Toaster uses a nichrome heating coil and operates at 120 V. When the toaster is turned on at 20°C, the current in the cold coil is 1.5 A. When the coil warms up, the current has a value of 1.3 A. If the thermal coefficient of resistivity for nichrome is 4.5x10-4 1/Co, what is the temperature of the coil?Group of answer choices68oC490oC160oC360oC260oC

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

$\alpha=4.5\times10^{-4}^{}\text{ }^{\circ}C^{-1}$

We have to find the final temperature of the coil, T2.

The initial resistance of the coil is

$\begin{gathered} R1=\frac{V}{I1} \\ =\frac{120}{1.5} \\ =80\Omega \end{gathered}$

The final resistance of the coil is

$\begin{gathered} R2\text{ =}\frac{V}{I2} \\ =\frac{120}{1.3} \\ =92.307\Omega \end{gathered}$

The formula to calculate the final temperature of the coil is

$\begin{gathered} \alpha=\frac{(R2-R1)}{R1(T2-T1)} \\ T2-T1=\frac{(R2-R1)}{\alpha\times R1} \\ T2=\frac{(R2-R1)}{\alpha\times R1}+T1 \end{gathered}$

Substituting the values, the final temperature will be

$\begin{gathered} T2=\text{ }\frac{92.307-80}{4.5\times10^{-4}\times80}+20 \\ \approx360^{\circ}\text{ C} \end{gathered}$

Thus, the final temperature is 360 degrees Celsius.

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