Explain the following terms as applied to three-phase induction motors: - Rotor frequency - Induced EMF of the rotor - Rotor reactance

Rotor frequency: The rotor frequency in a three-phase induction motor is the frequency at which the rotor conductors experience a changing magnetic field due to the rotating magnetic field produced by the stator. The rotor frequency is directly proportional to the synchronous speed of the motor and is given by the formula: Rotor frequency = (Synchronous speed * Number of poles) / 120.

Induced EMF of the rotor: The induced electromotive force (EMF) of the rotor in a three-phase induction motor is the voltage generated in the rotor conductors due to the changing magnetic field produced by the stator. This induced EMF causes current to flow in the rotor conductors, which in turn creates a magnetic field that interacts with the stator's magnetic field to produce torque and drive the motor.

Rotor reactance: Rotor reactance is the opposition that the rotor windings present to the flow of alternating current in a three-phase induction motor. It is a measure of the inductive and resistive components of the rotor windings that affect the flow of current and the performance of the motor. Rotor reactance is important in determining the impedance of the rotor circuit and the overall performance of the motor, including its efficiency and power factor.

Rotor Frequency

- Definition: The frequency of the current induced in the rotor conductors.
- Formula: f_r = s - f where f_r is rotor frequency, s is slip, and f is stator frequency.
- Significance: Rotor frequency determines the speed of the motor (synchronous speed - slip speed).

Induced EMF of the Rotor

- Definition: The electromotive force (EMF) generated in the rotor conductors due to the relative motion between the stator magnetic field and the rotor.
- Formula: E_r = V_s - s where E_r is rotor EMF, V_s is stator voltage per phase, and s is slip.
- Significance: Rotor EMF determines the torque produced by the motor.

Rotor Reactance

- Definition: The inductive reactance offered by the rotor windings to the flow of induced current.
- Types:
- Leakage reactance (XLr): Resistance due to the magnetic flux leakage between the stator and rotor.
- Magnetizing reactance (XMr): Resistance due to the magnetic flux that links the stator and rotor windings.
- Significance: Rotor reactance limits the amount of current that can flow in the rotor and affects the motor's speed-torque characteristics.