How is synchronous speed calculated for alternating current motors?

Synchronous speed is an essential concept in understanding the operation of alternating current (AC) motors, particularly in determining the speed at which the magnetic field rotates. The calculation uses the formula Ns = 120F/P, where Ns represents the synchronous speed in revolutions per minute (RPM), F is the frequency of the AC supply in hertz (Hz), and P is the number of poles in the motor.

The factor of 120 in the formula arises from the need to convert frequency and pole configuration into RPM. Specifically, the formula is derived from the relationship between electrical frequency, the number of cycles per second (frequency), and the number of magnetic poles. The formula accounts for the fact that each complete cycle corresponds to two rotations of the magnetic field when considering both positive and negative halves of the AC waveform, hence the multiplication by 2. The division by P accounts for how many times the magnetic field completes a cycle per rotation based on the number of poles.

In summary, using the formula Ns = 120F/P correctly calculates the synchronous speed of AC motors, reflecting the interplay between frequency and the motor's design (number of poles). Meanwhile, other formulas provided do not factor in the necessary conversion accurately or may misrepresent the relationship between these