A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A which settles after a few seconds to due to a steady value of 2.8 A. What is the steady temperature of the heating element if the room temperature is 27.0 °C? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 × 10^–4 °C^–1.

Given Supply Voltage = 230 Volt

And it draws current I₁ = 3.2 Ampere

Resistance is given by R₁ = V/I

R₁ = 230V/3.2A

R₁ = 71.87 Ω

Steady value of current I₂ = 2.8Ampere

Resistance R α is given by R₂ = 230V/2.8A

R₂ = 82.14 Ω

Temperature coefficient of nichrome wire α = 1.70 × 10^-4 per °C

Initial temperature of nichrome T₁ = 27 ° C

Steady Temperature attained by nichrome = T₂

The formula is: R₂ = R₁[1 + α(T₂-T₁)]

⇒ R₂ - R₁ = R₁α(T₂ - T₁)

⇒ R₂ - R₁ = R₁α (T₂ - T₁)

⇒

⇒ T₂-27°C = 840.5°C

⇒ T₂ = 840.5°C + 27°C = 867.5° C

Hence Steady Temperature attained by nichrome = 867.5 ° C.