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
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 email@example.com
remove the X to answer
On 1/15/07 6:45 PM, in article MJWdnRHcBZD4oTHYnZ2dnUVZ firstname.lastname@example.org,
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
-- Fermez le Bush
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
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
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
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
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.
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