|MadSci Network: Engineering|
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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