JEE Mains · Physics · STD 12 - Current electricity
- JEE Mains 2024
- Hard
- MCQ
To measure the temperature coefficient of resistivity \(\alpha\) of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of the semiconductor. The experiment is being conducted at \(25^{\circ} \mathrm{C}\) and resistance of the semiconductor arm is \(3 \mathrm{~m} \Omega\). Arm BC is cooled at a constant rate of \(2^{\circ} \mathrm{C} / \mathrm{s}\). If the galvanometer \(\mathrm{G}\) shows no deflection after \(10 \mathrm{~s}\), then \(\alpha\) is _______.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(-1 \times 10^{-2}\ { }^{\circ} \mathrm{C}^{-1}\)
Step-by-step Solution
Detailed explanation
For no deflection \(\frac{0.8}{1}=\frac{R}{3}\)
\(\Rightarrow \mathrm{R}=2.4 \mathrm{~m} \Omega\)
Temperature fall in \(10 \mathrm{~s}=20^{\circ} \mathrm{C}\)
\(\Delta \mathrm{R}=\mathrm{R} \alpha \Delta \mathrm{t}\)
\(\alpha=\frac{\Delta \mathrm{R}}{\mathrm{R} \Delta \mathrm{t}}=\frac{-0.6}{3 \times 20}\)
\(=-10^{-2} \mathrm{C}^{-1}\)
\(\Rightarrow \mathrm{R}=2.4 \mathrm{~m} \Omega\)
Temperature fall in \(10 \mathrm{~s}=20^{\circ} \mathrm{C}\)
\(\Delta \mathrm{R}=\mathrm{R} \alpha \Delta \mathrm{t}\)
\(\alpha=\frac{\Delta \mathrm{R}}{\mathrm{R} \Delta \mathrm{t}}=\frac{-0.6}{3 \times 20}\)
\(=-10^{-2} \mathrm{C}^{-1}\)
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