College

Calculate the speed at which a 6-pole synchronous generator must rotate to produce an AC voltage at a frequency of 60 Hz.

If a frequency of 50 Hz is desired, calculate the speed of rotation of the generator.

Answer :

Final answer:

To produce a 60 Hz voltage, a 6-pole synchronous generator must rotate at 1200 rpm. For a 50 Hz frequency, the required rotation speed is 1000 rpm.

Explanation:

To calculate the speed of rotation of a 6-pole synchronous generator necessary to produce an AC voltage at 60 Hz, we use the equation for the synchronous speed of an AC generator:

N_s = (120 × f) / P

Where N_s is the synchronous speed in revolutions per minute (rpm), f is the frequency in hertz (Hz), and P is the number of poles.

For a frequency of 60 Hz, the calculation would be:

N_s = (120 × 60) / 6

N_s = 1200 rpm

Thus, to produce a voltage at 50 Hz, the speed of rotation would need to be:

N_s = (120 × 50) / 6

N_s = 1000 rpm