At the point of saturation in a DC series motor, the torque becomes proportional to:

Torque in a DC Series Motor at Saturation

Definition: In a DC series motor, torque is initially proportional to the square of the armature current under unsaturated conditions. However, as the motor approaches magnetic saturation, the relationship between torque and armature current changes due to the limitation in further increase of flux.

Working Principle: The torque (T) produced in a DC series motor is generally given by the expression:

T ∝ Φ × I_a

Here:

• T = Torque
• Φ = Magnetic flux produced by the field winding
• I_a = Armature current

Under normal unsaturated conditions, the magnetic flux (Φ) is directly proportional to the armature current (I_a). As a result, the torque becomes proportional to the square of the armature current:

T ∝ Φ × I_a ∝ I_a²

However, as the motor operates at higher currents, the magnetic circuit of the motor approaches saturation. Once saturation occurs, further increases in armature current do not lead to a proportional increase in flux (Φ). Instead, the flux becomes nearly constant, and the torque becomes proportional to the armature current only:

T ∝ I_a

Correct Option Analysis:

The correct option is:

Option 1: Armature current only

At the point of saturation, the magnetic flux (Φ) produced by the field winding becomes constant due to the limitations in further magnetizing the core material. Therefore, the torque is no longer dependent on the flux and becomes directly proportional to the armature current (I_a). This is why, under saturation, the torque in a DC series motor is proportional to the armature current only.

Additional Information

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

Option 2: Both armature current and field flux

Under normal (unsaturated) conditions, torque in a DC series motor is proportional to both the armature current and the magnetic flux (Φ × I_a). However, once saturation occurs, the flux becomes constant and no longer varies with armature current. Hence, this option is incorrect under saturation conditions.

Option 3: Field flux only

This option is incorrect because the torque in a DC series motor is never solely dependent on the field flux (Φ). Torque is always a product of flux and armature current (Φ × I_a). Therefore, even under saturation, armature current is essential in determining the torque.

Option 4: The square of the armature current

This option is correct only under unsaturated conditions, where flux is proportional to armature current (Φ ∝ I_a) and torque becomes proportional to the square of the armature current (T ∝ I_a²). However, under saturation conditions, flux becomes constant, and torque is no longer proportional to the square of the armature current.

Conclusion:

At the point of saturation in a DC series motor, the torque becomes proportional to the armature current (I_a) only. This is due to the magnetic saturation of the core material, which prevents further increases in flux despite increases in armature current. Understanding this behavior is crucial for analyzing the performance characteristics of DC series motors in various operating conditions.