The number of poles of a three phase induction motor running at 750 rpm with 50Hz frequency is
8
Calculating Induction Motor Poles from Speed and Frequency
The question asks us to determine the number of poles of a three-phase induction motor given its running speed and the supply frequency. We are told the motor is running at 750 rpm with a supply frequency of 50 Hz.
Understanding Synchronous Speed and Motor Speed
For any AC motor, especially an induction motor, the speed of the rotating magnetic field produced by the stator is called the synchronous speed ($N_s$). This speed depends directly on the supply frequency ($f$) and the number of poles ($P$) for which the motor is wound. The relationship is given by the formula:
$$N_s = \frac{120f}{P}$$
where:
- $N_s$ is the synchronous speed in revolutions per minute (rpm)
- $f$ is the supply frequency in Hertz (Hz)
- $P$ is the number of poles
A key characteristic of an induction motor is that its rotor speed (the actual running speed, often denoted as $N$ or $N_r$) is always slightly less than the synchronous speed ($N_s$). This difference in speed is necessary to induce current in the rotor, which creates the torque to turn the shaft. The difference is quantified by slip ($s$).
In this problem, the motor is specified as "running at 750 rpm". Given the options and the typical nature of such problems, it's highly probable that 750 rpm is intended to be the synchronous speed ($N_s$) corresponding to a standard number of poles, or that the slip is considered negligible for the purpose of finding the approximate number of poles.
Let's assume that 750 rpm corresponds to the synchronous speed for the purpose of finding the number of poles using the formula.
Step-by-Step Calculation of Poles
We need to find the number of poles ($P$). We can rearrange the synchronous speed formula to solve for $P$:
$$P = \frac{120f}{N_s}$$
Given:
- Supply frequency, $f = 50$ Hz
- Synchronous speed, $N_s = 750$ rpm (assuming the running speed given is effectively the synchronous speed for calculation)
Now, substitute the given values into the formula:
$$P = \frac{120 \times 50}{750}$$
First, calculate the numerator:
$$120 \times 50 = 6000$$
Now, divide the numerator by the synchronous speed:
$$P = \frac{6000}{750}$$
$$P = 8$$
So, the number of poles calculated based on a synchronous speed of 750 rpm and a frequency of 50 Hz is 8.
This result aligns with the standard possible synchronous speeds for a 50 Hz supply:
| Number of Poles (P) | Synchronous Speed ($N_s = \frac{120 \times 50}{P}$) |
|---|---|
| 2 | $\frac{120 \times 50}{2} = 3000$ rpm |
| 4 | $\frac{120 \times 50}{4} = 1500$ rpm |
| 6 | $\frac{120 \times 50}{6} = 1000$ rpm |
| 8 | $\frac{120 \times 50}{8} = 750$ rpm |
As shown in the table, an 8-pole motor operating at 50 Hz has a synchronous speed of exactly 750 rpm. Therefore, the induction motor in question has 8 poles, assuming the given running speed is close enough to the synchronous speed for the number of poles to be determined this way.
Conclusion on Induction Motor Poles
Based on the standard formula relating synchronous speed, frequency, and the number of poles, a three-phase induction motor operating at 50 Hz with a synchronous speed of 750 rpm must have 8 poles. Although an induction motor's running speed is typically slightly less than synchronous speed, the problem likely implies that 750 rpm is the basis for determining the number of poles.
Revision Table: Induction Motor Speed and Poles
| Concept | Description | Formula |
|---|---|---|
| Synchronous Speed ($N_s$) | Speed of the rotating magnetic field in the stator. Determined by frequency and poles. | $N_s = \frac{120f}{P}$ |
| Running Speed ($N$) | Actual speed of the motor shaft. Always less than $N_s$ for induction motors. | $N = N_s(1-s)$ |
| Frequency ($f$) | Frequency of the AC power supply (Hz). | Input parameter |
| Number of Poles ($P$) | Number of magnetic poles the stator winding creates. Must be an even integer. | $P = \frac{120f}{N_s}$ |
Additional Information on Induction Motor Speed
It is important to understand the difference between synchronous speed and running speed in an induction motor. The rotating magnetic field spins at the synchronous speed ($N_s$), determined by the frequency and the number of poles.
- Slip ($s$): The percentage difference between the synchronous speed and the actual rotor speed ($N$). It is calculated as $s = \frac{N_s - N}{N_s}$. Slip is crucial for the motor's operation, as it is what induces the current in the rotor needed to generate torque.
- Running Speed: The actual mechanical speed of the rotor, given by $N = N_s (1-s)$. For typical induction motors under load, slip is usually small, ranging from 2% to 5%. This means the running speed is very close to, but always less than, the synchronous speed.
- Problem Context: In questions like this, if a specific running speed is given which perfectly matches a standard synchronous speed for one of the pole options, it simplifies the problem, implying that synchronous speed should be used to find the poles. If the running speed was, for instance, 720 rpm, we would look for the nearest synchronous speed (which would be 750 rpm for an 8-pole motor at 50 Hz) and calculate the slip ($s = \frac{750 - 720}{750} = \frac{30}{750} = 0.04$ or 4% slip). But here, 750 rpm is given, and 8 poles yield exactly 750 rpm synchronous speed, making the calculation straightforward based on $N_s=750$ rpm.
Important Questions from Polyphase Induction Motors
Which type of rotor consists of a cylindrical laminated core with parallel slots for carrying rotor conductors?
The speed of an induction motor decreases with the increase in:
Direct Online Starters are generally used with motors of:
If a 3-phase 100 Hz induction motor has a slip of 4%, then what will be the frequency of motor induced emf?
The angular phase difference between each phase winding of a three-phase induction motor is
