The filament of a certain lamp has a resistance that increases linearly with temperature. when a constant voltage is switched on, the initial current decreases until the filament reaches its steady-state temperature. the temperature coefficient of resistivity of the filament is 4.5 times 10-3 k-1. the final current through the filament is one- eighth the initial current. what is the change in temperature of the filament?

a. 0100 k
b. 378 k
c. 1627 k
d. 814 k
e. 1162 k

To solve this problem we can apply the concept related to thermal expansion, including the analogy with resistance and final intensity.

The mathematical expression that describes the expansion of a material by a thermal process is given by

Where

= Initial resistance

Thermal expansion coefficient

Change in the temperature

If we want to directly obtain the final value of the resistance of the object, you would simply add the initial resistance to this equation - because at this moment we have the result of how much resistance changed, but not of its final resistance - So,

Re-arrange to find the change at the temperature,

Since the resistance is inversely proportional to the current and considering that the voltage is constant then

Then,

(It is possible that there is a typing error and the value is not 4.5 but 4.3, so the closest approximate result would be 1627K and mark this as the correct answer)

there are no atoms