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 :
JEE MAIN 2024, Diffcult
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For no deflection $\frac{0.8}{1}=\frac{R}{3}$
$\Rightarrow \mathrm{R}=2.4 \mathrm{~m} \Omega$
Temperature fall in $10 \mathrm{~s}=20^{\circ} \mathrm{C}$
$\Delta \mathrm{R}=\mathrm{R} \alpha \Delta \mathrm{t}$
$\alpha=\frac{\Delta \mathrm{R}}{\mathrm{R} \Delta \mathrm{t}}=\frac{-0.6}{3 \times 20}$
$=-10^{-2} \mathrm{C}^{-1}$
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