Re: [Phys-l] Current as Vector

[John Denker <jsd@av8n.com>]

James McLean wrote:

> Consider a specific example (ASCII art: fixed width 
> font required):
>             I1=2A                         I2=1A
> --------->---------------------->------------
>                            |
>                           V  I3=1A
>                            |
> If you try to make vectors out of these, I2=(1A)i-hat, I3=-(1A)j-hat, 
> and I2+I3 has a magnitude of 1.414A, which has no useful physical 
> meaning that I can detect.  It certainly doesn't make the "junction 
> rule" any easier to handle.

An excellent point.

> No question that when analyzing circuits, one needs to establish a 
> "positive direction" for each segment of a circuit.  But that doesn't, 
> in an of itself, make the quantity a vector.
>
> This whole discussion is a microcosm of the more general fact that all 
> fluxes are signed quantities that depend on a choice of positive 
> direction, but are not vectors.  

Help me out here.  We have something that is not a scalar.  It has
magnitude *and direction*.  But is not a vector.  So, what is it?
Do mathematicians have a name for this type of non-scalar non-vector
quantity?


> So current is a signed quantity, and properly dealing with it requires 
> defining a positive direction on each circuit segment.  Why not just say 
> that, instead of trying to make it a vector?  In fact, even here the 
> vector model defeats the point: one of the salient properties of vectors 
> is that only a single coordinate system choice is required to solve a 
> problem; but for a circuit, you often want to pick a *different* 
> positive direction for each segment.

I don't see much merit in that argument.  I can imagine lots of
mechanics problems where I might decide that this force is a multiple
of this unit vector, and that force is a multiple of that unit vector,
with lots of different unit vectors.  A spaceship with N thrusters
for maneuvering springs to mind.

> BTW, at the above web link, it says "To label the voltage of a node in 
> the diagram, it suffices to put a symbol next to the node."  While this 
> is true, I think it might be a tad misleading.  To obtain proper voltage 
> *differences*, reference must be made to the same orientation choices 
> that are made for description of the currents.  

That's news to me.  What means "proper"?  What's the penalty for
making an "improper" choice?

> See 
> <http://www.geneseo.edu/~mclean/AnalytII/demo/CircuitAnalysis.pdf>.

The soi-disant "sure-fire never-fail technique" described there may
be good enough for the most elementary applications, but is, to say
the least, far from complete.
 -- The near-universal convention for positive output voltage and positive
  output current for a _battery_ violates rule 1.
 -- The whole approach has to go back to Square One when we consider three-
  terminal devices such as transistors.