. The armature, series and shunt field resistances are 0.1 Ω, 0.15 Ω and 250 Ω respectively. The armature is lap wound with 300 conductors. If the flux per pole is 50 mWb, calculate the speed of the generator.

For a long shunt machine the series field is in the armature circuit, and the shunt field is across the output terminals. The speed follows from E = PΦZN / 60A. Brush drop is not given, so it is ignored.

Equivalent circuit

 Ia --[Ra=0.1]--[Rse=0.15]--+--> IL
 (E)                        |
                      Rsh=250 ohm, V=250 V

Currents

  • Load current I_L = 10 000 / 250 = 40 A
  • Shunt current I_sh = 250 / 250 = 1 A
  • Armature (and series) current I_a = 40 + 1 = 41 A

Generated emf

E = V + I_a(R_a + R_se) = 250 + 41 × (0.1 + 0.15) = 250 + 10.25 = 260.25 V

Speed

Lap winding: A = P = 4, Z = 300, Φ = 50 mWb = 0.05 Wb.

E = PΦZN / (60A), so N = 60 A E / (P Φ Z)

N = (60 × 4 × 260.25) / (4 × 0.05 × 300) = 62 460 / 60 = 1041 rpm

QuantityValue
I_L40 A
I_sh1 A
I_a41 A
E260.25 V
N1041 rpm

Answer: speed of the generator = 1041 rpm.

✓ Answer checked by Claude Opus 5.5 (high effort)

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