Formula for resistance of filament lamp?

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#1
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I already know that the filament lamp is a non-ohmic conductor and the resistance isn't proportional to voltage, but is there a mathematical formula of working out the resistance of a filament lamp (or any other non-ohmic conductor that has non linear resistance) given some other information like the temperature and length of wire.

Thanks for helping!

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teachercol
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R = Ro (1 + kT)

Resistance increases linearly with temp for a metal wire. This only applies for filament lamps not for any non-ohmic conductor eg LED

Ro = resistance at zero Celesius

k is a constant. which depends on the metal (temp coefficient of resistance)
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lerjj
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Just to expand upon what he teachcol said, I'm guessing (because I haven't seen it before) that that formula actually outputs a resistivity. If you haven't come across resistivity before, it's the letter rho is the equation:


R=\dfrac{\rho l} {A}

R is resistance, l is length and A is cross sectional area. The greek letter rho is the one that looks like a p
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(Original post by lerjj)
Just to expand upon what he teachcol said, I'm guessing (because I haven't seen it before) that that formula actually outputs a resistivity. If you haven't come across resistivity before, it's the letter rho is the equation:


R=\dfrac{\rho l} {A}

R is resistance, l is length and A is cross sectional area. The greek letter rho is the one that looks like a p
I've seen the equation before, thanks for helping though

Why would it output a resistivity? Everything in that equation cancels out to leave you with ohms (  \Omega \cdot \ q \cdot q^{-1} ) isn't it?

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lerjj
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(Original post by majmuh24)
I've seen the equation before, thanks for helping though

Why would it output a resistivity? Everything in that equation is dimensionless except from R_0,

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Yeah sorry, I kinda meant that conceptually it feels like it should be resistivity... but it works fine for both.

Changed by post around a bit to make more sense. I only posted that because your OP mentioned length, and that was the only relevant equation I could think of.
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Stonebridge
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It doesn't output resistivity.
It tells you the resistance at a temperature T in deg Celsius given that you know the value at 0 deg Celcius (Ro)
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(Original post by lerjj)
Yeah sorry, I kinda meant that conceptually it feels like it should be resistivity... but it works fine for both.

Changed by post around a bit to make more sense. I only posted that because your OP mentioned length, and that was the only relevant equation I could think of.
The resistance of the wire would also depend on the resistivity of the material, so it might be a factor if you think of it like that, but I think the overall resistance is what really matters.

(Original post by Stonebridge)
It doesn't output resistivity.
It tells you the resistance at a temperature T in deg Celsius given that you know the value at 0 deg Celcius (Ro)
That's what I thought it did in the first place

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lerjj
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(Original post by majmuh24)
The resistance of the wire would also depend on the resistivity of the material, so it might be a factor if you think of it like that, but I think the overall resistance is what really matters.



That's what I thought it did in the first place

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Ok, just to be 100% clear: I typed something too quickly and it was wrong. That equation has to output resistance because of it's units.

However, you can multiply both sides of the equation by the area of the wire over the length of the wire (because it doesn't change) and voila, it now gives resistivity. Which I think is a nicer analogy, because we're talking about how the material changes with temperature.

But yes, I made a mistake and am currently googling Hari Kari.
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There's a lot of simultaneous posting here.
I think we've sorted out the resistance and resistivity confusion.
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(Original post by lerjj)
O

But yes, I made a mistake and am currently googling Hari Kari.
I wouldn't worry about it.
Making the odd mistake is part of the fun.
I've had many a laugh at my own expense.
Thanks for your answers on here recently.
Keep up the good work.
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(Original post by lerjj)
Ok, just to be 100% clear: I typed something too quickly and it was wrong. That equation has to output resistance because of it's units.

However, you can multiply both sides of the equation by the area of the wire over the length of the wire (because it doesn't change) and voila, it now gives resistivity. Which I think is a nicer analogy, because we're talking about how the material changes with temperature.

But yes, I made a mistake and am currently googling Hari Kari.
Right, I was getting confused for a second there

I guess so, I just prefer to think of it as a linear relationship because resistance just seems easier to deal with in my head (besides, you can use the resistivity in working out the resistance of a given length of material with a certain cross sectional area anyway.)

Haha, don't worry, it happens to me all the time

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lerjj
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(Original post by majmuh24)
Haha, don't worry, it happens to me all the time

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*pulls knife out of stomach*
You tell me this now?
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