The motor is delivering its rated output power at a speed

Question

Q1. A 400 V, 6-pole, 50 Hz, Y-connected, three-phase induction motor has the following parameters all referred to stator side:

R₁ = 0.62Ω, X₁ = 0.95Ω, R₂ = 1.2Ω, X₂ = 1.5Ω, R_C = 962Ω, X_M = 1250Ω.

The motor is delivering its rated output power at a speed of 910 rpm. Rotational loss of the motor is 600 watts. Using the approximate equivalent circuit, (a) determine the rated power of the motor, (b) the output torque, (c) the efficiency of the motor at rated load, (d) the speed at which the motor will develop its maximum power and (c) the maximum power developed.

Q2. A 15 kVA, 440 V, 4-pole, 50 Hz star-connected synchronous generator with wound rotor is supplying its rated load at a lagging power factor of 0.72 and at its rated speed and rated voltage. The per-phase synchronous impedance of the generator is (0.2 + j 2) U. The field voltage is 220 V and the field winding resistance is 50 Ω. Assume the rotational losses amount to 2 % of developed power. Determine (a) the induced emf/phase, (b) load angle in degrees, (c) the mechanical torque input to the generator in N-m, and (d) the efficiency of the generator.

Q3. A 50-hp, 440-V, three-phase, 4-pole, 50 Hz, delta-connected synchronous motor is supplied from an infinite bus at its rated values and at a power factor of 0.77 lagging. The synchronous impedance of the armature is (1.2 + j8) Ω/phase. The rotational loss is 700 watts. When the motor is delivering its rated output, (a) determine the input current, (b) load angle (c) its efficiency, and (d) output torque. (Note 1-hp = 746 watts).