Question

A 4 pole, 400 V, 50 hz, 3 phase induction motor is running at 1425 rpm, what will be the frequency of the rotor current at this speed?
A- 50 Hz
B- 100 hz
C- 2.5 Hz
D- 5 hz

Answer 1

Hint: This problem involves the use of formulas of finding the running frequency of induction motor. Here, we are given that it is a 4 pole. There can be 8 pole and 12 pole motors too. Also, the motor mentioned is a 3 phase one.

Step by step answer:
Number of poles=p= 4
Voltage= 400V
Frequency =f= 50 hz
\[{{N}_{s}}\] = synchronous speed
\[{{N}_{r}}\]= rotor speed= 1425
We know, here initially it was running at 1425 rpm, thus \[{{N}_{r}}=1425\]
Also, the running frequency is 50 hz so, \[{{N}_{s}}=\dfrac{120\times f}{p}\]
\[
   {{N}_{s}}=\dfrac{120\times 50}{4} \\
   \Rightarrow {{N}_{s}}=1500 \\
\]
Thus, putting the values, we get,
\[
   {{N}_{r}}={{N}_{s}}(1-s) \\
  \Rightarrow 1425=1500(1-s) \\
 \Rightarrow 0.95=1-s \\
  \Rightarrow s=1-0.95 \\
  \therefore s=0.05 \\
\]
Now, to find the frequency of the rotor current at this speed we use the formula,
\[
 F =s\times f \\
 \Rightarrow F =0.05\times 50 \\
\therefore F =2.5Hz \\
\]
So, the correct option is C.

Additional information: We must keep in mind that frequency is the characteristic of the source. It does not change with the change of the medium. It practically remains constant throughout. On the other hand, other characteristics of sound like wavelength changes with the change of the medium and are not constant. Also, the speed which is the product of frequency and wavelength changes on account of change in wavelength.

Note: induction motor is a kind of motor which involves self starting and in this motor rotation of rotor occurs due to Faraday's law of electromagnetic induction. The frequency that we have calculated as the final answer is Slip frequency of rotor induced EMF frequency.