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 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

Supply voltage, V = 230 V

Initial current drawn, I₁ = 3.2 A

Initial resistance = R₁, which is given by the relation,

R₁=V/I =230 /3.2 =71.87 Ω

Steady state value of the current, I₂ = 2.8 A

Resistance at the steady state = R₂, which is given as

R₂=230/2.8 = 82.14 Ω

Temperature co-efficient of nichrome,α = 1.70 x 10⁻^{4 o}C⁻¹

Initial temperature of nichrome, T₁= 27.0°C

Study state temperature reached by nichrome = T₂

T₂can be obtained by the relation for α,

α =(R₂-R₁)/R ₁(T₂-T₁)

(T₂-T₁) =(R₂-R₁)/α 

=> T₂-27 = (82.14-71.87 ) /(71.87 x 1.7 x 10⁻⁴) = 840.5

=> T₂ =840.5 + 27 =867.5 °C

Therefore, the steady temperature of the heating element is 867.5°C