Question

At room temperature $\left({27.0}^{\circ }\text{C}\right)$ the resistance of a heating element is $100\Omega$. Calculate the temperature of the element if the resistance is found to be $117\Omega$ (the temperature coefficient of resistance of the material is $1.7\times {10}^{-4}$ ${}^{\circ }{\text{C}}^{-1}$)

• A. ${200}^{\circ }\text{C}$
• B. ${1027}^{\circ }\text{C}$
• C. ${800}^{\circ }\text{C}$
• D. ${1000}^{\circ }\text{C}$

Answer 1

The correct option is B ${1027}^{\circ }\text{C}$

The variation of resistance with temperature is given by :

$R_{\theta }=R_0(1+\alpha \Delta \theta )$

$\therefore 117=100(1+\alpha \Delta \theta )$

$\Rightarrow \Delta \theta =\frac{117-100}{100\alpha }$

$=\frac{17}{100\times 1.7\times {10}^{-4}}$

$={1000}^{\circ }C$

$\Delta \theta$ $=$ ${1000}^{\circ }\text{C}$

$\theta -{\theta }_0=$ ${1000}^{\circ }\text{C}$

$\theta$ $=$ ${1027}^{\circ }\text{C}$

Hence, option ($b$) is the correct answer.

Why this Question? The temperature dependence of resistance is given by: $R_{\theta }$ $=$ $R_0$( $1$ $+$ $\alpha \Delta \theta$ )