In indicating instruments, the controlling and restoring torque can be obtained by using

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Examoogle · Accepted Answer

The correct answer is Option C: Either by spring or by gravity. In indicating instruments, the controlling torque (Tc) is essential to bring the pointer to a position where the deflecting torque (Td) is balanced by the controlling torque. This torque is typically provided by either mechanical springs or gravity, which exert an opposing force to ensure the pointer returns to the zero position when the input is removed.

Step-by-Step Solution & Concepts:
In indicating instruments, the controlling torque (Tc) is essential to bring the pointer to a position where the deflecting torque (Td) is balanced by the controlling torque. This torque is typically provided by either mechanical springs or gravity, which exert an opposing force to ensure the pointer returns to the zero position when the input is removed.

Working Principle: 1. Spring Control: A hairspring (usually phosphor-bronze) provides a restoring torque proportional to the deflection angle ($	heta$), such that $T_c \propto 	heta$. It offers high sensitivity and is used in portable instruments. 2. Gravity Control: A small adjustable weight attached to the pointer system uses gravitational force as the restoring mechanism, providing a torque proportional to the sine of the angle of deflection ($T_c \propto \sin 	heta$). This is generally restricted to panel-mounted instruments due to its dependence on the vertical orientation of the device.

Key Formulas: $T_c = k	heta$ — Controlling torque for spring control; $T_c = W \cdot l \cdot \sin 	heta$ — Controlling torque for gravity control

Key Points: Spring control is independent of the instrument's position, whereas gravity control requires the instrument to be used in a vertical position.; Spring-controlled scales are linear (uniform), whereas gravity-controlled scales are cramped at the beginning (non-linear).; Controlling torque ensures that the steady-state deflection of the pointer is a function of the electrical quantity measured.

Advantages: Spring control allows for high sensitivity and precise measurements.; Gravity control is cheaper, temperature-independent, and does not degrade over time.

Disadvantages: Springs are subject to fatigue and temperature sensitivity.; Gravity control is restricted to vertical mounting and is less sensitive.

Applications: Spring Control: Portable analog multimeters, PMMC meters.; Gravity Control: Switchboard-mounted meters, industrial panel indicators.

Additional Info: Option A is incomplete because gravity is also a valid method.. Option B is incomplete because springs are widely used in most high-precision instruments.. Gravity control cannot be used in portable equipment as it requires precise leveling.

Answer: C is correct — Indicating instruments utilize either spring or gravity control to provide the necessary restoring torque to balance the deflecting torque.

Exam Tip: Always remember that the scale linearity is directly dictated by the controlling torque characteristic: $T_c \propto 	heta$ yields a uniform scale, while $T_c \propto \sin 	heta$ results in a non-uniform scale.

Examoogle · Answer

Option A: Spring

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Option B: Gravity

Examoogle · Answer

Option D: Neither by spring nor by gravity

Feature	Spring Control	Gravity Control
Scale Linearity	Uniform (Linear)	Non-uniform (Cramped)
Position Sensitivity	Independent	Dependent (Vertical only)

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