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If the voltage and current of a circuit containing a light bulb are measured using a multimeter after consecutively lowering the voltage (building of a data set), what (type of) function will describe the trendline of the data when graphed (voltage as a function of current)? Is there a limit to the function or would it be theoretically exponential?

The goal of this is to find the resistance (graphically) of the bulb; which I do know will not be a constant value as the filament heats up. Is it good enough to assume a linear relationship and therefore use Ohm's Law, V=IR, as the basis for finding the resistance? Or is there a better way to do this?

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  • $\begingroup$ In a tungsten filament bulb, the resistance goes up with temperature, in a carbon filament bulb it goes down. $\endgroup$
    – R.W. Bird
    Commented Dec 30, 2019 at 18:58

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Tungsten has a pretty linear relationship between temperature and resistivity in the range being considered here.

So the resistance of the bulb will be quite linear with the temperature.

But the temperature is a complicated function of the electrical heating power, the environmental cooling, and the history: you can find different temperatures hence resistances depending on whether you’re raising or lowering the voltage.

Given all that anyway, what does R as a function of V look like? At low voltage it starts at some constant value, then starts to rise linearly. This ends up creating a (mostly) constant current at the voltage rises:

enter image description here

Image from this SE answer, which has more info.

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  • $\begingroup$ I have a data set of voltages between 9V (but really less from uncharged batteries) all the way down to what should be 1.5V. And the bulbs used are not full sized. They are small bulbed used in a classroom circuit set. Where on that curve would those voltages fit? From what you say, only knowing the Voltages and Currents, is the best that can be done a linear relationship? $\endgroup$
    – TTL
    Commented Dec 30, 2019 at 17:02
  • $\begingroup$ Note: that the exact shape of the green curve will depend on the rate at which the voltage is changed when you take the data. That's because the "resistance" of a light bulb does not directly depend on the voltage: It depends on the temperature of the filament, and the temperature depends on both the voltage and time. After a practically instantaneous change in Voltage, the temperature will follow more slowly. $\endgroup$
    – Solomon Slow
    Commented Dec 30, 2019 at 17:47

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