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Re: Ohm's 'law' & minus sign



Robert Cohen wrote:

It seems to me that the typical relationship between V, I and R is a
relationship between scalars and, as such, does not need a minus
sign. Is this correct?

Some scalars have mandatory signs.
The derivative of cos is -sin.
The sign of the sin is non-optional.


(That's one of the few cases where the
written statement is clearer than the
corresponding spoken statement. :-)


On the other hand, can we start with E = rho j (which is a vector
relationship) and replace E with - Del V, rho = AR/L, and I = JA, to
get a vector equation with Del V, L, R and I? In that case, the
vector equation would necessarily have a minus sign, no?

I get -L Del V = R I, with
L = scalar
I = vector
Del = vector

The usual form of Ohm's law is delta V = R I, with
everything a scalar.


Apparently it is conventional to define
delta V := -L Del V
which can be thought of as an instruction as to
where you put the red lead and where you put the
black lead of the voltmeter.