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Question #42006

Difficulty: 8/10 | 🟢 Free

The Question

A galvanometer of resistance $G$ and temperature coefficient of resistance $\alpha_1$ is converted into an ammeter of range $I$ using a shunt of resistance $S$ and temperature coefficient $\alpha_2$ . Assuming the full-scale deflection current $I_g$ of the galvanometer is independent of temperature, which of the following expressions represents the fractional change in the range of the ammeter, $\frac{\Delta I}{I}$ , for a small temperature rise $\Delta T$ ?

Options

A.
$\frac{G}{G+S}(\alpha_1 - \alpha_2)\Delta T$
B.
$\frac{S}{G+S}(\alpha_1 - \alpha_2)\Delta T$
C.
$(\alpha_1 - \alpha_2)\Delta T$
D.
$\frac{G}{G+S}(\alpha_1 + \alpha_2)\Delta T$

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

Common Mistakes

This question tests the propagation of relative error through a function where the variable of interest (range $I$ ) is not directly proportional to the ratio of the changing parameters ( $G/S$ ).

A common trap is assuming $I \propto G/S$ , leading students to incorrectly state the fractional change as $(\alpha_1 - \alpha_2)\Delta T$ .

Furthermore, it forces students to recognize that the shunt resistance is not a static parameter and its temperature coefficient $\alpha_2$ must be accounted for using the quotient rule during differentiation, breaking the intuition of a 'fixed' ideal resistor.

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