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A toaster using a Nichrome heating element operates on 120 V. When it is switched on at 20∘C, the heating element carries an initial current of 1.39 A. A few seconds later, the current reaches the steady value of 1.25 A. The average value of the temperature coefficient of resistivity for Nichrome over the temperature range from 20∘C to the final temperature of the element is 4.5×10−4(∘C)−1.

Respuesta :

Explanation:

The given data is as follows.

            Voltage (V) = 120 V

           Current (I) = 1.39 A

Now, we will calculate the initial resistance using ohm's law as follows.

                R = [tex]\frac{V}{I}[/tex]

                   = [tex]\frac{120}{1.39}[/tex]

                   = 86.33 ohm

Now, final resistance will be calculated as follows.

                  R = [tex]\frac{V}{I}[/tex]

                   = [tex]\frac{120}{1.25}[/tex]

                   = 96 ohm

Now,

         [tex]\Delta R = R \times \alpha \times \Delta T[/tex]

     [tex]96 ohm - 86.33 ohm = 88.9 \times 4.5 \times 10^{-4}^{o}C^{-1} \times (T - 20)^{o}C[/tex]

               T = [tex]20.02^{o}C[/tex]

Thus, we can conclude that final temperature of the element is [tex]20.02^{o}C[/tex].