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Re: [Phys-L] positive sign in Ohm's law ... or not



One more thing:

In conjunction with Lenz's law, there has been a fair bit of
discussion about the "positive sign in Ohm's law".

It should be pointed out that this so-called positive sign
is really a thinly-disguised negative sign!

By way of analogy, if I move from a lower place to a higher
place, the Δh is considered positive, according to any sane
definition of "Δ".

By the same token, if we go around a circuit measuring the
local changes in voltage, a positive ΔV corresponds to an
/increase/ in voltage.

HOWEVER (!) ... people write Ohm's law in terms of the
voltage /drop/, not the voltage increase. If you write
the law as V=IR it is non-committal, but if you write
it as ΔV=IR then you are either using a highly idiosyncratic
definition of "Δ" or you are going around the circuit
backwards relative to the direction of current-flow.

For those of us who have been using Ohm's law every day
for the last ten thousand days, we have long since grown
accustomed to this. We know that the ΔV in Ohm's law
stands for voltage /drop/.

However, it is quite possible for people to get this
wrong. As a case in point, the _Matter and Interaction_
book writes Ohm's law with the wrong sign about half
the time. You can argue over which half is right and
which half is wrong, but they can't both be right.

==========

I don't have any particularly brilliant constructive
suggestions for how to deal with this. The ΔV=IR
formulation is so deeply entrenched that I see little
hope of overturning it anytime soon. Personally I
tend to avoid it entirely, and write Va-Vb=IR ... but
students need to know how to read ΔV=IR, and need to
recognize it as being backwards from any sane definition
of "Δ".

BTW, putting absolute value bars around one side or the
other in Ohm's law is *not* an acceptable arrangement.
Believe it or not, I've seen that done.