The number of poles in an induction motor directly affects its synchronous speed, which is the theoretical speed at which the motor's rotating magnetic field would rotate if there were no slip (difference between synchronous speed and actual speed) in the motor's operation. The formula to calculate synchronous speed (Ns) is given by:
Ns = 120 * f / P
Where:
Ns is the synchronous speed in revolutions per minute (RPM)
f is the frequency of the power supply in Hertz (Hz)
P is the number of poles in the motor
From this formula, it's clear that the synchronous speed is inversely proportional to the number of poles. This means that a motor with more poles will have a lower synchronous speed, and a motor with fewer poles will have a higher synchronous speed.
However, in actual operation, induction motors are designed to run at speeds slightly lower than their synchronous speed due to slip. Slip is necessary for the motor to generate torque and overcome the load it's connected to. The slip allows the motor's rotor to turn at a speed that is slightly slower than the rotating magnetic field produced by the stator. The difference between the synchronous speed and the actual operating speed is known as slip speed.
So, in summary, the number of poles in an induction motor affects its synchronous speed, but the actual operating speed will be slightly lower due to slip. Motors with more poles will have lower synchronous speeds and are often used for applications where higher torque at lower speeds is required, while motors with fewer poles will have higher synchronous speeds and are suitable for applications requiring higher speeds.