Re: Filament resistance

[brian whatcott <inet@intellisys.net>]

At 14:26 4/7/98 -0700, you wrote:
> > > > 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
> > ...
> Here's my reasoning:
> ...
> 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? ...
> Dan M

You took the power dissipation when incandescent, and the Rho for room
temperature. The temperature range is so large and somewhat non-linear too
that this leads to large errors.

 Jones & Langmuir published this:
temp K    Resistivity (micro ohm cm) (NOTE UNITS)
300       5.65
1000     24.93
2000     56.67
3000     92.04

(If you feel this critique is cogent, perhaps you would write the 
publishers, as a public-service.)

Whatcott    Altus OK