Question

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? The temperature coefficient of resistance of nichrome averaged over the temperature range involved is 1.70 × 10⁻⁴ °C⁻¹.

Answer 1

Given: Supply voltage, V = 230 V

Initial current drawn, I₁ = 3.2 A

Initial resistance = R₁

`R_1 = V/I`

= `230/3.2`

= 71.87 Ω

Steady-state current, I₂ = 2.8 A

Resistance at the steady state = R₂

R₂ = `230/2.8`

= 82.14 Ω

Temperature coefficient of nichrome, 

α = 1.70 × 10⁻⁴ °C⁻¹

Initial temperature of nichrome, 

T₁ = 27.0°C

Let the steady-state temperature be T₂.

T₂ can be obtained by the relation for α,

α = `(R_2 - R_1)/(R_1(T_2 - T_1))`

`1.7 xx 10^-4 = (82.14 - 71.87)/(71.87(T_2 - 27°C))`

`T_2 − 27°C = (82.14 - 71.87)/(71.87 xx 1.7 xx 10^-4)`

`T_2 − 27°C = 10.27/(122.18 xx 10^-4)`

`T_2 − 27°C = 10.27/0.012218`

T₂ − 27°C = 840.5

T₂ = 840.5 + 27

T₂ = 867.5°C

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