In electrical measuring instruments, a controlling torque is essential to bring the pointer back to zero when the current is removed and to ensure a steady deflection for a given current. Two primary methods for providing this controlling torque are gravity control and spring control.

Gravity Control Explained

Gravity control is a method where the controlling torque is produced by the weight of a small adjustable mass attached to the moving system. This mass is usually placed on one side of the spindle, and its weight provides the restoring force. For the instrument to function correctly, it must be mounted in a perfectly vertical position so that gravity can act effectively.

Spring Control Explained

Spring control, on the other hand, utilizes two finely wound spiral hairsprings made of non-magnetic material like phosphor bronze. These springs are attached to the moving system and provide the controlling torque by twisting as the pointer deflects. When the current is removed, the springs return to their natural position, bringing the pointer back to zero.

Gravity Control Advantages

When comparing gravity control to spring control, gravity control offers several distinct advantages:

• Cost-effectiveness: It is generally cheap to implement as it involves simpler components compared to delicate hairsprings.
• Temperature Independence: It is largely unaffected by temperature changes. Unlike springs, which can change their elasticity with temperature, gravity's effect remains constant.
• Durability: It is not subjected to fatigue or deterioration with time. Springs can lose their elasticity or develop permanent set over extended use, but gravity control does not suffer from such issues.
• Friction Reduction: There is no friction in the control system itself, unlike spring control where the springs can sometimes cause slight friction.

Gravity Control Disadvantages

Despite its advantages, gravity control also has some disadvantages, especially when compared to spring control:

• Cramped Scale: One significant drawback is that it gives a cramped scale, especially at the lower end. The controlling torque in gravity control is proportional to the sine of the angle of deflection ($\tau_c \propto \sin \theta$). This relationship results in a non-uniform or cramped scale, where divisions are not equally spaced, making it harder to read precise values across the entire range.
• Position Dependency: Instruments using gravity control must always be kept in a perfectly vertical position. Any tilt will affect the accuracy of the reading.
• Bulky Design: The mechanism tends to be somewhat heavier and bulkier than spring control mechanisms.

Control Method Comparison Analysis

The question asks which of the given options is NOT an advantage of gravity control when compared to spring control. Let's analyze each option based on the characteristics discussed:

• Option 1: It is cheap. This is an advantage of gravity control. Gravity control mechanisms are simpler and generally less expensive to manufacture than those using delicate springs.
• Option 2: It gives cramped scale. This is NOT an advantage; in fact, it is a significant disadvantage of gravity control. A cramped scale means the divisions are uneven and clustered, making accurate readings difficult, especially at the lower end of the scale. This characteristic is a limitation, not a benefit.
• Option 3: It is unaffected by temperature. This is an advantage of gravity control. The controlling force depends only on gravity and mass, not on material properties like elasticity that can change with temperature.
• Option 4: It is not subjected to fatigue or deterioration with time. This is an advantage of gravity control. Unlike springs which can suffer from material fatigue and lose their properties over time, gravity provides a constant, unchanging force over its operational life.

Therefore, among the given options, the characteristic that is NOT an advantage of gravity control when compared to spring control is that "It gives cramped scale". This is a known limitation of gravity-controlled instruments.