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

Here `R_(27) = (230)/(3.2) = (2300)/(32) Omega`
`R_(t) = (230)/(2.8) = (2300)/(28) Omega`
`alpha = 1.7 xx 10^-(4) .^(@)C^(-1)`
`alpha = (R_(1) - R_(27))/(R_(27) xx (t - 27))`
or `t - 27 = (R_(t) - R_(27))/(R_(27) xx alpha)`
or
`= 840.2 + 27 = 867.2^(@)C`