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Question #77821

Difficulty: 8/10 | 🟢 Free

The Question

A galvanometer of resistance $G_0$ and a constant full-scale deflection current $I_g$ is converted into an ammeter of range $I_0 = n I_g$ (where $n > 1$ ) at a reference temperature $T_0$ by connecting a shunt resistor $S_0$ in parallel. The temperature coefficients of resistance for the galvanometer coil and the shunt material are $\alpha_g$ and $\alpha_s$ respectively. If the temperature of the system increases by a small amount $\Delta T$ , what is the fractional change in the full-scale range of the ammeter, $\frac{\Delta I}{I_0}$ ? (Assume $\alpha_g \Delta T \ll 1$ and $\alpha_s \Delta T \ll 1$ ).

Options

A.
$\left(\frac{n-1}{n}\right) (\alpha_g - \alpha_s) \Delta T$
B.
$(\alpha_g - \alpha_s) \Delta T$
C.
$\left(\frac{n}{n-1}\right) (\alpha_g - \alpha_s) \Delta T$
D.
$\left(\frac{1}{n}\right) (\alpha_g - \alpha_s) \Delta T$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Shunt Resistance Conversion|Temperature Coefficient (Alpha)|Relative Error Propagation in Powers

Why This Question Is Tricky

Examiner Levers

Logical Assertion

Tests the causal relationship between two true statements.

Difficulty Boost : +4

Visualization Stress

Requires mental rotation or 3D mapping (Optics/Geometry/Vectors).

Difficulty Boost : +4

Dimensional Analysis

Tests if the student verifies units/dimensions before selecting.

Difficulty Boost : +2

Common Mistakes

This question tests the propagation of relative error in a derived quantity where the variable is not a simple product or quotient.

Students often memorize that for $z = x/y$ , the fractional change is $\Delta z/z = \Delta x/x - \Delta y/y$ .

They blindly apply this to the ammeter range $I$ , assuming $\Delta I/I = \Delta G/G - \Delta S/S = (\alpha_g - \alpha_s)\Delta T$ , leading to the lethal trap in Option B.

They fail to recognize that $I = I_g(1 + G/S)$ , meaning the constant '1' dampens the fractional change.

The correct application requires differentiating the entire expression $I(T)$ or applying the chain rule properly, yielding the dampening factor $(n-1)/n$ .

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Units and Measurements - Class 11 Part 1
Concept	Relative Error Propagation in Powers
Difficulty	8
Cognitive Load	8
Target Solve Time	180 sec
Access	Free