Rotating Machines and Electromagnetic Devices
Rotating machines and magnetic devices
For any AC machine, first find synchronous speed from n_s = 120f/P, where P is the number of poles. An induction motor runs below n_s; slip is s = (n_s − n_r)/n_s, and rotor frequency is sf. A negative slip indicates generating operation, while s = 1 is standstill. The equivalent circuit explains the traps: rotor resistance is divided by slip, so small slip means high rotor current and torque; at high slip the rotor reactance dominates. Synchronous machines are set by field excitation and load angle: overexcitation supplies reactive power, underexcitation absorbs it, and steady-state stability depends on the power-angle curve.
Transformers and electromagnetic devices follow flux and turns relationships. Voltage per turn is constant, so V1/V2 = N1/N2; impedance referred across a transformer scales by the turns ratio squared. Watch dot convention: dots mark terminals of the same instantaneous polarity, and a reversed dot flips the sign of mutual flux or secondary voltage. In DC machines, back emf is proportional to flux and speed, and electromagnetic torque is proportional to flux and armature current.
Worked example: a four-pole, 60 Hz induction motor has 4% slip. Synchronous speed is 120 × 60/4 = 1800 rpm, so rotor speed is 1800(1 − 0.04) = 1728 rpm, and rotor frequency is 0.04 × 60 = 2.4 Hz. Rule of thumb: a 2-pole 60 Hz machine runs near 3600 rpm, a 4-pole near 1800 rpm, and a 6-pole near 1200 rpm.