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

Given: Temperature coefficient of filament,

α = 1.70 × 10^-4 per °C

Let T₁ be the temperature of element, R₁ = 100Ω (Given: T₁ = 27°C)

Let T₂ be the temperature of element, R₂ = 117Ω

To find T₂ = ?

The formula is: R₂ = R₁[1 + α(T₂-T₁)]

⇒ R₂ - R₁ = R₁α(T₂ - T₁)

⇒ R₂ - R₁ = R₁α (T₂ - T₁)

⇒

⇒ T₂-27°C = 1000°C

⇒ T₂ = 1000°C + 27°C

Hence Temperature of element, T₂ is 1027 °C.

Note: The temperature coefficient of resistance (α) gives the change in resistance per degree change in temperature. For pure metals, it is positive means- The resistance increases with temperature.