Re: R = V/I with real lightbulbs

[Robert A Cohen <bbq@ESU.EDU>]

On Thu, 11 May 2000, Bernard G. Cleyet & Nancy Ann Seese wrote:

> I (assuming I haven't missed a post) am surprised no one has compared
> ohms law to another law.  Hook's law! I invite a rancorous debate on how
> it's not a law either.

I am glad that Hooke's Law has been brought up because I think it brings
out very nicely the problem I've been having with Ohm's Law.

Regarding Ohm's law, in my ideal world I'd first define R as...
(1)    R = V_r/I    [I use V_r to distinguish R from X_L, Z, etc.]
and then state Ohm's law as
(2)    R = constant.

It seems the first problem being debated is whether equation (1)
necessarily implies equation (2).  The second issue being debated is
whether Ohm's law (equation 2) holds for a material for which R depends
upon temperature but is otherwise constant.

I think Hooke's law can shed some light on these two issues.

Regarding Hooke's law, in my ideal world I'd define k first as...
(3)  k = - F/x
and then state Hooke's law as
(4)  k = constant.

The first problem, then, is whether equation (3) necessarily implies
equation (4).  I don't think so - it is the words that are the problem.
The statement "a varying spring constant" doesn't seem to sound right but
if we called k the "spring stiffness" then it would seem okay.  In other
words, we could describe a spring that had a low stiffness when not
stretched and a high stiffness when stretched.  Similarly, if we had
called R the resistance constant, then it wouldn't make much sense to say
a varying resistance constant. However, many posts have specifically
referred to a substance having a different resistance at different
temperatures and/or currents.

The second problem (when applied to Hooke's law) is whether Hooke's law
(4) holds for a spring for which k varies with temperature (but is
constant otherwise).  My feeling is that if Hooke's law is to be applied,
the assumption of k=constant must also apply.  If the temperature is
varied and that affects the ratio F/x, then Hooke's law cannot be applied.
Similarly, for Ohm's law to be applied, the assumption of R=constant must
also apply.  If the temperature will vary and that affects R, then Ohm's
law cannot be applied.

The two issues, in my mind, are separate.  Just because a material doesn't
follow Ohm's law does not mean we still can define resistance as V_r/I.
The two expressions (1 and 2) are independent.  We can debate the utility
of the definition in such a case, but I'd argue that it is nice if only to
be able to say that the resistance of such a material is not constant
given the operating conditions.

I'd like to see what everyone else thinks.

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| Robert Cohen               Department of Physics       |
|                            East Stroudsburg University |
| bbq@esu.edu                East Stroudsburg, PA  18301 |
| http://www.esu.edu/~bbq/   (570) 422-3428              |
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