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Re: R = V/I ?

Whoa! Stop!

I would like to say that I go out of my way to never write R=V/I or even
R=deltaV/I. Instead, I consistently write
R = deltaV/I (for EFFective Resistance)
EFF
I also sometimes call it RsubEQ (for EQuivalent Resistance)

I do this (and similar things with C and L, see below) because I
continually have students solve the defining equation for R (which I
believe to be
deltaVsubR = I*R
to yield
R = deltaVsubR/I
and say that this means that the resistance R is directly proportional
to the voltage difference VsubR and inversely proportional to the
current I. The resistance of a linear device should be a constant and
therefore cannot, mathematically speaking, be proportional (or inversely
proportional) to anything! Of course, even for a non-linear device, the
resistance is certainly NOT inversely proportional to the current. Were
that true, we would then be able to drive the resistance of this device
lower and lower simply by pushing more and more current through it.
Preposterous! Weather constant (as in a true Ohmic or linear device) or
non-constant, R should be thought to be related to geometrical and
material properties
R = Rho*L/A
and not to either deltaVsubR or I.


Similarly, I believe the defining equation for capacitance to be
Q = C*deltaVsubC
where we think of the magnitude of Q (on either "plate") as proportional
to deltaVsubC (or deltaVsubC as proportional to Q) with C (or 1/C) as the
constant of proportionality.

While we may solve the above equation for C to yield
CsubEQ = Q/deltaVsubC ,
we would certainly not want to suggest that this implies that C is
directly proportional to Q and inversely proportional to the deltaVsubC.
Just as with resistance, the capacitance of a linear device is a constant
and therefor cannot be proportional (or inversely proportional) to
anything. Again, weather constant or non-constant, capacitance, C, should
be thought of as related to geometrical and material properties and not to
either Q or deltaVsubC.


Lastly, I tend to think of the definition of inductance as analogous that
of either resistance or capacitance. That is, I consider the defining
equation for inductance to be
deltaVsubL = L*(dI/dt)
This says that an inductive circuit element which is linear will have a
deltaVsubL which is proportional to the rate of change for the current
passing through it with a proportionality constant which is L. Once
again, I would write this as
LsubEQ = deltaVsubL/(dI/dt)
While this is a good way to calculate the inductance of a circuit element,
I think of L as a constant and would never think it as proportional to the
voltage difference across that element and inversely proportional to the
rate of change of the current. Because, of course, it just isn't true.
Once again, weather constant or non-constant, inductance, L, should be
thought of as related to geometrical and material properties and not to
either deltaVsubL or dI/dT.

+=================================+=================================+

On Fri, 5 May 2000, Michael Edmiston wrote:

Robert Cohen asks why we cannot use V/I as the definition of resistance. I
think this is a sufficiently different topic that I will boldly change the
subject.

I believe many people, and many textbooks, do use this definition. The
textbook I am using (Tipler) says this.

The problem is: this sometimes leads people to assign a resistance to
something that does not really have a resistance. Of course we assume a
current-carrying device has a current through it and potential difference
across it. But that does not mean it has a resistance. Semiconductor
devices are mostly what I am thinking of here. We don't typically refer to
the collector-emitter "resistance" of a transistor.

Here is a better example. In the old days (analog meters) one had to
consider the resistance of the ammeter to understand how it perturbed the
circuit it was inserted into. It indeed behaved as if we added an Ohm's-Law
resistor into the circuit. Today, with digital multimeters, the digital
ammeter does not have a resistance. It has a "voltage burden." It does not
act like a resistor because it in no way acts like an Ohm's-Law device. As
the current through it varies, the potential difference across it stays
fairly constant (assuming the scale switch is not changed). Look in the
manual (or on the meter back) for an analog meter and you'll probably find a
resistance value. Look in the manual for a digital ammeter and you'll find
a "voltage burden."

Hence, I am not in complete agreement with defining resistance as V/I
because this definition doesn't make any sense when applied to some types of
devices.


Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817


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