Question

In an analogue instrument, the Controlling torque is provided by:

• A. Springs only
• B. Damping
• C. Spring or gravity
• D. Gravity only

Hint:

Spring control is independent of instrument orientation, whereas gravity control instruments must be kept perfectly vertical to function.
Phosphor-bronze is preferred for springs due to its low specific resistance and low temperature coefficient.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks to identify the physical mechanism through which controlling torque is developed in analogue indicating instruments.
Analogue instruments require three distinct torques to function: deflecting torque, controlling torque, and damping torque.

Step 2: Key Formula or Approach:
The deflecting torque (\( T_d \)) causes the pointer to move away from the zero position.
To limit this movement and bring the pointer to a stable resting position corresponding to the measured value, an opposing torque called controlling torque (\( T_c \)) is required.
The final steady deflection is achieved when:
\[ T_d = T_c \] There are two primary methods to produce this controlling torque: Spring Control and Gravity Control.

Step 3: Detailed Explanation:
Let us explore both methods in detail:

• Spring Control:
This is the most common method. Two hairsprings made of non-magnetic materials like phosphor-bronze are wound in opposite directions on the spindle.
When the spindle rotates, one spring winds while the other unwinds. The restoring torque is directly proportional to the angle of deflection (\( \theta \)):
\[ T_c \propto \theta \implies T_c = k_s \theta \] This gives a uniform scale if \( T_d \propto I \).

• Gravity Control:
In this method, a small control weight is attached to the moving system.
When the spindle rotates, this weight is lifted against gravity. The restoring force creates a controlling torque proportional to the sine of the angle of deflection (\( \theta \)):
\[ T_c \propto \sin\theta \implies T_c = k_g \sin\theta \] This produces a non-uniform, crowded scale, but it is highly robust and free from temperature-aging issues.

Step 4: Final Answer:
In analogue instruments, the controlling torque is provided by either spring or gravity control mechanisms.