John Denker commented that my suggestion for finding independent loops
might not be 100% reliable.
I almost added a statement to my post stating I was not sure that my
technique was rigorously accurate. I probably should have done that,
but I didn't because I have found that for students solving problems in
the typical textbook, my method has always seemed to work and it has
proven very helpful to students as they try to find independent loops.
It may be it has been luck that we have not run into circuits where this
method has not worked. However, as a general problem-solving guide, I
think it still is a very useful technique to teach. Once I began
telling students to make sure their "new loops" contain a new component,
and they can quit looking for loops once every circuit component is
included in a loop, the students' circuit analysis made a dramatic
improvement, and their attitude toward these problems also made a
dramatic improvement.
Prior to my use of this technique, students were wasting a lot of time
coming up with "new equations" that were not independent, and they grew
bitter because they didn't have a clue how to determine if a new loop
was likely to yield an independent equation. That made them think
circuit analysis was mostly luck and/or magic.
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