Final answer:
The question involves computing the operating speed and torque of an induction motor using the provided load torque formula and motor's synchronous speed and maximum torque values.
Step-by-step explanation:
The student's question focuses on calculating the speed and torque of an induction motor that operates near its synchronous speed, powered by a 50 Hz, 400 V (line-line) source, with two poles and an armature resistance (RR) of 0.5Ω. The load torque is given as TL = 63 · 10⁻³ω², with ω representing the angular velocity in radians per second (rad/s). We are also given the synchronous speed, ω₀ = 104.1 rad/s, and the maximum torque, Tₘ = 682.34 Nm.
To solve this problem, we would typically use the torque equation of an induction motor and the relationship between load torque and motor torque to find the operating speed and torque of the motor. The data given in the problem statement, such as the rated line voltage and resistance, would normally help calculate the electrical parameters contributing to the motor's operation, but in this case, they are not directly needed for the given formula. The synchronous speed represents the maximum speed at which the motor can operate, which occurs when the rotor rotates at the same speed as the magnetic field produced by the stator.
If we were to proceed with the calculation, we would identify the relationship between load torque and motor speed, usually represented by a torque-speed characteristic curve, to determine the operating speed of the rotor.