Final answer:
The value of the rotor resistance (R2) for the specified induction motor can be found using a formula based on the motor's torque equation and the per-unit system, taking into account the given slip, frequency, and circuit model impedances without considering mechanical, core, or stray losses.
Step-by-step explanation:
The student's question pertains to finding the value of rotor resistance (R2) for a 460-V, 4-pole, 50-hp, 60-Hz, Y-connected three-phase induction motor that develops full-load induced torque at 3.8% slip with given per-phase circuit model impedances. The following formula derived from the torque equation and the per-unit system can be used:
T = (3*V^2*R2') / (w_s * [(R1 + R2'/s)^2 + (X1 + X2')^2])
Where T is the developed torque, V is the phase voltage, R1 is the stator resistance, R2' is the rotor resistance referred to the stator, s is the slip, w_s is the synchronous speed, X1 is the stator reactance, and X2' is the rotor reactance referred to the stator.
Since the motor is Y-connected, the phase voltage V is equal to the line voltage divided by √3. All other impedances are given, and the synchronous speed w_s can be calculated from the frequency (f) and number of poles (p) using the formula w_s = 120f/p. With mechanical, core, and stray losses neglected, solving for R2' will give us the value of the rotor resistance.
Calculations must be performed by taking the slip (s) as 3.8% or 0.038, and the frequency of 60 Hz to find R2 using the equation above.