Re: kirchoff's rules and linear dependence

["James R. Frysinger" <frysingerj@COFC.EDU>]

I'm beginning to think that my understanding has been incorrect for many years
now. So I call upon those of you who are more rigorously trained and perhaps
have more knowledge of topology to enlighten me. Here we do a lab on circuits
involving only resistors, but my understanding is that what I write below is
also true of circuits involving reactive components (inductors and
capacitors).

What I have been teaching students is this:
1. Kirchhoff's rules can uniquely solve any "flat" circuit, that is, any
circuit that can be laid down on paper without using "crossovers" (wires that
pass over one another without making contact).
2. Kirchhoff's rules might be able to solve non-flat circuits but there is no
guarantee that they will provide enough independent equations to derive an
exact solution.
3. For flat circuits, at least,
        a. the number of independent node equations will equal the number of nodes
minus one and
        b. the number of independent loop equations will equal the number of
"smallest" loops. (A "smallest" loop is one that does not contain two or more
loops.)
4. The best strategy is to
        a. write a node equation for all but one node; any one of the nodes may be
the one that is disregarded; and
        b. identify all the smallest loops, the ones containing only one "hole" and
to write a loop equation for each of those.

If I have been telling my students something false, I would appreciate hearing
it. I happen to be in the middle of writing a Kirchhoff's rules tutorial for
our lab manuals so this would be quite timely for me.

Thanks in advance!

Jim

On Friday, 2004 March 05 02:45, Michael Edmiston wrote:
> John Denker commented that my suggestion for finding independent loops
> might not be 100% reliable.
....
> As experienced solvers of physics problems, we certainly rely on our
> experience and intution.  Students often possess neither of these.  Even
> if it is not 100% reliable, my loop advice turns out to be an example of
> experience and intution that is pretty easy to explain, and it really
> does help.
>
> Michael D. Edmiston, Ph.D.
> Professor of Physics and Chemistry
> Bluffton College
> Bluffton, OH 45817
> (419)-358-3270
> edmiston@bluffton.edu

--

James R. Frysinger
Lifetime Certified Advanced Metrication Specialist
Senior Member, IEEE

http://www.cofc.edu/~frysingj
frysingerj@cofc.edu
j.frysinger@ieee.org

Office:
  Physics Lab Manager, Lecturer
  Dept. of Physics and Astronomy
  University/College of Charleston
  66 George Street
  Charleston, SC 29424
  843.953.7644 (phone)
  843.953.4824 (FAX)

Home:
  10 Captiva Row
  Charleston, SC 29407
  843.225.0805