In field resistance control ,with increased field resistance, field current decreases,hence flux produced by field current also decreases.N is indirectly proportional to field flux so speed increases by this method.

Introduction:
In this question, we are given a DC shunt motor with a rated RPM of 480. We are required to run the motor at 540 RPM for some time in an industrial application. We need to determine which speed control method would be desirable in this scenario.

Explanation:
To understand which speed control method is desirable, we need to consider the characteristics and limitations of the DC shunt motor.

1. Ward Leonard Control:
Ward Leonard control is a method of speed control that uses a separate motor-generator set to control the speed of the DC motor. While this method allows for precise control of the motor speed, it is typically used for applications that require very fine speed adjustments and high precision. In this scenario, where we need to increase the motor speed from 480 RPM to 540 RPM, the Ward Leonard control may be considered overkill and unnecessary.

2. Armature Current Control:
Armature current control involves adjusting the armature current of the motor to control its speed. By increasing the armature current, we can increase the motor speed. However, there are limitations to this method. Increasing the armature current beyond a certain point can lead to overheating and damage to the motor. Therefore, it may not be a desirable speed control method in this scenario.

3. Field Resistance Control:
Field resistance control is a widely used method for speed control in DC shunt motors. By adjusting the field resistance, we can vary the flux in the motor, which in turn affects the speed. By decreasing the field resistance, we can increase the motor speed. This method provides a simple and effective way to control the speed of the motor within certain limits. Therefore, it is a desirable speed control method in this scenario.

4. Not possible to run the motor at more than the rated RPM:
This statement is incorrect. While it is generally not recommended to run a motor at speeds higher than its rated RPM for extended periods, it is possible to temporarily increase the motor speed using appropriate speed control methods, such as field resistance control.

Conclusion:
In conclusion, the desirable speed control method for running the DC shunt motor at 540 RPM in this scenario is field resistance control. This method allows for effective speed control while staying within the motor's operational limits. Ward Leonard control and armature current control may not be necessary or suitable for this specific requirement. Additionally, it is possible to run the motor at speeds higher than the rated RPM temporarily using appropriate speed control methods.