Respuesta :
Given that the operating voltage is V = 120 V.
The initial temperature of the toaster is T1 = 20 degrees Celsius
The initial current in the coil is I1 = 1.5 A
The final current in the coil is I2 = 1.3 A
The thermal coefficient of resistivity for nichrome is
[tex]\alpha=4.5\times10^{-4}^{}\text{ }^{\circ}C^{-1}[/tex]We have to find the final temperature of the coil, T2.
The initial resistance of the coil is
[tex]\begin{gathered} R1=\frac{V}{I1} \\ =\frac{120}{1.5} \\ =80\Omega \end{gathered}[/tex]The final resistance of the coil is
[tex]\begin{gathered} R2\text{ =}\frac{V}{I2} \\ =\frac{120}{1.3} \\ =92.307\Omega \end{gathered}[/tex]The formula to calculate the final temperature of the coil is
[tex]\begin{gathered} \alpha=\frac{(R2-R1)}{R1(T2-T1)} \\ T2-T1=\frac{(R2-R1)}{\alpha\times R1} \\ T2=\frac{(R2-R1)}{\alpha\times R1}+T1 \end{gathered}[/tex]Substituting the values, the final temperature will be
[tex]\begin{gathered} T2=\text{ }\frac{92.307-80}{4.5\times10^{-4}\times80}+20 \\ \approx360^{\circ}\text{ C} \end{gathered}[/tex]Thus, the final temperature is 360 degrees Celsius.
