Question

An 8-pole, 3-phase, 50 Hz induction motor is operating at a speed of 720 rpm. The frequency of the rotor current of the motor in Hz is __________

(a) 2

(b) 4

(c) 3

(d) 1

I had been asked this question in exam.

My doubt stems from DC Motors in portion Characteristics of DC & AC Motors of Electric Drives

Answer 1

To find the frequency of the rotor current in an induction motor, we can use the following formula:

fr=s×f2f_r = \frac{s \times f}{2}fr​=2s×f​

Where:

• frf_rfr​ is the frequency of the rotor current,
• sss is the slip of the motor,
• fff is the supply frequency.

Step 1: Calculate the synchronous speed (NsN_sNs​)

The synchronous speed for a 3-phase induction motor is given by the formula:

Ns=120×fPN_s = \frac{120 \times f}{P}Ns​=P120×f​

Where:

• NsN_sNs​ is the synchronous speed in rpm,
• fff is the supply frequency in Hz,
• PPP is the number of poles.

Given:

• P=8P = 8P=8 poles,
• f=50f = 50f=50 Hz.

Substitute the values:

Ns=120×508=750 rpmN_s = \frac{120 \times 50}{8} = 750 \, \text{rpm}Ns​=8120×50​=750rpm

Step 2: Calculate the slip (sss)

The slip sss is given by the formula:

s=Ns−NNss = \frac{N_s - N}{N_s}s=Ns​Ns​−N​

Where:

• Ns=750 rpmN_s = 750 \, \text{rpm}Ns​=750rpm (synchronous speed),
• N=720 rpmN = 720 \, \text{rpm}N=720rpm (actual speed).

Substitute the values:

s=750−720750=30750=0.04s = \frac{750 - 720}{750} = \frac{30}{750} = 0.04s=750750−720​=75030​=0.04

Step 3: Calculate the rotor frequency

Now, use the formula for the rotor frequency:

fr=s×f2=0.04×502=22=1 Hzf_r = \frac{s \times f}{2} = \frac{0.04 \times 50}{2} = \frac{2}{2} = 1 \, \text{Hz}fr​=2s×f​=20.04×50​=22​=1Hz

Thus, the frequency of the rotor current is 1 Hz.

The correct answer is (d) 1.