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Re: Ohm's 'law' & minus sign



As Bob Sciamanda points out, this might be coming from the "loop
theorem."

Discussions of the loop theorem often speak of the "voltage drop" across
a resistor, and texts often write delta-V = -IR in sections dealing with
the loop theorem. These texts write the loop theorem as 0 = sum(E's) -
sum (IR's), or even 0 = sum(E's) + sum(-IR's).

I don't appreciate that notation very much. I prefer 0 = sum(delta-V's)
because it avoids worrying about some things being emf's and some things
being IR-drops, and also makes it easier to know what to do with
capacitors and transistors and other devices besides batteries and
resistors.

I think it is practical to say that each circuit component has a
potential difference (or voltage) across it as measured with a
voltmeter. And if the voltages are measured across each device in a
loop, the sum must be zero. When doing this you keep the same
orientation of the voltmeter probes as you work your way around the
circuit. That is, if you are working your way clockwise around the
loop, and if you make your first voltage measurement with the red probe
in the more clockwise position, then you must keep the red probe in the
more clockwise position as you work around the loop. (I suppose I
should add the condition that there are no changing magnetic fluxes
through the loop, because if I don't, someone else will.)

To make it more practical yet, I would say the voltages measured across
each of several devices (not necessarily making a loop) must add up to
the same voltage reading you get if you place the voltmeter across all
these devices. This is simply a matter of conservation of energy
because voltage = potential difference = energy change per coulomb of
charge passed through the potential difference.

Anyway, the delta-V measured across a resistor is +- IR with the +-
depending on which way the probes are placed. Therefore, for a resistor
I don't associate delta-V with -IR; I associate |delta-V| = |IR|.

By viewing the loop theorem as conservation of energy and the junction
theorem as conservation of charge we remove a lot of mystery from
elementary circuit analysis.

Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Chair of Sciences
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu