Study the given statements with reference to single phase induction motor and select the appropriate option.

1. Single-phase induction motor is a self-starting machine.

2. Double-revolving field theory can be used for performance analysis of 1-phase induction motors.

Explanation:

Single-Phase Induction Motor

Definition: A single-phase induction motor is an electric motor that operates on a single-phase power supply. It is widely used in domestic and industrial applications where three-phase power is not available. The motor consists of a stator and a rotor, with the stator carrying a single-phase winding that produces an oscillating magnetic field when connected to a single-phase AC supply.

Working Principle: The working principle of a single-phase induction motor can be explained using the double-revolving field theory. According to this theory, the single-phase alternating current (AC) supply creates an oscillating magnetic field, which can be considered as the sum of two rotating magnetic fields of equal magnitude but rotating in opposite directions. These rotating magnetic fields induce currents in the rotor, producing torque. However, at standstill, these torques cancel each other out, resulting in no net torque and hence, the motor is not self-starting.

Detailed Solution of the Correct Option:

The correct option is:

Option 4: Statement 1 is false, but statement 2 is true.

Let's analyze the given statements to understand why this is the correct option:

Statement 1: Single-phase induction motor is a self-starting machine.

This statement is false. A single-phase induction motor is not inherently self-starting. When a single-phase AC supply is applied to the stator winding, it creates an alternating magnetic field. However, this alternating field does not produce a rotating magnetic field at standstill, resulting in no starting torque. Therefore, an external starting mechanism, such as a starting capacitor, auxiliary winding, or split-phase design, is required to produce the initial rotating magnetic field to start the motor.

Statement 2: Double-revolving field theory can be used for performance analysis of 1-phase induction motors.

This statement is true. The double-revolving field theory is a fundamental concept used to analyze the performance of single-phase induction motors. According to this theory, the single-phase alternating current creates two rotating magnetic fields of equal magnitude but in opposite directions. These fields interact with the rotor to produce torque. The analysis of these rotating fields helps in understanding the motor's behavior, performance, and the development of starting mechanisms.

Correct Option Analysis:

The correct option is:

Option 4: Statement 1 is false, but statement 2 is true.

This option correctly identifies the nature of single-phase induction motors and the applicability of double-revolving field theory. Single-phase induction motors are not self-starting due to the absence of a rotating magnetic field at standstill, and the double-revolving field theory is indeed used for performance analysis of these motors.

Additional Information

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

Option 1: Statement 1 is true, but statement 2 is false.

This option is incorrect because statement 1 is false. As explained, single-phase induction motors are not self-starting. Additionally, statement 2 is true, as the double-revolving field theory is used for performance analysis.

Option 2: Both the statements are true.

This option is incorrect because statement 1 is false. Single-phase induction motors are not self-starting, although statement 2 is true.

Option 3: Both the statements are false.

This option is incorrect because statement 2 is true. The double-revolving field theory is a valid and essential concept for analyzing the performance of single-phase induction motors.

Conclusion:

Understanding the operational characteristics of single-phase induction motors is crucial for accurately evaluating their performance and identifying their limitations. These motors require external mechanisms to start, as they do not produce a rotating magnetic field at standstill. The double-revolving field theory is an essential tool for analyzing their performance, making it an important concept in the study of single-phase induction motors.