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I have two light bulbs, both for 230 volts. One has 100 watts, the other 15 watts.

It is clear that the 15W bulb has the higher resistivity. But is its filament

a) longer

b) thinner

c) both,

and why?

Thanks!

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- Thread starter arcnets
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- #1

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I have two light bulbs, both for 230 volts. One has 100 watts, the other 15 watts.

It is clear that the 15W bulb has the higher resistivity. But is its filament

a) longer

b) thinner

c) both,

and why?

Thanks!

- #2

Chi Meson

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So your logic so far is correct, but it is clear that the 15 W bulb has the largest resistance. All of the bulbs' filaments have (I assume) the same resistivity.

- #3

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[tex]R = \frac{\rho l}{A}[/tex]

Therefore:

[tex]R\ \alpha\ \frac{1}{A}[/tex]

[tex]R\ \alpha\ l[/tex]

So longer filament means larger resistance, and thinner cross section also means larger resistance.

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- #5

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[tex]R_T = R_0(1 + \alpha T)[/tex]

Where [itex]\alpha[/itex] is a property of the material the wire is made of (similar to the resistivity [itex]\rho[/itex]).

But I don't see how this would affect the answer? It's true that the resistance of the wire is not constant, but the numbers specified on the bulbs refers to their power at the same temperature (might be room temperature, but doesn't really matter actually). So at the same temperature, the resistance of the 15W bulb is higher than that of the 100W bulb and the answer remains.

However we can't know for certain if the wire is thinner, longer or both. It could be really really long but just as thin, or it could be really really thin but just as long, or it's both thinner and longer.

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However we can't know for certain if the wire is thinner, longer or both. It could be really really long but just as thin, or it could be really really thin but just as long, or it's both thinner and longer. [/B]

That's exactly my question. Well, you need a certain surface area so the wire can radiate at the correct power...

- #7

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Still, though, the wire can either be:

a) somewhat thinner

b)

There is probably some fixed ratio between how much thinner and how much longer the wire should be.

- #8

Chi Meson

Science Advisor

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