Question

An electric toaster uses nichrome for its heating element. When a negligibly small current passes through it. It resistance at room temperature `(27.0^@C)` is found to be `75.3Omega`. 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 steady temperature of the nichrome element? The temperature coefficient of resistance of nichrome averaged over the temperature range involved , `1.70xx10^-4C^-1`

Answer 1

Given `T_0=27^@C` and `R_0=75.3Omega`
At temperature `T, R_T=V_T/i_T (R=V/i)`
`=230/268=85.82Omega`
Using the equation `R_T=R_0[1+alpha(T-T_0)]`
We have `85.82=75.3[1+(1.70xx10^-4)(T-27)]`
Solving this equation we get `T~~850^@C`
Thus, the steady temperature of the nichrome element is `850^@C`