Question

Explain working of resistance split phase single phase induction motor with vector diagram.

Answer 1

A resistance split-phase single-phase induction motor is commonly used in applications requiring low starting torque, such as fans, pumps, and small tools. The motor operates using a split-phase system, which creates a phase difference between the currents in two windings to generate a rotating magnetic field. Here's a detailed explanation of its working, along with a vector diagram.

### Construction

1. **Stator**: The stator has two windings:
   - **Main Winding (or Run Winding)**: Connected directly to the AC supply.
   - **Auxiliary Winding (or Start Winding)**: Connected through a resistor to create a phase difference.
  
2. **Rotor**: Typically a squirrel cage rotor, which consists of conductive bars shorted at the ends.

### Working Principle

1. **AC Supply**: When an AC voltage is applied to the motor, the main winding creates a magnetic field that induces a current in the rotor.

2. **Current in Windings**: The current in the auxiliary winding, through the series resistor, lags the current in the main winding. This lag creates a phase difference that is crucial for starting the motor.

3. **Rotating Magnetic Field**: The combination of the currents in both windings generates a rotating magnetic field. The direction of rotation is determined by the phase relationship between the currents in the two windings.

4. **Starting Torque**: The rotor experiences a torque due to the interaction of the rotating magnetic field and the induced current in the rotor. This torque allows the motor to start.

5. **Running Condition**: Once the motor reaches about 70-80% of its full speed, the auxiliary winding is disconnected (either manually or automatically via a centrifugal switch), and the motor continues to run on the main winding alone.

### Vector Diagram

The vector diagram helps illustrate the phase relationship and the resulting magnetic fields:

- **Vectors**:
  - \( I_1 \) represents the current in the main winding (usually taken as the reference vector).
  - \( I_2 \) represents the current in the auxiliary winding, which lags behind \( I_1 \) due to the resistance in the auxiliary circuit.

- **Phase Angle**: The angle \( \phi \) between \( I_1 \) and \( I_2 \) represents the phase difference created by the resistor in series with the auxiliary winding.

- **Resultant Current**: The resultant current \( I_R \) is the vector sum of \( I_1 \) and \( I_2 \), which creates a resultant magnetic field that rotates.

### Vector Diagram Representation

Here’s how to visualize the vector diagram:

1. Draw a horizontal line for \( I_1 \) (the main winding current).
2. From the tip of \( I_1 \), draw \( I_2 \) at an angle \( \phi \) (lagging).
3. The resultant vector \( I_R \) can be drawn from the origin to the tip of \( I_2 \), illustrating the overall magnetic effect.

### Summary

- The resistance split-phase motor utilizes two windings to create a phase difference, enabling the generation of a rotating magnetic field.
- The starting torque is facilitated by the interaction of the magnetic fields produced by the two windings.
- Understanding the vector diagram allows for a visual representation of how phase differences contribute to motor operation.

This combination of resistive splitting and vector analysis helps make the resistance split-phase induction motor an efficient choice for various low-torque applications.

Answer 2

A resistance split-phase single-phase induction motor is a type of single-phase AC motor that is commonly used in applications requiring moderate starting torque. It is equipped with a split-phase winding and an additional resistor in series with one of the windings to improve its starting characteristics.

### Working Principle

1. **Construction:**
   - **Stator:** Consists of a main winding (also called the running winding) and a start winding. The start winding is connected in series with a resistor (the starting resistor).
   - **Rotor:** Typically a squirrel-cage type, which is similar to other induction motors.

2. **Starting Mechanism:**
   - When the motor is initially powered, the current flows through both the start winding and the main winding.
   - The additional resistor in series with the start winding creates a phase shift between the currents in the start and main windings. This phase shift produces a rotating magnetic field that is essential for starting the motor.

3. **Operation:**
   - Once the motor reaches a certain speed, a centrifugal switch (or a relay) disconnects the starting resistor and the start winding from the circuit.
   - The motor then continues to operate using only the main winding.

### Vector Diagram

The vector diagram of a resistance split-phase induction motor illustrates the phase relationship between the currents in the stator windings and the resulting magnetic field.

1. **Current in Main Winding (I1):** Represented by a reference vector, usually along the horizontal axis.

2. **Current in Start Winding (I2):** This current lags the main winding current due to the resistance in the start winding. Its vector is shown at an angle relative to the main winding current.

3. **Magnetic Field (Φ):** The resultant magnetic field produced by the combination of currents in both windings. The field vector will be somewhere between the vectors of the main and start winding currents, depending on the angle of phase shift introduced by the resistor.

#### Steps to Draw the Vector Diagram:

1. **Draw the Main Winding Current (I1):** Draw a horizontal line representing the main winding current.

2. **Draw the Start Winding Current (I2):** Draw a line at an angle to the horizontal line. The angle depends on the resistance of the start winding and the start winding's position in relation to the main winding.

3. **Draw the Resultant Magnetic Field (Φ):** This is the vector sum of the magnetic fields created by each winding. It will be at an angle to the main winding current, reflecting the combined effect of both windings.

4. **Determine the Rotation Direction:** The direction of rotation of the magnetic field (and hence the rotor) can be determined by the direction of the resultant magnetic field vector. This direction will be counterclockwise or clockwise depending on the phase relationship between the currents in the windings.

The vector diagram helps in understanding how the phase shift between the start and main winding currents creates a rotating magnetic field necessary for the motor's starting torque. Once the motor starts and the start winding is disconnected, the operation continues with the main winding only, providing a uniform magnetic field for steady operation.