An electric toaster uses nichrome for its heating element. When a negllgibly small current pases 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 `2.68A.` 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

Here `I_(1) = 3.2 A, I_(2) = 2.8A , V = 230 V `
`alpha = 1.70 xx 10^(-4)" "^(@) C^(-1)`,
`t_(1) = 27.5^(@) C, t_(2) = ? `
Resistance at room temperature,
`R_(2) = (V)/(I_(2)) = (230)/(2.8)`
`= R_(2) approx 82.143 Omega`
`R_(2) = R_(1) [ 1 + alpha (t_(2) - t_(1)) ] `
`therefore t_(1) - t_(1) = (R_(2) - R_(1))/(R_(1) alpha )`
`therefore t_(2) - 27 = (82.143 - 71.875)/(71.875 xx 1.7 xx 10^(-4))`
`therefore t_(2) = 27 + (10.268)/(0.01222)`
= 27 + 840.26
`= 867.26^(@)C = 867^(@)` C