Re: R = V/I ?

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

On Mon, 8 May 2000, Michael Edmiston wrote:

> I don't want to put words in his mouth, but Robert Cohen seems to be
> thinking along the same lines as I am.  It strikes us as inappropriate to
> apply R = V/I to some objects like batteries, capacitors, inductors.  He
> says, "in my mind, it is the 'cause or 'reason' why the current is
> impeded..."
>
> That's what I've been trying to say all along.  I would probably reword his
> statement say "We have to determine why the device has a potential
> difference across it."  A battery has a potential difference across it
> because of an electrochemical reaction, not because of I*R.  A capacitor has
> a potential difference across it because V = Q/C, not because if I*R.  A
> reverse-biased zener diode has a potential difference across it because the
> potential difference is required to get breakdown and obtain charge carriers
> at the junction, not because of I*R.  Whether you use Robert's words or
> mine, the conclusion is the same... don't calculate a resistance for these
> devices using R = V/I... it is inappropriate to assign a resistance to these
> devices.
>
> On this basis, I fully agree with Robert that it is appropriate to assign a
> resistance to a light bulb.  I've tried to say that all along.  The
> potential difference across an operating light bulb is due to I*R where R
> can be calculated by rho*L/A where rho is the resistivity, and rho is
> temperature dependent.

We agree that using V/I as a universal definition for R is inadequate - we
need to distinguish between the various sources of the potential
difference across it*.  However, I'm also weary of using R=rho*L/A as a
definition because it seems derived from certain assumptions.  Can we also
use that definition for a copper sphere, for example?

Perhaps my definition of R is really the ratio V_r/I, where V_r is the
potential difference due to...[fill in the appropriate term here]?

* From the recent discussion on potential difference, I'm now hesitant
(confused?) to use potential difference for all elements (e.g.,
inductors).  I felt "impedance of current" sounded better for this reason.

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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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