As I was sitting doing my Physics homework wondering what I should do my blog on, I began doing a sample problem about current, power, and resistivity. All of a sudden, it his me- I have a very close-at-hand example of all three of these: the lamp next to my computer. It has a bulb that contains two filaments, and the lamp is made in such a way that it can produce three different levels of light: one filament, the other filament, and both together. As I worked on problems pertaining to legnth of the resistor, cross-sectional area, resistance, power, and current, I began to wonder how the bulb worked from a Physics standpoint. This is what I have decided: there are two possibilities for this bulb. The first possibility (depicted above) is that each of the filaments have different legnths, but same cross-sectional areas. Since R=(coeff.)L/A, the filament with the longer legnth would have a greater resistance than the shorter one. Then since P=(I^2)R, and I(current) is the same for each of the filaments since the current comes from the same source, the power in the longer/higher resistance wire would be greater, resulting in more electron movement and more transfered energy to the filament's atoms, and therefore more light.
The second possibility was that the filaments have different cross-sectional areas but the same legnth. Then, since R=(coeff.)L/A, the filament with the smaller cross-sectional area would have the greater resistance. Then since P=(I^2)R, and I is the same for both, the power for the thinner filament would be larger, resulting in more collisions and more light.
There is actually a third possibility: the filaments could have both different areas and legnths. However, companies may want to save money by using the same wire, as well as try to increase the longevity of their bulbs by using the same thicker wire with different legnths. Or would they want to use the thinner one so that the thinner filament will break more quickly so consumers will have to buy more? :-)
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