Re: kirchoff's rules and linear dependence

[Bernard Cleyet <anngeorg@PACBELL.NET>]

I'm late to this, but ...

Could one not write all the eqs. (except ones the student sees as
obviously not independent),  put in determinant form, and solve;  then
as necessary remove serially one 'till it doesn't go tilt.  In the
unlikely event there are TWO dependent eqs. it'll just take longer.  The
computer lit. ones could write a program to do this iteration.

I think most of this isn't about Physics, but math.

bc

Michael Edmiston wrote:

> 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