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To measure the temperature coefficient of resistivity $α$ of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of semiconductor. The experiment is being conducted at $25^{0} C$ and resistance of the semiconductor arm is $3 m Ω$ . Arm BC is cooled at a constant rate of $2^{0} C / s$ . If the galvanometer G shows no deflection after 10s, then $α$ is :

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$- 1 \times 10^{- 2}^{0} C^{- 1}$

$- 1.5 \times 10^{- 2}^{0} C^{- 1}$

$- 2.5 \times 10^{- 2}^{0} C^{- 1}$

$- 2 \times 10^{- 2}^{0} C^{- 1}$

answer is C.

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Detailed Solution

For no deflection $\frac{0.8}{1} = \frac{R}{3}$
$\Rightarrow R = 2.4 m Ω$
Temperature fall in 10s = $20^{0} C$
$Δ R = R α Δ t$
$α = \frac{Δ R}{R Δ t} = \frac{- 0.6}{3 \times 20}$
$= - 10^{- 2} C^{- 1}$

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