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I am given the rated values of a squirrel cage induction motor:

A 300hp, 2300V, 3‐phase, 60Hz squirrel‐cage induction motor turns at a full‐load speed of 590r/min. What is the approximate value of the rotor I2R losses?

However, the synchronous speed is not given, nor are the amount of poles in the motor. How would one solve this problem without knowing these values?

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The rated speed is usually about 90-95% of synchronous speed. You can guess the synchronous speed and number of poles by looking for a number of poles that gives a rated speed slightly less than synchronous speed.

In this case, I would guess you are dealing with a 60Hz 12-pole motor, which would have a synchronous speed of 600 rpm.

I've done a quick lookup table below for reference.

Poles    50hz    60hz
2        3000    3600
4        1500    1800
6        1000    1200
8        750     900
10       600     720
12       500     600
16       375     450
20       300     360
24       250     300
30       200     240
40       150     180
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It will be a 12 pole motor with a sync speed of 600 RPM.

Speed = 2 · 60 · f / n

where f = frequency (Hz, cycles/sec) and n = number of poles

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