The rotating magnetic field in a three-phase, 6-poles, 50 Hz slip ring induction motor will rotate at-
1000 RPM
Understanding Rotating Magnetic Field Speed in 3-Phase Induction Motors
The question asks for the speed of the rotating magnetic field in a three-phase, 6-poles, 50 Hz slip ring induction motor. This speed is also known as the synchronous speed (\(N_s\)). The synchronous speed is the speed at which the magnetic field produced by the stator windings rotates.
For a three-phase induction motor, the synchronous speed is determined by the frequency of the power supply (\(f\)) and the number of poles (\(P\)) for which the stator winding is designed. The relationship is given by the following formula:
\(N_s = \frac{120f}{P}\)
Where:
- \(N_s\) is the synchronous speed in revolutions per minute (RPM)
- \(f\) is the frequency of the power supply in Hertz (Hz)
- \(P\) is the number of poles
In this specific question, we are given:
- Frequency, \(f = 50\) Hz
- Number of poles, \(P = 6\)
Now, we can substitute these values into the formula to calculate the synchronous speed:
\(N_s = \frac{120 \times 50}{6}\)
\(N_s = \frac{6000}{6}\)
\(N_s = 1000\) RPM
Thus, the rotating magnetic field in the three-phase, 6-poles, 50 Hz slip ring induction motor will rotate at 1000 RPM.
Analyzing the Options
Let's compare our calculated synchronous speed with the given options:
| Option | Speed (RPM) | Matches Calculation? |
|---|---|---|
| 1 | 1500 | No |
| 2 | 1000 | Yes |
| 3 | 2000 | No |
| 4 | 1200 | No |
Our calculated value of 1000 RPM matches Option 2.
Conclusion on Rotating Magnetic Field Speed
The speed of the rotating magnetic field, or synchronous speed, for a 6-pole, 50 Hz motor is 1000 RPM. This is a fundamental characteristic determined by the design of the stator winding (number of poles) and the frequency of the power source.
Revision Table: Induction Motor Fundamentals
| Term | Description | Formula/Relationship |
|---|---|---|
| Synchronous Speed (\(N_s\)) | Speed of the rotating magnetic field in the stator. | \(N_s = \frac{120f}{P}\) |
| Frequency (\(f\)) | Frequency of the AC power supply (in Hz). | Provided value (e.g., 50 Hz or 60 Hz) |
| Number of Poles (\(P\)) | Total number of magnetic poles created by the stator winding. Always an even number. | Design parameter of the motor. |
| Slip (\(s\)) | The difference between synchronous speed and rotor speed, expressed as a fraction or percentage of synchronous speed. | \(s = \frac{N_s - N_r}{N_s}\) |
| Rotor Speed (\(N_r\)) | Actual speed of the motor shaft. Always less than synchronous speed in an induction motor under load. | \(N_r = N_s(1-s)\) |
Additional Information on Induction Motor Speed
The rotating magnetic field is crucial for the operation of a three-phase induction motor. This field induces a voltage and current in the rotor winding (hence "induction" motor). The interaction between the induced rotor current and the rotating magnetic field produces torque, causing the rotor to spin.
It is important to remember that the rotor in an induction motor always rotates at a speed (\(N_r\)) slightly less than the synchronous speed (\(N_s\)). If the rotor were to spin at synchronous speed, there would be no relative motion between the rotating magnetic field and the rotor conductors, no voltage would be induced in the rotor, no current would flow, and therefore no torque would be produced. The difference between synchronous speed and rotor speed is called slip, which is essential for the motor to develop torque.
The number of poles is determined by how the stator coils are wound and connected. More poles result in a lower synchronous speed for a given frequency.
Important Questions from Three Phase Induction Motor
For a slip 's' and supply frequency 'f', the frequency of current in rotor will be-
The synchronous speed of a three phase induction motor having 20 poles and connected to a 50 Hz source is-
The rotor current frequency in a slip-ring induction motor depends on-
The power factor of an induction motor operating at no load is around:
Cogging in an induction motor is caused
