Re: [Phys-L] more about basic DC circuits

[John Denker <jsd@av8n.com>]

On 12/16/2013 08:30 AM, Rauber, Joel wrote:
> In Knight's defence, He defines the Law of Conservation of Current
> as follows:  " The current is the same at all points in a current 
> carrying wire." A very limited piece of applicability for a 
> conservation law.

Agreed.

That is, however, a weak defense.  I suppose it is "legal" for an 
author to redefine conservation in that way ... but it's amazingly 
bad pedagogy.
 -- For starters, you might think it makes the subject twice as 
  difficult as it needs to be, because now students need to learn 
  two different notions of "conservation" rather than just one.
 -- Really, though, it's much worse than that.  If students had
  to learn two separate definitions (conservation of charge and
  blorkivation of current) that would be twice as much work as
  necessary ... but if they have to learn two ideas that share
  the *same name* it imposes the additional burden of confusion
  ... utterly needless confusion.

This is on top of the pre-existing painful confusion between physics
conservation and endangered-wildlife conservation.

A /major/ goal of the course is for students to develop a solid
understanding of conservation.  This is immediately applicable to
charge, energy, momentum, and angular momentum.  It can eventually 
be extended to other things such as lepton number.  It can be
approximately extended to yet other things, such as the conservation
of the number of carbon atoms during a chemical reaction.

The idea referred to in the previous paragraph cannot be extended
to current, not even approximately.  Example:  the current in an
RC circuit just dies away.  It doesn't flow away into some nearby
region;  the current just stays in place and decreases, violating 
any halfway-reasonable notion of conservation.

It is a serious disservice to students to speak of «conservation
of current» in the same breath as conservation of charge.  It
seriously undercuts one of the major goals of the course.

Since by any reasonable definition, current is not conserved but
energy is, page 896 expresses two misconceptions in one sentence, 
when it says that current is not used up but energy is.

> I view "the current is the same at all points in a current carrying
> wire" as a special case of Kirchoff's junction rule where you pick a
> point on the wire as a node which has one incoming lead and one
> outgoing lead.

Exactly.

Given that we already have a perfectly good name for the concept in
question -- Kirchhoff's Current Law -- it is all the more insane to
abuse the word "conservation" by referring to the KCL as «conservation 
of current».

While we are on the subject, Knight also implicitly redefines the
word "junction" in an unhelpful way.  On page 899 he speaks of 
resistors in series as having «no junction» between them.  This 
is nuts.  A junction is the joining of two or more things (not three 
or more things) ... for example in a semiconductor PN junction.  The 
two resistors are joined at a junction, and in the DC limit we can 
apply Kirchhoff's Current Law to this junction, as JR quite rightly 
noted.