Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: R = V/I ?



At 9:36 AM -0700 5/9/00, Mark Sylvester wrote a lengthy rebuttal to
my lengthy rebuttal to...

Anyway, I'll comment on just part of what Mark adds here, and of
course I'll concentrate on the parts about which I feel otherwise.

I had a look at the textbooks in my office to check on how they approach
the question:

PSSC, Project Physics and Hecht take Leigh's line, defining resistance only
in the context of Ohm's Law.

Hecht is in good company here, but I still don't like the book.

Giancoli explicitly acknowledges both views.

So do I. I claim it is not helpful to allow two *differing* views to
be introduced at a student's first exposure to Ohm's law. The varying
"resistance" of light bulbs, in particular, make them unsuitable as
introductory examples.

Halliday & Resnick define R as V/I, and don't mention Ohm's Law for another
5 pages (this was my first undergraduate text, so maybe this is where my
view comes from).

You said (I paraphrase) your view is that resistance is the property
of a device that causes the dissipation of energy. That's quite
different from defining it as H&R do. I claim that two definitions
of resistance is confusing.

Most interestingly, the 5 British A-level books that I have (Breithaupt,
Duncan, Whelan & Hodgeson, Cackett Lowrie & Steven, and a brand new one by
Dobson Grace & Lovett) all define resistance as R = V/I and then later
introduce Ohm's Law. The last one even introduces the concept as
"Resistance is the electrical property of a material that makes moving
charges dissipate energy" in bold type.

I quote this only in response to Leigh's classification of my view as
"unconventional".

Your view is certainly superior to that last one, since resistance is
not a property of a material at all. "Resistivity" would correct it,
but I still don't think it is helpful. The power dissipation density
p is, indeed, p = rho j^2, where rho is the resistivity.

If I were to plug a Mixmaster into the wall and use it to stir cake
batter, then the system would be dissipating energy. One could
calculate a resistance R = V/I, and I^2 R would, indeed be the
dissipated power. Could one usefully treat the mixmaster and cake
batter system as having a resistance R? Not in my world view. Many
such examples come to mind, and I would rather reserve the concept
of resistance to those devices which obey Ohm's law*. [corrected]

Yes, but an electric motor in the first place does work, and is not a
dissipative device, so I'm not convinced by this example. It does remind me
that the real and imaginary axes on a phasor diagram are usually labelled
"resistance" and "reactance". Presumably you would want to use some other
word than resistance here, since the phasor diagram could well apply to the
Mixmaster.

Let's not complicate things. My system is a Mixmaster and a bowl of
cake batter. It has two terminals. Mixmasters can be run perfectly
well off DC mains because they have universal (AC/DC) motors, as
anyone watching an old TV next to a running Mixmaster will readily
perceive. Let's say I run my Mixmaster on DC. My system dissipates
energy, it has an IV characteristic, and the power dissipated P = IV.
I can define R for this system by your causal relation: R = P/I^2.
Like the light bulb however, this relation will yield a variable
resistance. Unlike the light bulb, electrical resistivity plays no
important part in dissipating energy in this system.

I, too, checked a textbook, the one I had in my introductory college
course, Sears & Zemansky, First Edition revised. S&Z introduce first
conductivity sigma by J = sigma E. Then they define the resistance
of a conducting wire by R = rho L/A (with a box around it). In the
next paragraph Ohm's law is introduced: Vab = Ri. (the usual suspects).
They then state:

"Note carefully that this relation between Vab, R, and i, applies
only when the path between a and b is a so-called `pure resistance,'
that is, it does not contain any batteries, motors, generators, etc.
...

"It must also be remembered that in deriving [this equation] from
the basic equation J = [sigma] E we assumed the constancy of the
conductivity [sigma]. If (and only if) [sigma] is independent of J,
the resistance R is a constant independent of i, and the potential
difference Vab between the terminals of the conductor is a *linear*
[*italics*] function of the current in the conductor. This direct
proportionality between the current in a metallic conductor and the
potential difference between its terminals was first discovered by
the German scientist, Georg Simon Ohm (1789-1854), and it is known
as *Ohm's law*."

Now it would seem to me that this is a useful law, though it may be
only approximate. R, to me, is a constant in any application. That
may include resistors operating at other temperatures (in heat baths
for example) but it does not include light bulbs. Note that Ohm's
law is useless when applied to light bulbs. From the web:

"Tungsten-filament incandescent lamps exhibit a very-high positive
temperature coefficient of resistance with the cold filament
resistance being approximately 10% of the hot filament resistance.
When an incandescent lamp is initially turned ON, the cold filament
is at minimum resistance and will normally allow a 10x to 12x peak
current. Within 3 to 5 ms the current falls to approximately 2x the
hot current. This high lamp turn-ON current (commonly called
"in-rush" current), can contribute to poor lamp reliability and can
destroy semiconductor lamp drivers. Even if the active part of the
device output can survive the short-duration peak current, the
internal bonding wires can "fuse" open. High-current drivers or
paralleled drivers, rated to handle the peak inrush current, may
prove cost prohibitive. Two simple methods are shown here for
controlling the lamp in-rush current in standard power driver
applications.

Here again the term "resistance" is understood among the cognoscienti.
We understand that Ohm's law is of no use here because we are talking
about light bulbs.

Bottom line: light bulbs should not be used to introduce Ohm's law.

Leigh