This question contains statement$-1$ and statement$-2$. Of the four choices given after the statements, choose the one that best describes the two statements.

statement$-1$ : The temperature dependence of resistance is usually given as $R=R_{0}(1+\alpha \Delta t)$. The resistance of a wire changes from $100\; \Omega$ to $150\; \Omega$ when its temperature is increased from $27^{\circ} C$ to $227^{\circ} C$. This implies that $\alpha=2.5$ $\times 10^{-3} /{ }^{\circ} C$

statement$-2\;: R=R_{0}(1+\alpha \Delta t)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R=\left(R-R_{0}\right) < < R_{0}$

Q: This question contains statement$-1$ and statement$-2$. Of the four choices given after the statements, choose the one that best describes the two statements. statement$-1$ : The temperature dependence of resistance is usually given as $R=R_{0}(1+\alpha \Delta t)$. The resistance of a wire changes from $100\; \Omega$ to $150\; \Omega$ when its temperature is increased from $27^{\circ} C$ to $227^{\circ} C$. This implies that $\alpha=2.5$ $\times 10^{-3} /{ }^{\circ} C$ statement$-2\;: R=R_{0}(1+\alpha \Delta t)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R=\left(R-R_{0}\right) < < R_{0}$

$R =150 ; R _{0}=100$ and $\Delta t =227^{\circ} C -27^{\circ} C =200^{\circ} C$ $R = R _{0}(1+\alpha \Delta t )$ $150=100(1+\alpha(200))$ $\therefore \alpha=2.5 \times 10^{-3} /{ }^{\circ} C$ for $\Delta R =150-100=50$ , $R - R _{0}<< R _{0}$ cannot say . Statement $-2$ is false

Question

This question contains statement$-1$ and statement$-2$. Of the four choices given after the statements, choose the one that best describes the two statements.

statement$-1$ : The temperature dependence of resistance is usually given as $R=R_{0}(1+\alpha \Delta t)$. The resistance of a wire changes from $100\; \Omega$ to $150\; \Omega$ when its temperature is increased from $27^{\circ} C$ to $227^{\circ} C$. This implies that $\alpha=2.5$ $\times 10^{-3} /{ }^{\circ} C$

statement$-2\;: R=R_{0}(1+\alpha \Delta t)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R=\left(R-R_{0}\right) < < R_{0}$

AIEEE 2009, Diffcult

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Solution

$R =150 ; R _{0}=100$ and $\Delta t =227^{\circ} C -27^{\circ} C =200^{\circ} C$

$R = R _{0}(1+\alpha \Delta t )$

$150=100(1+\alpha(200))$

$\therefore \alpha=2.5 \times 10^{-3} /{ }^{\circ} C$

for $\Delta R =150-100=50$ , $R - R _{0}<< R _{0}$ cannot say .

Statement $-2$ is false

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