Question

A certain toaster has a heating element made of Nichrome wire. When the toaster is first connected to a 120-V source (and the wire is at a temperature of 20.0°C, the initial current is 1.80 A . The current decreases as the heating element warms up. When the toaster reaches its final operating temperature, the current is 1.53 A.(b) What is the final temperature of the heating element?

Answer 1

The final temperature of the heating element is 462.5 Celsius 462.5 Celsius.

What is power?

Power can be described as the ability to do work, however, it can be found through the resistance and the current by using the formular, P=VI.

Voltage V1= 120V

initial current  I=  1.80 A

The power can be calculated using the formula as :

P=VI

where

I= current is 1.53

Voltage V1= 120V

Power= (120 * 1.53)

= 183.6 Watts

Therefore, power delivered to the toaster when it is at its operating temperature is 183.6 Watts

then , when the wire is at a temperature of 20.0°C, we have,

Resistance, $R_{1} =\frac{V_{} }{I_{1} }$

=120/1.80

=66.6 ohm

Then at the operating temperature,

$R_{2} =\frac{V_{} }{I_{2} }$

=120/53

=78.43 ohm

To calculate the final temperature of the heating element, we can calculate it using the formula,

R= R0[ (1+α)H]

Then we can substitute the values as :

78.43 =[66.6(1+0.0004(t-20)]

note that α for  Nichrome is 0.0004.

Then, 1.177=1+0.0004(t-20)

Then, (t-20)= 1.177/ 1+0.0004

t-20 =422.5

t=462.5 Celsius

Therefore, final temperature of the heating element is 462.5 Celsius 462.5 Celsius.

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