The synchronous speed of a three phase induction motor having 20 poles and connected to a 50 Hz source is-
300 RPM
Understanding Synchronous Speed in Three-Phase Induction Motors
This question asks us to calculate the synchronous speed of a three-phase induction motor given its number of poles and the frequency of the power source. The synchronous speed is the speed at which the magnetic field rotates in the stator of an AC motor.
Calculating Synchronous Speed
The synchronous speed ($\(N_s\)$) of a three-phase induction motor is directly proportional to the frequency of the power supply (\(f\)) and inversely proportional to the number of poles (\(P\)) of the motor. The formula connecting these parameters is:
\(N_s = \frac{120f}{P}\)
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 the motor
Applying the Formula
We are given the following values:
- Frequency (\(f\)) = 50 Hz
- Number of poles (\(P\)) = 20 poles
Now, we can substitute these values into the formula to find the synchronous speed:
\(N_s = \frac{120 \times 50}{20}\)
First, calculate the numerator:
\(120 \times 50 = 6000\)
Now, divide by the number of poles:
\(N_s = \frac{6000}{20}\)
\(N_s = 300\) RPM
Result and Option Analysis
The calculated synchronous speed of the three-phase induction motor with 20 poles connected to a 50 Hz source is 300 RPM.
Let's compare this result with the given options:
- Option 1: 1200 RPM
- Option 2: 1000 RPM
- Option 3: 600 RPM
- Option 4: 300 RPM
Our calculated value, 300 RPM, matches Option 4.
| Parameter | Value |
|---|---|
| Frequency (f) | 50 Hz |
| Number of Poles (P) | 20 |
| Calculated Synchronous Speed (\(N_s\)) | 300 RPM |
Revision Table: Three-Phase Induction Motor Speed Calculation
| Concept | Description | Formula |
|---|---|---|
| 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 (Hz) | Given |
| Number of Poles (P) | Total number of magnetic poles in the stator (must be an even integer) | Given |
Additional Information on Induction Motor Speed
The actual speed of the rotor in a three-phase induction motor is always slightly less than the synchronous speed. This difference in speed is called slip. Slip is essential for the motor to produce torque.
The rotor speed (\(N_r\)) is given by:
\(N_r = N_s (1 - s)\)
Where \(s\) is the slip, usually expressed as a decimal or percentage. Slip is defined as:
\(s = \frac{N_s - N_r}{N_s}\)
For example, if the synchronous speed is 300 RPM and the slip is 4%, the rotor speed would be:
\(N_r = 300 (1 - 0.04) = 300 \times 0.96 = 288\) RPM
Understanding both synchronous speed and slip is crucial for analysing the performance of induction motors.
Important Questions from Three Phase Induction Motor
For a slip 's' and supply frequency 'f', the frequency of current in rotor will be-
The rotating magnetic field in a three-phase, 6-poles, 50 Hz slip ring induction motor will rotate at-
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
