Question

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.

Answer 1

Step-by-step 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 =
`(V)/(I)`

=
`(120)/(1.39)`

= 86.33 ohm

Now, final resistance will be calculated as follows.

R =
`(V)/(I)`

=
`(120)/(1.25)`

= 96 ohm

Now,

`\Delta R = R * \alpha * \Delta T`

`96 ohm - 86.33 ohm = 88.9 * 4.5 * 10^(-4)^(o)C^(-1) * (T - 20)^(o)C`

T =
`20.02^(o)C`

Thus, we can conclude that final temperature of the element is
`20.02^(o)C`.