Question

At room temperature $\left({27.0}^{o}C\right)$ the resistance of a heating element is $100\Omega$ . What is the temperature of the element if the resistance is found to be $117\Omega$, given that the temperature coefficient of the material of the resistor is $1.70\times {10}^{-4}{C}^{-1}$.

Answer 1

$\text{Step 1: Relation between value of resistance and temperature}$

$R=R_0[1+\alpha (T-T_0\left)\right]$

$\text{Step 1: Temperature calculation}$

Let $T$ is the increased temperature of the element, putting all the values in the formula to find $T$

$T_0={27}^{o}C,R_0=100\Omega ,R=117\Omega ,\alpha =1.70\times {10}^{-4}{}^o{C}^{-1}$

$\Rightarrow 117=100[1+1.7\times {10}^{-4}(T-27\left)\right]$

$\Rightarrow T={1027}^{o}C$