Concept explainers
To explain:
The changes in the magnitude of current in a toaster having the heating element made of Nichrome wire just after it is turned on
Answer to Problem 15Q
Solution:
The magnitude of current in the toaster is decreasing.
Known:
It is known that the temperature coefficient of resistance of Nichrome is 0.00017 per °C. Its resistivity is equal to , which is quite high as compared to that of copper .
Formula used:
•The power loss in a resistance (R)is given as
•The rms current in an ac circuit having resistance R, is given as,
•The resistance at temperature is correlated to the reference temperature and the resistance at that temperature as,
where α is the temperature coefficient of resistance of the given material
Explanation of Solution
Nichrome wire is used as a heating element in different devices like hair dryers, ovens, toasters etc. due to its high resistivity. When
. Due to this Joule Heating, the temperature of the Nichrome filament keep on increasing just after the toaster is turned on.
Now, as we know that the temperature coefficient of resistance of Nichrome is 0.00017 per °C, which is ‘positive’, therefore with the increase in the temperature of the element, the resistance of the Nichrome wire keep on increasing, which is given by the formula .
Because the supply voltage to the toaster is assumed to be constant, from the formula , we can conclude that the increasing resistance of the Nichrome wire will result in a decreasing current , immediately after the toaster is turned on.
Chapter 18 Solutions
Physics: Principles with Applications
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