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Question #77816

Difficulty: 8/10 | 🟢 Free

The Question

A moving coil galvanometer has a rectangular coil made of a uniform wire. The material of the wire has a temperature coefficient of resistivity $\alpha_\rho = 4.00 \times 10^{-3} \text{ K}^{-1}$ and a coefficient of linear thermal expansion $\alpha_l = 2.00 \times 10^{-5} \text{ K}^{-1}$ . The galvanometer is converted into an ammeter of very large range $I$ (where $I \gg I_g$ , $I_g$ being the full-scale deflection current) by connecting a shunt resistor of resistance $S$ in parallel. The shunt resistor has a temperature coefficient of resistance $\alpha_s = 1.00 \times 10^{-4} \text{ K}^{-1}$ . Assume the torsional constant of the suspension and the uniform radial magnetic field remain strictly constant. If the temperature of the entire setup increases by $\Delta T = 10.0 \text{ K}$ , what is the fractional change in the full-scale range of the ammeter, $\frac{\Delta I}{I}$ ?

Options

A.
$3.90 \times 10^{-2}$
B.
$3.88 \times 10^{-2}$
C.
$3.84 \times 10^{-2}$
D.
$3.94 \times 10^{-2}$

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

Visualization Stress

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

Difficulty Boost : +4

Common Mistakes

This question tests the rigorous application of relative error propagation coupled with thermal expansion across multiple geometric dimensions.

Students commonly fall into three traps: (1) treating the full-scale deflection current $I_g$ as a constant, ignoring that the coil's area expands and thus increases magnetic torque sensitivity (requiring less current for the same deflection); (2) confusing the temperature coefficient of resistivity ( $\alpha_\rho$ ) with the temperature coefficient of resistance, failing to account for the dimensional expansion of the wire itself ( $\alpha_l$ for length, $2\alpha_l$ for cross-section); and (3) treating the shunt resistor as an ideal, temperature-independent component.

By forcing the student to differentiate the entire $I \approx I_g(G/S)$ relation and track the linear expansion coefficient $\alpha_l$ through both 2D coil area and 3D wire volume, the problem heavily penalizes rote application of the standard $R = R_0(1+\alpha \Delta T)$ formula.

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	7
Target Solve Time	160 sec
Access	Free