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Re: R = V/I ?



Leigh Palmer wrote:
.... it is not appropriate to describe light bulbs by their resistance
as they do not behave like resistors. A VI characteristic is
necessary to describe their behaviour in circuits. ...

I see two terms here, resistance (presumably the V/I ratio under
specified conditions) and resistor (presumably a device in which
V/I remains practically constant). In that context all is in order.
A light bulb is not a resistor but it has a well defined R when the
conditions are specified, for example, when I= 1A and V=100V.
What can be more simple than this? Measuring V/I ratios for
different I and V (light bulbs, wire rheostat, etc.) is a good old
activity for students.

Well, if one wishes to call the ratio V/I the resistance of a light
bulb at a specific operating point one may certainly do so. It is a
matter of some concern to me that this resistance can't be used to
calculate anything else. It does not condense the information in a
way that will simplify a later calculation - operating voltage or
current must still be specified along with this resistance, so how
is that an improvement over specifying two other numbers, say
voltage and power? The value of knowing the resistance of a real
resistor is that only one parameter is needed to characterize the
VI curve. I prefer to reserve the term "resistance" for devices
that obey Ohm's law, except in applications where it is clear that
both parties to a conversation are aware that what is being
discussed does not obey Ohm's law. This is clearly not the case
when one teaches Ohm's law for the first time; the reasonable
student should trust his teacher not to mislead him.

The apparent disagreements seem to be centered on what should
be called Ohm's law. Right? Is it a law of nature or a low of
devices. A device operating under specific conditions is said to
obey Ohm's law when V/I remains constant. Ohm's law is a
very useful idealization. It can also be expressed as a relation
of proportionality between the current density j (in a wire) and
E responsible for the drift of charges.

Ohm's law is not a law of Nature, even in its J = sigma E form*.

A device (or a natural system resembling a resistor electrically)
which "obeys" Ohm's law may be said to have a resistance, or that
term may be qualified to pertain to some operating region (e.g.
the reverse resistance of a diode). One may also define qualified
versions of the concept which have the same dimensions (e.g.
dynamic resistance). These qualified versions are not expected to
obey the simple form of Ohm's law. They should not be introduced
to the beginning student until the simple form of Ohm's law has
been mastered in appropriate contexts.

Ohm's law strictly applies only to ideal devices which we call
"resistors". Nearly ideal resistors are commonly encountered in
natural and technical contexts, so Ohm's law is useful. This
utility is the reason we include exercises in Ohm's law in our
physics curricula. Ohm's law can be used to model many natural
processes as well as being widely (but not generally) applicable
to technical constructs.

Light bulbs are not among the commonly encountered devices which
obey the simple form of Ohm's law. They should not be used to
exemplify the application of Ohm's law in introductory courses.
I will note that this does not preclude the discussion of light
bulbs; I always discuss them when I introduce the thermal
dependence of resistivity. This comes, however, after I have
introduced resistivity itself, so it is at least two large steps
beyond simple networks in the introduction to Ohm's law.

Leigh

*The J = sigma E form is unsuitable for introducing students to
the phenomenon of electrical resistance. As I have pointed out
before it is a vector algebraic law which may be further
complicated to matrix formalism in anisotropic media like
graphite, and which must be modified in crystalline materials
where it is not generally truly local. In its most general form
it is *still* not a law of Nature.