Statement (A) : The temperature dependence of resistance is usually given as ${R= R}_{0} (1 + α Δ t)$ The resistance of a wire changes from $100 Ω$ to $150 Ω$ when its temperature is increased from $27°C to 227°C$ This implies that $α = 2.5 \times 10^{- 3} / ° C$
Statement (B) : $R = R_{0} (1 + α Δ t)$ is valid only when the change in the temperature $Δ T$ is small and $Δ R = (R - R_{0}) < < R_{0.}$

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Both A and B are false

Both A and B are true

A is false, B is true

A is true, B is false

answer is D.

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Detailed Solution

We have In statement - I

$R = R_{0} (1 + α Δ t)$

$R = 150 Ω, R_{0} = 100 Ω$ $t_{1} = 27 ° {C t}_{2} = 227 ° C$

$150 = 100 (1 + α (227 ° C - 27 °))$ $\frac{150}{100} = 1 + 200 α$

$\frac{3}{2} = 1 + 200 α$

$\frac{3}{2} - 1 = 200 α$

$\frac{1}{2} = 200 α$

$0.5 = 200 α$

$α = \frac{0.5}{200}$

$α = \frac{5}{2000} \Rightarrow α = 2.5 \times 10^{- 3} / ° C$ In statement – II

$R = R_{0} (1 + α Δ t)$

$\frac{R - R_{0}}{R_{0}} = α Δ t$ Since $α$ is very small

Here $R - R_{0} < < R_{0} Δ t$

So $Δ t$ need not become small

So statement II is false.

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