Statement - 1: The temperature dependence of resistance is usually given as R = R₀(1 + αΔ t). The resistance of wire changes from 100 Ω to 150 Ω when its temperature is increased from 27 to 227. This implies that α = 2.5 × 10⁻³/C. Statement - 2: R = R₀(1 + αΔ t) is valid only when the change in the temperature Δ T is small and Δ R = (R - R₀) R₀. (a) Statement - 1 is true, Statement - 2 is true; Statement - 2 is the correct explanation of Statement - 1 (b) Statement - 1 is true, Statement - 2 is true; Statement - 2 is not the correct explanation of Statement - 1 (c) Statement - 1 is false, Statement - 2 is true (d) Statement - 1 is true, Statement - 2 is false

Answer: (c). Statement 2: the linear law R = R₀(1+αΔ t) is an approximation valid only for small changes, Δ R R₀. True. Statement 1: here Δ R = 50 Ω is half of R₀, not small, so the linear formula cannot be applied to get α reliably. False. The answer is (c).

Statement - 1: The temperature dependence of resistance is usually… | JEE Main 2009 (AIEEE)

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Ohm's Law, Resistivity & Temperature

Statement - 1: The temperature dependence of resistance is usually given as $R = R_0(1 + \alpha\Delta t).$ The resistance of wire changes from $100\ \Omega$ to $150\ \Omega$ when its temperature is increased from $27^\circ\text{C}$ to $227^\circ\text{C}$ . This implies that $\alpha = 2.5 \times 10^{-3}/\text{C}.$

Statement - 2: $R = R_0(1 + \alpha\Delta t)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R = (R - R_0) \ll R_0.$

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Answer: (c)

Statement 2: the linear law $R = R_0(1+\alpha\Delta t)$ is an approximation valid only for small changes, $\Delta R \ll R_0$ . True.
Statement 1: here $\Delta R = 50\ \Omega$ is half of $R_0$ , not small, so the linear formula cannot be applied to get $\alpha$ reliably. False.
The answer is (c).

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