Motors and generators

Question:

The output voltage and power of the DC shunt motor is 230V and 7.5 kW respectively. When the field current is 1.2 A the speed of the generator is 1450 rev/min. Total armature resistance 0.55 Ohm. This generator is used as a DC motor when output voltage is 220V and power delivered by the motor is 6 kW. The efficiency of the motor at this condition is 82%.
Calculate the speed of the motor when field current and magnetized flux resistance constant in each condition.

Answer:

I am still not really sure I follow each part. I think in some cases you mean generator and in others motor, also in some places output should probably read input.

1. As a GENERATOR
V = 230 V P = 7500 W Field current = 1.2 Amps
Armature current = 7500/230 – 1.2 = 32.60 – 1.2 = 31.4 Amps
Speed = 1450 rpm = 24.17 rps
Angular velocity (w) = 151.8 radians per second
Emf generated = 230 = Banw = BAn x 151.8 BAn = 1.515 (a constant for your apparatus)

(A is the area of the rotating coil with n turns)

2. As a MOTOR
New back emf = Banw₁ = 1.515 where w₁ is the new angular velocity
Input = 220 V Output power = 6000 W Efficiency = 82% So input power = 7317 W
Current in coil = 7217/220 – 1.2 = 33.25 – 1.2 = 32.06 Amps
Back emf = V – IR = 220 – 32.06x0.55 = 202.37 = BAnv
Angular velocity w₁ = 202.37/1.151 = 133.6 radians per second

Speed = 1275 rpm