To measure the temperature coefficient of resistivity α of a...

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

Options

A $- 2 \times {10}^{- 2} C - 1 ∘$
B $- 1 . 5 \times {10}^{- 2} C - 1 ∘$
C $- 1 \times {10}^{- 2} C - 1 ∘$
D $- 2 . 5 \times {10}^{- 2} C - 1 ∘$

Correct answer

C. $- 1 \times {10}^{- 2} C - 1 ∘$

Step-by-step solution

To measure the temperature coefficient of resistivity α of a semiconductor, an electrical arrangement shown in the

For no deflection(balanced condition) $\dfrac{0 . 8}{1} = \dfrac{R}{3}$

$⇒ R = 2 . 4mΩ$

Temperature fall in $10s = 20 ° C$

$\DeltaR = R\alpha \Delta t$

$⇒ \alpha = \dfrac{\DeltaR}{R\Delta t} = \dfrac{2 . 4 - 3}{3 \times 20}$

$= - 1 \times {10}^{- 2} ° {C}^{- 1}$

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