# Whenever a synchronous machine operates at normal conditions, what is the relation between the rotor speed N in rpm, the frequency f in Hz, and the nu

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Whenever a synchronous machine operates at normal conditions, what is the relation between the rotor speed N in rpm, the frequency f in Hz, and the number of poles P?
1. $f = \frac{{PN}}{{120}}$
2. $N = \frac{{120\;f}}{{s\;P}}$
3. $f = \frac{{120\;N}}{P}$
4. $N = s \times \frac{{120\;f}}{P}$

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Correct Answer - Option 1 : $f = \frac{{PN}}{{120}}$

Concept:

The synchronous speed of a synchronous machine is given by

${N_s} = \frac{{120f}}{P}$

Where f is frequency and P is the number of poles.

A synchronous machine always rotates with a synchronous speed.

Explanation:

From the above relation, the frequency can be written as,

$f = \frac{{PN}}{{120}}$