A three-phase induction motor is running at 1460 rpm when connected to 440 V three-phase, 50 Hz supply. The number of poles of the motor are:

Explanation:

Calculation of Number of Poles:

To determine the number of poles (P) for a three-phase induction motor, we use the formula that relates the synchronous speed (Ns) in revolutions per minute (rpm) to the frequency (f) of the supply in hertz (Hz) and the number of poles.

The formula is:

Ns = (120 * f) / P

Where:

• Ns = Synchronous speed in rpm
• f = Frequency of the supply in Hz
• P = Number of poles

Given that the supply frequency (f) is 50 Hz and the motor is running at 1460 rpm, we need to find the synchronous speed (Ns) first. However, the 1460 rpm given is the actual speed (N) of the motor, not the synchronous speed. The actual speed is slightly less than the synchronous speed due to slip.

Slip (s) in an induction motor is given by:

s = (Ns - N) / Ns

For small slip values, we can approximate the synchronous speed (Ns) as:

Ns ≈ N / (1 - s)

However, for simplicity, we can assume a small slip value and calculate the synchronous speed directly using common values for slip in induction motors (typically around 2-5%).

Let's assume a slip of around 3% (0.03):

Ns = N / (1 - s)

Substituting the values:

Ns ≈ 1460 / (1 - 0.03) ≈ 1460 / 0.97 ≈ 1505 rpm

For practical purposes, the synchronous speed for a 50 Hz supply is typically one of the standard synchronous speeds: 3000 rpm, 1500 rpm, 1000 rpm, 750 rpm, etc.

Given that 1505 rpm is very close to 1500 rpm, we can assume the synchronous speed Ns to be 1500 rpm.

Now, using the synchronous speed formula:

1500 = (120 * 50) / P

Simplifying, we get:

P = (120 * 50) / 1500

P = 6000 / 1500

P = 4

Therefore, the number of poles of the motor is 4.

The correct answer is option 2.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1 (22 poles):

If the motor had 22 poles, the synchronous speed Ns would be calculated as follows:

Ns = (120 * 50) / 22

Ns ≈ 272.7 rpm

This is far from the given running speed of 1460 rpm, so this option is incorrect.

Option 3 (6 poles):

If the motor had 6 poles, the synchronous speed Ns would be:

Ns = (120 * 50) / 6

Ns = 1000 rpm

Since the actual speed (1460 rpm) is much higher than 1000 rpm, this option is incorrect.

Option 4 (8 poles):

If the motor had 8 poles, the synchronous speed Ns would be:

Ns = (120 * 50) / 8

Ns = 750 rpm

The actual speed (1460 rpm) is much higher than 750 rpm, so this option is also incorrect.

Conclusion:

By understanding the relationship between the synchronous speed, frequency, and the number of poles, we can accurately determine the number of poles in a three-phase induction motor. In this case, the correct number of poles is 4, as determined from the given speed and frequency. This type of motor is common in industrial applications where a balance between speed and torque is required.