The line marked as x in the figure is torque-armature characteristics of: 

Explanation:

DC Cumulative Compound Motor

Definition: A DC cumulative compound motor is a type of direct current (DC) motor that combines the characteristics of both series and shunt motors. It has both series and shunt field windings, with the series winding connected in series with the armature and the shunt winding connected in parallel with the armature. This combination allows the motor to have a high starting torque while maintaining a relatively constant speed.

Working Principle: In a DC cumulative compound motor, the series field winding provides a high starting torque due to its strong initial magnetic field, which helps in overcoming the initial inertia of the load. The shunt field winding ensures that the speed of the motor remains relatively constant under varying load conditions. The cumulative effect of both windings allows the motor to handle heavy loads efficiently without significant changes in speed.

Characteristics:

• High starting torque due to the series winding.
• Relatively constant speed under varying loads due to the shunt winding.
• Can handle heavy loads efficiently.

Applications: DC cumulative compound motors are commonly used in applications that require high starting torque and relatively constant speed under load variations. These applications include elevators, cranes, conveyors, and heavy machinery.

Correct Option Analysis:

The correct option is:

Option 3: A DC cumulative compound motor.

The torque-armature characteristics of a DC cumulative compound motor are such that it combines the benefits of both series and shunt motors. The series field winding provides high starting torque, while the shunt field winding ensures that the speed remains relatively constant under varying loads. This combination makes the DC cumulative compound motor suitable for applications with varying load conditions.

Additional Information

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

Option 1: An SC shunt motor

A DC shunt motor has the field winding connected in parallel with the armature. It provides a constant speed under varying load conditions but does not have a high starting torque. The torque-armature characteristics of a shunt motor show a relatively flat curve, indicating constant speed, which is different from the cumulative compound motor characteristics.

Option 2: A DC series motor

A DC series motor has the field winding connected in series with the armature. It provides a high starting torque, but the speed varies significantly with the load. The torque-armature characteristics of a series motor show a steep curve, indicating a high starting torque and a decrease in speed with an increase in load. This is not the same as the cumulative compound motor characteristics.

Option 4: A DC differential compound motor

A DC differential compound motor has both series and shunt windings, but the series field winding is connected in opposition to the shunt field winding. This configuration results in a motor that can have poor speed regulation and may not handle heavy loads efficiently. The torque-armature characteristics of a differential compound motor are not suitable for applications requiring high starting torque and constant speed.

Conclusion:

Understanding the torque-armature characteristics of different types of DC motors is crucial for selecting the right motor for specific applications. A DC cumulative compound motor offers the advantages of both series and shunt motors, making it ideal for applications that require high starting torque and relatively constant speed under varying load conditions. This combination of characteristics is why option 3 is the correct answer.