An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it, its resistance at room temperature `(27.0^(@)C)` is found to be 75.3 `Omega` . When the toaster is connected to a 230 V supply, the current settles, after a few seconds, to a steady value of 2.68 A. What is the steady temperature of the nichrome element ? The temperature coefficient of resistance of nichrome averaged over the temperature range involved , is `1.70 xx 10^(-4) ""^(@) C^(-1)`.

Explanation

Initially when extremely small current passes through nichrome filament, its temperature can be taken equal to room temperature `T_(1) = 27^(@) `C.
At this temperature its resistance is `R_(1) = 75.3 Omega. `
Now when given toaster is connected across V = 230 volt steady current passing through it (after very short time) is I = 2.68 A and its temperature increases to `T_(2)`, which is to be found out. At this temperature resistance of nichrome filament is given by formula
`R_(2) = R_(1) { 1 + alpha (T_(2) - T_(1))} `
( where `alpha ` = temperature coeffeicient of resistance )
`therefore (V)/(I) = R { 1 + alpha (T_(2) - T_(1) ) } `
(` because R_(2) = (V)/(I) `= resistance of hot filament )
`therefore (230)/(2.68) = 75.3 { 1 + 1.7 xx 10^(-4) (T_(2) - 27)} `
`therefore 1.1397 = 1 + 1.7 xx 10^(-4) (T_(2) - 27)`
`therefore T_(2) - 27 = (0.1397)/(1.7 xx 10^(-4))`
`therefore T_(2) - 27 = 821.76`
`therefore = 848.76^(@)` C