Question

At room temperature (27.0 °C) the resistance of a heating element is 100 W. What is the temperature of the element if the resistance is found to be 117 W, given that the temperature coefficient of the material of the resistor is 1.70 × 10–4 °C–1.

Answer 1

answer : 1027°C

explanation : we know relation between resistance and temperature . it is given by

$\boxed{\bf{R=R_0[1+\alpha(T-T_0)]}}$

where, R is the resistance at temperature T, $R_0$ is the resistance at temperature $T_0$ and α is the temperature coefficient of the material of the resistor.

Given, R = 117Ω , R₀ = 100Ω , α = 1.7 × 10^-4 /°C and T₀ = 27°C

so, 117 = 100 [ 1 + 1.7 × 10^-4(T - 27)

⇒117 = 100 + 1.7 × 10^-2 (T - 27)

⇒17 = 1.7 × 10^-2(T - 27)

⇒1000 = T - 27

⇒T = 1027°C

hence, temperature of the element if the resistance is found by 117Ω is 1027°C