A heating element using nichrome connected to a 230 V supply draws a 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 elemtn if the room temperature is `27.0^(@)C`? Temperature coefficient of resistance of nichrome of nichrome averaged over the temperature range involved is `70xx10^(-4)C^(-1)`
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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_(t)-R_(27))/(R_(27) xx ( t - 27)) or t - 27 = R_(t)-R_(27)/R_(27) xx alpha` or ` t= (R_(t)-R_(27))/(R_(27) xx alpha) + 27 = ((2300//28) - (2300//32))/((2300//32) xx 1.7 xx 10^(-4)) + 27 = 840.2 + 27 = 867.2 ^@C`.
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