My initial reaction to Jim Frysingers's post is he using a sound
approach.
After Denker said that my method is not 100% reliable, he suggested
using the loop theorem on the smallest loops and keep doing that until
all small loops are finished. This is also what Frysinger is stating.
I think my method of requiring that "new loops" each contain a new
component is roughly the same thing. When you go to the next small loop
you typically add at least one new component.
I did think of a situation where the two methods would yield different
advice, but I have not taken the time to see which is correct. Draw a
3-by-3 array of squares. Imagine that each line segment contains a
resistor or some other circuit element. If you come up with a loop
equation for each of the small squares you will come up with 9
equations. My method would say one of these is not linearly
independent. After getting loop equations for the 8 perimeter squares,
every component in the inner square has been included in a loop.
I am sorry to say that I do not have the time or energy to analyze this
further in the next day or so.
One thing I don't like about the small loop method is the possibility
students might think the loop theorem only applies to these small loops.
Take two squares joined along a side. Yes, you can use the loop theorem
on each small loop and then it would be redundant to use it on the big
perimeter loop. But you can also use the loop theorem on the big
perimeter loop then either one (but not both) of the small loops. The
"new component" method does not contain a bias against using big loops.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu