At room temperature $\left(27^{\circ} \mathrm{C} ight)$, the resistance of a heating element is $50 \Omega$. The temperature coefficient of the material is $2.4 imes 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$. The temperature of the element, when its resistance is $62 \Omega$, is _____ ${ }^{\circ}…

Question

At room temperature $\left(27^{\circ} \mathrm{C}ight)$, the resistance of a heating element is $50 \Omega$. The temperature coefficient of the material is $2.4 	imes 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$. The temperature of the element, when its resistance is $62 \Omega$, is _____ ${ }^{\circ} \mathrm{C}$.

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{R}=\mathrm{R}_0(1+\alpha \Delta \mathrm{T}) \ & 62=50\left[1+2.4 	imes 10^{-4} \Delta \mathrm{T}ight] \ & \Delta \mathrm{T}=1000^{\circ} \mathrm{C} \ & \Rightarrow \mathrm{T}-27^{\circ}=1000^{\circ} \mathrm{C} \ & \mathrm{T}=1027^{\circ} \mathrm{C}\end{aligned}$

At room temperature $\left(27^{\circ} \mathrm{C}\right)$, the resistance of a heating element is $50 \Omega$…

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