Resistance of a wire at $0^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C}$ and $t^{\circ} \mathrm{C}$ is found to be $10 \Omega, 10.2 \Omega$ and $10.95 \Omega$ respectively. The temperature $t$ in Kelvin scale is _________

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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{R}=\mathrm{R}_0(1+\alpha \Delta \mathrm{T}) \ & \frac{\Delta \mathrm{R}}{\mathrm{R}_0}=\alpha \Delta \mathrm{T}\end{aligned}$ Case-I $\begin{aligned} & 0{ }^{\circ} \mathrm{C} ightarrow 100^{\circ} \mathrm{C} \ & \frac{10.2-10}{10}=\alpha(100-0)\end{aligned}$ ...(1) Case-II $0^{\circ} \mathrm{C} ightarrow \mathrm{t}^{\circ} \mathrm{C}$ $\frac{10.95-10}{10}=\alpha(\mathrm{t}-0)$ ...(2) $\begin{aligned} & \Rightarrow \frac{\mathrm{t}}{100}=\frac{0.95}{0.2}=475^{\circ} \mathrm{C} \ & \mathrm{t}=475+273=748 \mathrm{~K}\end{aligned}$

Resistance of a wire at $0^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C}$ and $t^{\circ} \mathrm{C}$ is found…

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