MadSci Network: Engineering

Re: Modeling the resistance of a tungsten filament , incadescent light bulb.

Date: Sat Jun 20 11:26:49 1998
Posted By: Lawrence Skarin, Faculty, Electrical Engineering, Monroe Community College
Area of science: Engineering
ID: 897876294.Eg

Hi, Jerry.  

Approaching this problem strictly theoretically is difficult.  For a pure 
tungsten circular cylinder representing the filament it's difficult enough.  
You'd need a resistivity versus temperature relation on the doped tungsten 
lamps use and make lots of simplifying assumptions you probably have no right 
to make.  At any given current, a temperature equilibrium is established where 
the radiated electromagnetic power equals electrically-created power so the 
filament "glows" at a steady temperature. "Glows" is parenthesized because it 
glows even if you can't see it.  The glow then is dominantly infrared.

Here's what I suggest.  Use experimentation.  Take Voltage/Current data with a 
variable DC voltage source and draw a voltage (V) versus current (I) curve for 
the incandescent lamp.  Pick any current on the curve.  Draw a line from this 
point to the origin. The line slope is the resistance.

Want something more analytic?  Use a third-order polynomial curve fit for the 
VI curve.  Let V = A*I + B*I^3.  Two nonzero experimental data points (half 
rated and full rated current are good choices) will allow you to solve for A 
and B.  Then, because resistance (R) = V/I, R = A + B*I^2.

Here's example lamp data--                V: 0.0,  3.0,   6.0 volts.  
		     Respectively, I: 0.0,  0.71, 1.0 amps.

Plugging in, I get A = 2.43 and B = 3.57.  So: V = 2.43*I + 3.57*I^3.  This 
makes the resistance, R = 2.43 + 3.57*I^2 ohms.

As to temperature, the color of the glow can give you an estimate.  Optical 
pyrometers do this with some precision, but in absence of this, the library 
with books on blackbody radiation and (possibly) heat-treating steel might 
help.  Hey -- color telling temperature was good enough for Japanese sword 
makers before instruments were available!

Hope this helps.

Larry Skarin.

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