A single-phase induction motor of 100 W is connected to 230 V AC. If its auxiliary winding is open at the start, then the resultant torque on the rotor is:

Explanation:

Single-Phase Induction Motor

Definition: A single-phase induction motor is an AC motor that operates on single-phase power supply. It has two main parts: the stator and the rotor. The stator carries the alternating current and produces a rotating magnetic field, which induces current in the rotor and causes it to turn, producing mechanical motion.

Working Principle: In a single-phase induction motor, the stator winding is connected to a single-phase AC supply. When the current flows through the stator winding, it creates a pulsating magnetic field. This pulsating field can be thought of as two rotating magnetic fields of equal magnitude but rotating in opposite directions. The interaction of these fields with the rotor induces a current in the rotor, which produces torque and causes the rotor to rotate.

However, at the start, a single-phase induction motor does not produce a rotating magnetic field; it produces a pulsating magnetic field. This pulsating field is not sufficient to start the motor. Therefore, an auxiliary winding (or starting winding) is used to create a phase difference and produce a rotating magnetic field that can start the motor.

Correct Option Analysis:

The correct option is:

Option 1: zero

This option is correct because if the auxiliary winding is open at the start, the motor does not have the necessary phase difference to create a rotating magnetic field. Without a rotating magnetic field, the motor cannot produce any starting torque. Therefore, the resultant torque on the rotor is zero.

Additional Information

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

Option 2: maximum

This option is incorrect because, without the auxiliary winding, the motor cannot produce a rotating magnetic field at the start. Therefore, it cannot produce maximum torque. The motor requires the auxiliary winding to create the phase difference and start the rotation.

Option 3: 0.5 N-m

This option is also incorrect. As explained, without the auxiliary winding, the motor cannot produce any starting torque, so it is not possible for the torque to be 0.5 N-m. The torque would be zero.

Option 4: 2.0 N-m

This option is incorrect as well. Similar to option 3, the motor cannot produce any starting torque without the auxiliary winding. Therefore, the torque cannot be 2.0 N-m; it would be zero.

Conclusion:

Understanding the role of the auxiliary winding in a single-phase induction motor is crucial. The auxiliary winding is essential for creating a phase difference and producing a rotating magnetic field, which is necessary to start the motor. Without the auxiliary winding, the motor cannot produce any starting torque, resulting in zero torque on the rotor. This makes option 1 the correct answer.