Re: kirchoff's rules and linear dependence

[STRatliff@NWC.EDU]

In response to:

> I would like to talk to the students about this tomorrow but
> a)  I can't convince myself why the three loop rule equations are not
linearly >independent

Consider a circuit with a left-hand loop, a right-hand loop, and an outer
loop.  If you were to draw it out it would look like two boxes side by
side.  Each loop will give an equation.  However you only have two
linearly independent equations, as you pointed out.  Consider the
situation physically.  The sum of the right-hand loop and the left-hand
loop is the same as the larger, outer loop.  The two smaller loops have
currents that go in opposite directions along the common center section.
This is why you don't get three independent equations.  I hope that this
helps.





Steven T. Ratliff
Professor of Physics
Northwestern College
3003 Snelling Ave. N.
St. Paul,  MN     55113-1598
U. S. A.

Internet:  stratliff@nwc.edu