NapkinCalc

AC Motors

Induction motors: synchronous speed, slip, full-load current, shaft torque, and power-factor correction.

The three-phase induction motor runs most of the industrial world. Three windings create a magnetic field that ROTATES at a speed fixed by the line frequency; the rotor chases it, always lagging slightly — that lag is what makes torque.

  1. 01 Synchronous speed The field rotates at n_sync = 120·f / p, where p is the number of magnetic poles. More poles = slower field. At 60 Hz: 2 poles → 3600 rpm, 4 → 1800, 6 → 1200.
  2. 02 Slip — why the rotor lags If the rotor ever caught up with the field, no field lines would be cut, no current induced, no torque made. So it settles just below: the shortfall, as a…
  3. 03 Power, efficiency & full-load current The nameplate gives SHAFT power (what the load receives). The line must supply more, to cover losses (efficiency η) and the magnetizing current that does no…
  4. 04 Shaft torque Power is torque times rotational speed: P = T·ω. Same power at half the speed means TWICE the torque — why low-rpm motors are physically bigger.
  5. 05 Power-factor correction That 0.86 power factor means the line carries current that does no work. A capacitor bank supplies the reactive part locally, unloading the wiring upstream.…

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