Question

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

Answer 1

Room temperature, T = 27 °C
Resistance of the heating element at T, R = 100 Ω
Let \(T_1\) is the increased temperature of the filament.
Resistance of the heating element at \(T_1, R_1 = 117 Ω \)
Temperature co-efficient of the material of the filament,
\(α = 1.70\times 10^{-4} \degree C^{-1}\)
α is given by the relation,
\(α = \frac{R_1-R}{R(T_1-T)}\)
\(T_1-T =\frac{ R_1-R}{Rα}\)
\(T_1-27 = \frac{117 - 100}{100( 1.70\times10^{-4})}\)
\(T_1-27 = 1000\)
\(T_1 = 1027 °C\)
Therefore, at 1027°C, the resistance of the element is 117Ω.