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Question #42001

Difficulty: 8/10 | 🟢 Free

The Question

A standard resistor has a resistance $R_0 = 10.00 \, \Omega$ at an initial temperature $T_0 = 20.0 \, ^\circ\text{C}$ . It is connected across an ideal DC voltage source of $V = 12.00 \, \text{V}$ . The resistor is then placed in a thermal bath at $T_f = 32.4 \, ^\circ\text{C}$ . The temperature coefficient of resistance is given as $\alpha = 0.018 \, ^\circ\text{C}^{-1}$ . Assuming the voltage remains exactly constant, what is the current in the circuit at the new temperature, calculated with the correct application of significant figure rules?

Options

A.
$0.984 \, \text{A}$
B.
$0.981 \, \text{A}$
C.
$1.00 \, \text{A}$
D.
$1.20 \, \text{A}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Significant Figures in Mixed Operations|Temperature Coefficient (Alpha)|Kirchhoff’s Junction Rule

Why This Question Is Tricky

Common Mistakes

This question tests the strict application of significant figure rules across mixed operations (addition and multiplication) in a physical context.

Students frequently treat the entire expression $R_0(1 + \alpha \Delta T)$ as a single continuous calculation, failing to truncate the intermediate product $\alpha \Delta T$ to the correct number of significant figures (2 sig figs, dictated by $\alpha$ ).

Furthermore, they must recognize that the '1' in the formula is an exact number, meaning the addition $1 + 0.22$ is limited by the decimal places of $0.22$ , resulting in $1.22$ (3 sig figs).

Failing to truncate at the intermediate step propagates false precision, leading to the trap answer of $0.981 \, \text{A}$ .

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Units and Measurements - Class 11 Part 1
Concept	Significant Figures in Mixed Operations
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free