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Three Way Light Bulb

See the attached file.
You are probably familiar with "three-way" light builds, such as 1100/200/300W bulbs which have two filaments. As you turn the switch to its various settings the 100-W filament filament comes on by itself, then the 200-W filament comes on by itself, and then both filaments come on (connected in parallel) giving the sum of the two wattages. You may also have noticed that when you step through the three brightnesses, there seems to be a big change from 100 to 200, but going from 200 to 300 seems like less of a change. As mentioned previously in class, this si because the eye is sensitive to the ratio of wattages rather than the difference.

a) The problem here is to design an "ideal" three-way light bulb which appears equally-spaced in its three brightnesses. If the first filament is 100 watts, what wattage should the other filament have, and what will the wattages be fore the three settings? (Optional: If you have some business experience you might be able to market this "ideal 3-way light bulb" and make millions! If you do, remember who suggested it...)

b) You can get a fourth wattage out of your 3-way light bulb by connecting the two filaments in series to the power supply (this is not done in real 3-way light bulbs, as it would require an unconventional wiring of the bulb and sockey). Assuming you have designed the ideal bulb in Part (a), and ignoring the change of resistances with temperature, what will the fourth wattage be? Will these four wattages all appear equally spaced in brightness?

Note: Part (a) does not actually require any knowledge of electricity, though Part (b) does.

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Solution Summary

This solution contains step-by-step calculations and explanations to determine the wattages for the three settings and four wattage settings using concepts of resistance in series and parallel circuits.

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