Re: Filament resistance

["Daniel L. MacIsaac" <Dan.MacIsaac@Nau.Edu>]

> > > From Cutnell & Johnson PHYSICS 4th Ed. NY: Wiley p.618
> > Q20.12:  The filament in an incandescent light bulb is made from tungsten.
>  The radius of the tungsten wire is 0.045 mm...
> > Soln manual suggests a 150W bulb has a 11m long filament.  If the above
> radius is correct, I concur.
> > /rho_{tungsten} = 5.6 x 10^{-8} ohm * m

> I very much doubt this is the case. 
> Would Dan care to justify his position?
>
> Whatcott   Altus OK
Sorry about the delayed response (preparing an exam for friday).  
Here's my reasoning:

I = P/V = 150W/120V = 1.25A
R = V/I = 120V/1.25A = 96 ohms

R = rho L/A =>> L = RA/rho
where A = pi r^2 = 6.4 x 10^(-9) m^2

Finally L = RA/rho = 96 ohms * 10^(-9) m^2 / (5.6 x 10^{-8} ohm * m) 
so L = 10.9m or 11m to 2 sig digits.
 
note I completely neglected the effect of temperature here; this
will decrease the length required.  I don't have my CRC handy for
the temp corr.  I have taken the C&J thickness as given in this problem.

Ok -- so now's my turn: why do you very much doubt this is the case? 
I'm always looking to learn about the physics of real and everyday 
phenomena, please enlighten me.  Under a microscope it's clear there is
a lot of wire there; what is your claim about the filament length and
what reasoning lies behind your claim?  Inquiring minds want to know.

Incidentally, I just got an email suggesting a filament diameter of 20-40
microns compared to C&J's 2*45 = 90 microns; has anyone else got real data?  
By temp-free calcs as above 40microns wire is 2.1m long; 20microns is 54cm 
long.  I'd guess real-world filaments vary in diameter for different power
bulb filaments, and that thicker filaments are slightly more common (and are
probably easier to work with)...

regards,

Dan M

Dan MacIsaac, Assistant Professor of Physics and Astronomy, Northern AZ Univ
danmac@nau.edu  http://www.phy.nau.edu/~danmac/homepage.html