Question

A nichrome toaster element has a resistance of \(75.3\,\Omega\) at \(27^{\circ}\mathrm{C}\) and \(85.8\,\Omega\) at its operating temperature. If \(\alpha=1.7\times10^{-4}\,^{\circ}\mathrm{C}^{-1}\), what is the steady temperature approximately?

Options

• \(345.65^{\circ}\mathrm{C}\)

• \(27^{\circ}\mathrm{C}\)

• \(847^{\circ}\mathrm{C}\)

• \(100^{\circ}\mathrm{C}\)

Answer 1

Use \(R_2=R_1[1+\alpha(T_2-T_1)]\) with the given resistances and \(\alpha\). Solving for the operating temperature gives approximately \(847^{\circ}\mathrm{C}\).