How it works
The rotating magnetic field produced by the three-phase stator winding spins at synchronous speed Ns = 120f/P = 120 × 50/4 = 1500 RPM. The rotor, turning at N RPM, sees the field at slip frequency fs = s × f = 0.04 × 50 = 2 Hz. Rotor induced EMF is sE2 (where E2 is standstill EMF), rotor reactance is sX2, so rotor current I2 = sE2/√(R2² + (sX2)²). Torque T = (3/ωs) × I2²R2/s; maximum torque occurs at slip sm = R2/X2, typically 10–15% for squirrel-cage motors. Adding external resistance to a slip-ring rotor shifts sm without changing maximum torque — this is the Kramer/rotor resistance control method.
Key points to remember
Squirrel-cage rotors cannot have external resistance added; slip-ring (wound rotor) motors can, which is why slip-ring motors are used for high starting torque applications like cranes. At standstill (s = 1) the motor is equivalent to a short-circuited transformer. Rotor copper loss = s × air-gap power Pg; so at s = 0.04 only 4% of air-gap power is lost as rotor heat, which is why high-slip operation wastes energy. Starting methods — DOL, star-delta, autotransformer — all reduce starting current at the cost of reduced starting torque; star-delta cuts both to one-third.
Exam tip
The examiner always asks you to draw the torque-slip curve and mark the stable and unstable regions — remember that operation is stable only for slips less than sm (the slip at maximum torque).