Editing Synchronous motor (section)

==Synchronous speed==
The [[synchronous speed]] of a synchronous motor is given:<ref>{{cite web|url=http://www.elec-toolbox.com/Formulas/Motor/mtrform.htm|title=Motor speed|publisher=Electrician's toolbox etc|url-status=usurped|archive-url=https://web.archive.org/web/19990508223135/http://www.elec-toolbox.com/Formulas/Motor/mtrform.htm|archive-date=1999-05-08}}</ref><br/>
in [[Revolutions per minute|RPM]], by:
: <math>N_s = 60\frac f P = 120\frac f p</math>
and in [[radian per second|rad·s<sup>−1</sup>]], by:
: <math>\omega_s = 2\pi\frac f P = 4\pi\frac f p</math>

where:
* <math>f</math> is the [[frequency]] of the AC supply current in [[hertz|Hz]],
* <math>p</math> is the number of magnetic [[magnet|poles]],
* <math>P</math> is the number of pole pairs (rarely, ''planes of commutation''), <math>P = p/2</math>.

===Examples===
A [[single-phase electric power|single-phase]], 4-pole (2-pole-pair) synchronous motor is operating at an AC supply frequency of 50&nbsp;Hz. The number of pole-pairs is 2, so
the synchronous speed is:
:<math>N_s = 60\;\frac\text{rpm}\text{Hz} \times \frac{50\text{ Hz}}{2} = 1500\,\,\text{rpm} </math>

A [[three-phase electric power|three-phase]], 12-pole (6-pole-pair) synchronous motor is operating at an AC supply frequency of 60&nbsp;Hz. The number of pole-pairs is 6, so the synchronous speed is:
:<math>N_s = 60\;\frac\text{rpm}\text{Hz} \times \frac{60\text{ Hz}}{6} = 600\,\,\text{rpm} </math>

The number of magnetic poles, <math>p</math>, is equal to the number of coil groups per phase. To determine the number of coil groups per phase in a 3-phase motor, count the number of coils, divide by the number of phases, which is 3. The coils may span several slots in the stator core, making it tedious to count them. For a 3-phase motor, if you count a total of 12 coil groups, it has 4 magnetic poles. For a 12-pole 3-phase machine, there will be 36 coils. The number of magnetic poles in the rotor is equal to the number of magnetic poles in the stator.