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Ohm's Law taking into account temperature coefficient of resistance

Discussion in 'Electronic Basics' started by Griff, Apr 4, 2004.

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  1. Griff

    Griff Guest

    Dear boffins

    How does one calculate the current flowing in a resistor if one wishes
    to take the temperature coefficient of resistance into account ?

    ie we know the Voltage applied to the resistor, we know the TCR of the
    resistor, and we know the initial values of resistance and
    temperature.

    I have looked around to find a straightforward formula for this, but
    can't find one anywhere.

    Help on this would be much appreciated,

    cheers

    Griff
     
  2. Non linear effects. Learn about tensors first.

    www.google.com "how to use google"
     
  3. You replace R in the formula, E=I*R, with R(t), which is resistance as
    a function of temperature. Any such function you can express is an
    approximation of the actual resistance and the kind of function that
    is a good enough approximation depends on your accuracy needs, and the
    range of temperature. For very narrow ranges, a linear function might
    work.

    E.G. R(t)=Rbase + (T-Tref)*deltaR/degree
    http://scienceworld.wolfram.com/physics/ThermalResistanceCoefficient.html
    http://www.utc.edu/Faculty/Tatiana-Allen/Temp.html
    page 8 of:
    http://www.utc.edu/Faculty/Tatiana-Allen/Temp.html

    This approximation can be improved by including terms for higher
    powers of temperature (search [polynomial curve fit]).

    For for many conductive materials, an exponential approximation is
    more accurate, since a %/degree description is closer to reality than
    increment/degree.

    see page 9 of:
    http://www.utc.edu/Faculty/Tatiana-Allen/Temp.html
     
  4. Mark Folsom

    Mark Folsom Guest

    Are you trying to take account of the resistance heating with a particular
    applied voltage? If so, you need to have rate of heat dissipation versus
    temperature. When the voltage is first applied, the temperature will change
    rapidly, and then it will asymptotically approach an equilibrium
    temperature. If you have an approximation for the heat dissipation, then
    the best approach is probably to do some kind of numerical approximation by
    difference equations.

    Mark Folsom

    Mark Folsom
     
  5. Rich Grise

    Rich Grise Guest

    If you know the TCR, isn't "The resistance at temp. T
    equals the resistance at 68F times X" provided? Then
    just do that, and use that value as the resistance
    in I = E/R.

    Cheers!
    Rich
     
  6. Griff

    Griff Guest

    Thanks to all of you for taking the trouble to reply (even Mr.Varney,
    who I suggest might benefit himself from going to Google and typing in
    "how to be helpful".)

    Rich, I take your point but I now also understand the arguments put
    forward by Mark and John, ie that it's not straightforward to
    ascertain a temperature "T" to plug into the formula. You know the
    ambient temperature when you switch the voltage on, but then: (1) the
    temperature of the resistor will go up as the current flows through
    it, and (2) the resistance of the resistor will go up or down as a
    consequence of the temperature changing, thus varying the current and
    bringing rule (1) back into play again, etc.

    Clearly it's a judgement call as to how accurately one wants to model
    the situation - I'll go away and think about it.

    - griffph
     
  7. I taught you how to fish rather than giving you a fish.

    Good for you.
     
  8. hanson

    hanson Guest

    Wow, you are holier than Jesus........ahahaha...AHAHAHA......
    How did you escape from the cross?.....in a bus?.....
    hahahaha......ahahanson
     
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