The frequencies of the stator and rotor currents flowing in a three-phase, 8-pole induction motor are 40 Hz and 1 Hz, respectively. The motor speed, in rpm, is ______. (round off to nearest integer)

The correct answer is 585.

To find the speed of the induction motor, we can break down the calculation into the following steps:

Step 1: Calculate the slip (s) of the induction motor
The relation between the rotor current frequency ($f_r$), stator supply frequency ($f_s$), and slip ($s$) is given by:
$f_r=s\times f_s$
Given:
Stator frequency, $f_s=40\text{Hz}$
Rotor frequency, $f_r=1\text{Hz}$
Rearranging the formula to find the slip:
$s=\frac{f_r}{f_s}=\frac{1}{40}=0.025$

Step 2: Calculate the synchronous speed ($N_s$)
The synchronous speed of the stator magnetic field in rpm is given by:
$N_s=\frac{120\times f_s}{P}$
where $P$ is the number of poles. Given $P=8$:
$N_s=\frac{120\times 40}{8}=600\text{rpm}$

Step 3: Calculate the actual speed of the rotor ($N_r$)
The rotor speed (motor speed) is related to the synchronous speed and slip by:
$N_r=(1-s)\times N_s$
Substituting the calculated values:
$N_r=(1-0.025)\times 600$
$N_r=0.975\times 600=585\text{rpm}$