Question

A three phase, 50 Hz induction motor runs at 960 rpm on full load. Find number of poles and percentage slip.

Answer 1

To find the **number of poles** and **percentage slip** of a three-phase induction motor, we can use the following formulas:

### 1. Synchronous Speed (Ns)
The synchronous speed of a three-phase induction motor is given by:

\[
N_s = \frac{120 \times f}{P}
\]

Where:
- \(N_s\) = Synchronous speed in RPM (Revolutions per minute)
- \(f\) = Frequency in Hz (50 Hz in this case)
- \(P\) = Number of poles

We can rearrange this formula to find the number of poles once we know the synchronous speed.

### 2. Slip (S)
The slip is the difference between the synchronous speed and the rotor speed. The percentage slip is given by:

\[
\text{Slip} (\%) = \frac{N_s - N_r}{N_s} \times 100
\]

Where:
- \(N_r\) = Rotor speed (actual speed of the motor, 960 rpm in this case)
- \(N_s\) = Synchronous speed

### Step 1: Find the Number of Poles (P)
First, we calculate the synchronous speed. Since the motor runs at 960 RPM and the frequency is 50 Hz, we assume the motor is close to synchronous speed, but slightly less because of slip.

We'll try different values of \(P\) to find the synchronous speed.

For \(P = 4\):

\[
N_s = \frac{120 \times 50}{4} = 1500 \text{ RPM}
\]

For \(P = 6\):

\[
N_s = \frac{120 \times 50}{6} = 1000 \text{ RPM}
\]

Since the motor's full-load speed is 960 RPM, and this is close to 1000 RPM, the motor must have **6 poles**.

### Step 2: Calculate the Percentage Slip
Now that we know the synchronous speed is 1000 RPM and the rotor speed is 960 RPM, we can calculate the percentage slip:

\[
\text{Slip} (\%) = \frac{1000 - 960}{1000} \times 100 = \frac{40}{1000} \times 100 = 4\%
\]

### Final Answer:
- **Number of poles (P): 6**
- **Percentage slip: 4%**

Answer 2

To determine the number of poles and percentage slip of a three-phase induction motor running at 960 RPM on full load, follow these steps:

### 1. Find the Number of Poles

First, you need to calculate the synchronous speed (\( N_s \)) of the motor, which is given by:

\[ N_s = \frac{120 \times f}{P} \]

where:
- \( N_s \) = Synchronous speed in RPM
- \( f \) = Frequency in Hz
- \( P \) = Number of poles

Rearrange this formula to solve for \( P \):

\[ P = \frac{120 \times f}{N_s} \]

The motor is running at 960 RPM on full load, which is the rotor speed (\( N_r \)).

To find the synchronous speed, you need to know the percentage slip.

### 2. Calculate Percentage Slip

The percentage slip (\( s \)) can be found using the formula:

\[ s = \frac{N_s - N_r}{N_s} \times 100\% \]

where:
- \( N_r \) = Rotor speed in RPM

### 3. Determine the Number of Poles and Synchronous Speed

The synchronous speed is always slightly higher than the rotor speed. Let's start with some common pole numbers and calculate the synchronous speed for each to see which one is close to 960 RPM.

**a. For a 2-pole motor:**

\[ N_s = \frac{120 \times 50}{2} = 3000 \text{ RPM} \]

**b. For a 4-pole motor:**

\[ N_s = \frac{120 \times 50}{4} = 1500 \text{ RPM} \]

**c. For a 6-pole motor:**

\[ N_s = \frac{120 \times 50}{6} = 1000 \text{ RPM} \]

**d. For an 8-pole motor:**

\[ N_s = \frac{120 \times 50}{8} = 750 \text{ RPM} \]

The synchronous speed closest to 960 RPM is 1000 RPM, which corresponds to a 6-pole motor.

**Let's confirm with a 6-pole motor:**

\[ N_s = 1000 \text{ RPM} \]

Calculate the percentage slip:

\[ s = \frac{1000 - 960}{1000} \times 100\% = \frac{40}{1000} \times 100\% = 4\% \]

### Summary

- **Number of Poles**: 6
- **Synchronous Speed**: 1000 RPM
- **Percentage Slip**: 4%

So, the induction motor has 6 poles and the percentage slip is 4%.