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

Explanation

Resistance at room temperature `R_(27)=(V)/(I)=(230)/(3.2)`
Resistance at `theta` temp. `R_(theta)=(230)/(2.8)`
`(R_(27))/(R_(theta))=(R_(0)(1+alphaxx27))/(R_(0)(1+alphaxx theta))rArr (2.8)/(3.2)=(1+27alpha)/(1+alpha theta)`
`rArr (7)/(8)=(1+27alpha)/(1+alpha theta) rArr theta=(1+216alpha)/(7alpha)=(1+216xx1.7xx10^(-4))/(7xx1.7xx10^(-4))`
`rArr theta = 867^(@)C`