Question

The gravity controlled instrument has crowded scale because current is proportional to

• A. gravitational force
• B. balancing weight
• C. deflection angle
• D. sine of deflection angle

Hint:

In gravity-controlled instruments, the deflection is proportional to the sine of the deflection angle, which makes the scale crowded.

Answer 1

The Correct Option is D

A gravity-controlled instrument's scale is "crowded" precisely because the relationship between current and deflection angle is non-linear — equal increases in current do not produce equal increases in angle. Since \( \sin\theta \) increases very gradually near \( \theta = 0^\circ \) but more rapidly as \( \theta \) approaches 90°, equal steps in current correspond to progressively larger angle changes, bunching up the low readings on the scale.

1. Gravitational force: This is a constant instrument parameter, not a variable quantity that could explain a non-uniform scale pattern.
2. Balancing weight: Also a fixed design parameter of the instrument rather than something that varies with the reading.
3. Deflection angle: A direct proportionality to the angle itself would give evenly spaced markings, not a crowded scale.
4. Sine of deflection angle: The non-linear, slowly-then-rapidly increasing nature of \( \sin\theta \) is exactly what produces the crowded appearance described in the question.

The non-linear behavior of \( \sin\theta \) explains why the scale of a gravity-controlled instrument is crowded.

Therefore, the correct answer is sine of deflection angle.

Answer 2

It helps to contrast this with spring-controlled instruments, where the controlling torque from a spring is directly proportional to the deflection angle itself (\( T_c \propto \theta \)), which — when balanced against a current-proportional deflecting torque — gives a UNIFORM scale. Gravity control behaves differently because its restoring torque depends on \( \sin\theta \), not \( \theta \) directly, which is what produces the characteristic crowded (non-uniform) scale unique to gravity-controlled instruments. Let's check each option against this comparison.

1. Gravitational force: This is the same fixed force in both spring- and gravity-controlled designs; it's the geometry (the angle dependence), not the force, that differs between them.
2. Balancing weight: Similarly fixed by instrument design and not the varying quantity responsible for the crowded-scale effect.
3. Deflection angle: This is what governs SPRING-controlled instruments (giving a uniform scale), which is a different case from what's being asked about here.
4. Sine of deflection angle: This is the distinguishing feature of gravity control that produces the non-uniform, crowded scale.

Comparing with spring control confirms that gravity-controlled instruments crowd their scale because current is proportional to the sine of the deflection angle.

Therefore, the correct answer is sine of deflection angle.