Question 326 of 380

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 $25^{\circ}C$ and resistance of the semiconductor arm is $3m\Omega$. Arm $BC$ is cooled at a constant rate of $2^{\circ}C{s}^{-1}$. If the galvanometer $G$ shows no deflection after $10s,$ then $\alpha$ is:

A$-2\times {10}^{-2}C-1^{\circ}$B$-1.5\times {10}^{-2}C-1^{\circ}$C$-1\times {10}^{-2}C-1^{\circ}$D$-2.5\times {10}^{-2}C-1^{\circ}$

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Answer: (C) $-1\times {10}^{-2}C-1^{\circ}$

For no deflection(balanced condition) $\dfrac{0.8}{1}=\dfrac{R}{3}$
$\Rightarrow R=2.4m\Omega$
Temperature fall in $10s=20^{\circ}C$
$\Delta R=R\alpha \Delta t$
$\Rightarrow \alpha =\dfrac{\Delta R}{R\Delta t}=\dfrac{2.4-3}{3\times 20}$
=-1\times {10}^{-2}^{\circ}{C}^{-1}