Re: Ohm's Laws

On Mon, 05 Nov 2007 22:25:30 -0600, John O'Flaherty
<quiasmox@xxxxxxxxx> 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.

If you think about their definition differently, as a statement about
a fixed circuit under fixed conditions of current flow, then it's
correct to say that the potential difference between any two points in
that circuit is proportional to the resistance between those two
points. That is, they're talking about the different Vs and Rs
encountered by examining various pairs of points in the circuit, not
by changing the existing circuit. They could have specified it more
clearly.

If you say voltage between the two points is proportional to
the resistance between them, you're implying that if you
vary the resistance the voltage will vary in proportion.
That is, a demonstration of the principle they're discussing
requires a modification of the circuit. So they're not
talking about "a fixed circuit under fixed conditions of
current flow".

I will concede that they could demonstrate the truth of
their assertion if they had a constant-current source rather
than the normal constant-voltage source. But where do you
go to get a constant-current source? You don't.

There's a discussion of current sources at
http://en.wikipedia.org/wiki/Current_source . There it's
brought out that if you had a true constant-current source,
the voltage at the output would be directly proportional to
the load across the output. The greater the load, the
higher the voltage, so that as you approach open-circuit
output, output voltage approaches infinity. That
illustrates the impracticability of achieving a true
constant-current source.

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.

I had never heard of that either, and according to Wikipedia, there's
an Ohm's phase law, same guy, that says "the phase of a waveform has
no effect on how the ear perceives it."
.

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