Re: Ohm's Laws
- From: Bob Cunningham <exw6sxq@xxxxxxxxxxxxx>
- Date: Mon, 05 Nov 2007 22:18:15 -0800
On Mon, 05 Nov 2007 21:55:30 -0700, Hatunen
<hatunen@xxxxxxx> said:
On Mon, 05 Nov 2007 18:01:15 -0800, Bob Cunningham
<exw6sxq@xxxxxxxxxxxxx> wrote:
A discussion in another thread made me curious to see how
the _New Shorter Oxford English Dictionary_ (_NSOED_)
defines Ohm's law. On pursing this curiosity, I found that
they have an error in their definition of the Ohm's law that
many people, but evidently not Mr or Ms Lodder, know about.
But the more startling finding was that there is yet another
Ohm's law, one having to do with the decomposition of a
complex sound into its component sounds.
First the error: They state that one of Ohm's laws says
[...] that the potential difference between any
two points of [a circuit] is proportional to the
resistance between them;
Only under special circumstances is it true that the
potential difference between any two points of a circuit is
proportional to the resistance between them. The potential
difference depends upon the amount of current flowing
between the two points, which in turn depends upon the total
resistance in series with the source. Their assertion is
easy to disprove by means of a counterexample: Let the
resistance between the two points be ten ohms. if the
circuit contains in series with the ten ohms another
resistance of ten ohms, then doubling the first ten-ohm
resistance will not double the voltage across it. it will,
instead, increase the voltage by 50 percent.
The definition is badly worded but can be taken to mean
"proportional to the rsistance between them with respect to the
ccircuit as a whole." In your example with the two ten ohm
resisters you have added resistance to the circuit by doubling
one of the resisters, which alters the circuit and the problem.
The definition very clearly states that the resistance in
question is that between any two points in the circuit. The
circuit could have a thousand points, but they choose to
mention only two of those points. When I add my ten-ohm
resistor, I'm not adding it between their two points, so I'm
not affecting the resistance between their two points. Their
statement is dead wrong.
Here, again, is what they say:
[...] that the potential difference between any
two points of [a circuit] is proportional to the
resistance between them;
Instead, consider that potential across one of the ten ohm
resisters is E volts, then the potential across both ten ohm
resisters, or twenty ohms, will be 2E volts. In other words, the
potential is, indeed, proportional to the resistance.
But the resistance between the two points they've chose to
mention is still 10 ohms, so the potential across their
points is not 2E volts. In fact, your application of Ohm's
law is quite faulty in that you've neglected to consider
that the ten ohms I've added in series outside their two
points will decrease the circuit current. You've added
resistance without decreasing the current. Wrong, wrong,
wrong.
This is, of course, simply a consequence of the current being the
same throughout the circuit and applying E=IR, the Ohm's Law we
learn first. Ohm's Laws e=ir and e=iz come later.
In addition to forgetting the current-reducing effect of the
extra resistance, you've neglected to consider that the
resistance "throughout the circuit" is not known. All you
know is that they speak of *any* two points in the circuit
and the resistance between them. When I add my ten ohms, I'm
not adding it between their two points.
I must admit that I oversimplified my discussion by assuming
that the current would be determined by a constant-voltage
source with only the original ten ohms and my added ten ohms
in the circuit. But the fact remains that the voltage
between *any* two points in the circuit will not be
proportional to the resistance between them, because the
current through that resistance also depends on that
resistance among other things.
As I've said in another posting, the voltage between the two
points will be proportional to the resistance between them
only if you have a constant current source, but there is no
such thing as a constant-current source. There are only
approximations to a constant-current source.
Again, the impracticability of achieving a constant-current
source is emphasized by considering what happens to the
voltage across the output as the load impedance is increased
toward an open circuit. it approaches infinity. So a true
constant-current source implies an infinite voltage source
with an infinite source resistance.
.The second Ohm's law is, according to _NSOED_
(b) that a complex musical sound is heard as the sum
of a number of distinct pure tones which can be
resolved by Fourier analysis. M19.
That principle was central to some of my work during my
working years, but I had never heard it attributed to Ohm.
New to me, too.
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