# Calculating light bulb resistance

Is there an equation to calculate the resistance of a light bulb as it heats up over time?
I'd assume this is an intergral formula and is not linear.

Thanks
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Right - and unfortunately it is somewhat dependent on external conditions which may not be present in any lab test because the thermal regime dictates the resistance at any time. One thing that can be done is to vary the voltage and measure the current to get a V-I curve. This still doesn't get you there as then one needs to consider external resistance and inductance to try to get a non-linear differential equation to give what you want. Even that would be an approximation.
A second thing is to use a scope and get traces of voltage and current on energisation of a bulb and from this get the variation of resistance with time, for that particular voltage source. Another source, another place, another R vs time curve.
--

Don Kelly snipped-for-privacy@shawcross.ca
remove the X to answer
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
On 1/15/07 6:45 PM, in article MJWdnRHcBZD4oTHYnZ2dnUVZ snipped-for-privacy@comcast.com,

This is a tough problem. The Standard Handbook for Electrical Engineers (probably from GE) has steady state graphs for various characteristics of tungsten lamps as a function of applied voltage. Making a mathematical model of transient heating that includes heat transfer in the filament would be a serious project.
Bill -- Fermez le Bush
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>

The only thing I have ever seen on this is a linear equation that was criticized at the time for its application because resistance is not linear with temperature. Here it is from an earlier post: Temperature is of major importance when determining DC resistance. For 100 per cent IACS copper dc resistance can be found with the following equation: Rdc=( (Pc/CMA)*((tah+T)/(tah.+20)) )*(length in feet)
Where Pc is the circular mil ohm resistance in ohms at 20 degrees C. tah is the inferred temperature of zero resistance. T is the temperature in degrees C at which we wish to find the DC resistance CMA is circular mil area (diameter of conductor in thousandths of an inch squared) Example: For the resistance of a copper conductor at 75 degrees C. with a CMA of 1620 circular mils (No. 18 AWG) 1000 feet long the resistance would be: Rdc=(10.371 ohms/1620 cma)(234.5 degrees C+75 degrees C)/(234.5 degrees C+20 degrees C))(1000 ft)
Rdc=7.8 ohms per thousand feet This matches the value in Table 8 or Chapter 9 in the NEC. For resistance of other metals used the circular mil ohms resistance per foot at 20 degrees C in place of the value of 10.371 used for copper. Typical vaues for Pc and tah are: copper (100 per cent IACS) is 10.371 ,tah is 234.5 Aluminum (61 per cent IACS) is 17.002, tah is 228.1 Brass (27.3 per cent IACS) (70 cu, 30 Zn) is 38.0 and tah is 912 Lead (7.84 per cent IACS) 132.3 and tah is 236
Reference: Neher McGrath paper The Calculation of the Temperature Rise and Load Capability of Cable Systems published by AIEE (now the IEEE) October 1957
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>

I found the circular mil ohm foot resistance of tungsten. It is 33.2 ohms. A simple method to find the inferred temperature of zero resistance is to measure the actual resistance of a tungsten filament at two temperatures and draw a straight line on x-y coordinate graph paper. Where the line crosses the X axes is the inferred temperature of zero resistance. The diameter can be found using a caliper and you have your constants for an approximation.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Peter wrote:

You could try sci.engr.lightning
-- bud--
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>

## Site Timeline

• ### where's all the political slagging-match gone?!

• - the site's newest thread. Posted in ⏣ General Metalworking

Polytechforum.com is a website by engineers for engineers. It is not affiliated with any of manufacturers or vendors discussed here. All logos and trade names are the property of their respective owners.