The usual value of slip of a 3Φ induction motor at full load is about:

Explanation:

Slip in Three-Phase Induction Motors

Definition: Slip in a three-phase induction motor is defined as the difference between the synchronous speed and the rotor speed, expressed as a percentage of the synchronous speed. Mathematically, slip (S) can be calculated using the formula:

S = [(Ns - Nr)/Ns] × 100

Where:

• Ns: Synchronous speed of the motor (in RPM).
• Nr: Rotor speed of the motor (in RPM).

The synchronous speed is determined by the supply frequency and the number of poles in the motor, using the formula:

Ns = (120 × f)/P

Where:

• f: Supply frequency (in Hz).
• P: Number of poles in the motor.

Slip is an essential parameter in induction motors as it determines the relative speed between the stator magnetic field and the rotor. A small slip ensures efficient operation of the motor while allowing torque generation.

Typical Value of Slip:

For a three-phase induction motor operating under full load conditions, the slip is typically very small, ranging between 0.05 (5%) and 0.1 (10%). This ensures the motor operates close to its synchronous speed while maintaining sufficient torque to drive the load.

Correct Option Analysis:

The correct option is:

Option 1: 0.05

The usual value of slip for a three-phase induction motor at full load is about 0.05 (5%). This small slip value indicates that the rotor speed is very close to the synchronous speed, which is desirable for efficient motor operation. At full load, the rotor speed slightly lags the synchronous speed, allowing current induction in the rotor, which generates torque to drive the load.

Why Slip Occurs:

Slip occurs in induction motors because the rotor must move slower than the synchronous speed to allow relative motion between the rotating magnetic field of the stator and the rotor conductors. This relative motion induces current in the rotor conductors, which interacts with the stator field to produce torque. Without slip, there would be no induced current, and thus no torque generation.

Factors Affecting Slip:

• Load on the motor: As the load increases, the slip increases because more torque is required to overcome the load.
• Rotor resistance: Higher rotor resistance generally results in higher slip values.
• Supply frequency and voltage: Variations in supply frequency and voltage can impact the synchronous speed and slip.

Advantages of Small Slip:

• Ensures high efficiency as the rotor operates close to the synchronous speed.
• Provides stable and consistent torque output under varying load conditions.
• Minimizes losses due to relative motion between the stator and rotor fields.

Important Information

To further understand the analysis, let’s evaluate the other options:

Option 2: 0.1

A slip value of 0.1 (10%) is higher than the typical range for full-load operation in standard three-phase induction motors. While some motors may operate with a slip value of 10% under specific conditions, such as high rotor resistance or low efficiency designs, it is not representative of the usual value for standard motors operating at full load. Generally, efficient motors have slip values closer to 5%.

Option 3: 0.3

A slip value of 0.3 (30%) is significantly higher than the typical range for three-phase induction motors under full load. Such high slip values are usually indicative of either a malfunctioning motor or a motor designed for specific applications where high slip is acceptable, such as certain types of wound rotor motors or applications requiring variable speed. In standard induction motors, a slip of 30% would lead to substantial losses and inefficiency.

Option 4: 0.8

A slip value of 0.8 (80%) is far outside the normal operating range for three-phase induction motors. At such high slip values, the rotor speed would be extremely low compared to the synchronous speed, resulting in poor efficiency and substantial energy losses. This condition may occur in cases of rotor stalling or severe overload, but it is not representative of typical motor operation under full load conditions.

Conclusion:

Slip is a critical parameter in the operation of three-phase induction motors, allowing torque generation while ensuring efficient operation. Under full load conditions, the usual value of slip for standard motors is about 0.05 (5%), as described in option 1. This small slip ensures the rotor operates close to the synchronous speed, minimizing losses and providing stable torque output. Understanding the factors affecting slip and its implications is essential for selecting and operating induction motors effectively.