Re: Ohm's Law

[David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>]

Regarding Stu's question:

> The discussion on the California Science Framework has reminded me
> that I am a bit confused about  Ohm's law and the meaning of "Ohmic".
>
> As I understand it, incandescent light bulbs are considered
> "non-ohmic" because the current will not vary in direct proportion
> to the voltage applied.

That depends.  The only way an incadescent light bulb could possibly
be considered as non-ohmic is if, while the voltage and current is
varied, care is not taken to keep the filament temperature constant.
If such care is taken then light bulb filaments are just as ohmic as
any other metallic conductor.  There are 3 simple ways to keep the
temperature effectively constant while varying the voltage and
current: 1) Don't apply any more power to the bulb than it can
effectively transport to its surroundings via its normal cooling
processes the thermal energy that was generated in the filament by
the internal dissipation of the electical work done on it without the
filament's absolute temperature significantly increasing much.
2) Vary the voltage and current so rapidly that the temperature of
the filament doesn't have time to readjust to the fluctuating power
dissipation levels.  IOW, take the I vs V data using different
parts of the cycle of a sufficiently high frequency AC waveform
applied to the bulb.  3) Break the bulb and submerge the filament
into a well stirred (nonconductive) liquid heat bath.

BTW, if we use method 2 and monitor I(t) vs V(t) over the various
phases of the AC cycle of ordinary 60 Hz AC power applied to an
ordinary light bulb there isn't that much hysteresis because
1/120 s is not much time for the bulb to heat & cool very much
above and below the average temperaure.  If the AC frequency is
increased to over 200 Hz then typically the hysteresis is
negligible and the bulb is seen to be completely Ohmic with
V(t) = R*I(t) where R is a constant at each moment of time.

> As I understand Ohm's law, it states that the current is directly
> proportional to the applied voltage, but only if the resistance
> remains constant.
>
> The filament of the incandescent bulb (again, as I understand it)
> depends on its dimensions (length, cross-sectional area), type of
> material (tungsten?) and the temperature.

I assume you mean the filament *resistance* here.

> Since the filament gets significantly hotter as current flows
> through it, its resistance changes significantly and thus "I" will
> not vary directly with "V".

only if sufficient care is not taken.

> But does this make it "non-ohmic"?

Not according to my definition.

> If we could somehow couple the filament to a heat sink so that the
> temperature of the filament does not change with the increasing
> voltage would "I" then vary directly with "V"?  (...and would it
> then be "Ohmic"?)

I can't imagine otherwise.

> Other materials that are considered "ohmic" will not have "I" and
> "V" vary directly if we allowed their resistance to somehow vary.
> In light bulbs is it because the change in resistance is brought
> about directly as a result of the application of a potential
> difference that they are considered "non-Ohmic"?

I would think fluorescent bulbs, neon bulbs, and LEDs could
legimately be considered as non-ohmic.  But I believe that we ought
to consider incandescent bulbs as ohmic.

> Still, what if the
> temperature were held fixed?  If the filament is then considered
> "ohmic", it seems to be an artificial distinction.

Amen.

The way I see it, calling an incandescent light bulb filament
non-ohmic is like saying that an ideal gas doesn't obey Boyle's law
simply because if we took a container containing an ideal gas and
thermally insulated it and compressed it we would find that the
pressure vs volume relationship obeyed P*V^gamma = constant (where
gamma > 1) rather than obey the P*V = constant relationship of
Boyle's law.  To me this is perverse.  The definition of Ohm's law
(or any physical relationship between two variables) is supposed to
be done under standard conditions such that all the other possibly
relevant variables (including the temperature) are held fixed, and
*only* the two variables of interest are varied in a way that
demonstrates the relatinship.  Varying other variables that couple to
the variables of interest while they are being varied is, to my way
of seeing things, cheating.

> Aren't there other materials whose resistance changes with voltage
> even without a change in geometry, type o' material or temperature?

Certainly, and such things *are* non-ohmic.

> Thanks for any "light" you can shed on this subject.
>
> Stu Leinoff

David Bowman