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Re: [Phys-L] circuit analysis : a simpler approach?




John makes excellent points here. Particularly, in our algebra-based physics
courses, Kirchoff's circuit analysis is of little conceptual use or practical
use to students. However, a textbook author would find it difficult to get
many adoptions of his/her book because the majority of teachers will continue
to do what they have always done.




Once upon a time, somebody gave me a wooden tricycle,
made entirely of toothpicks and crazy glue. Alas,
the thing is not very practical. Consider the various
use-cases:
*) If I want to get from here to the bathroom, it's
easier to just walk. I don't need a tricycle at all.
*) If I want to get from here to the grocery store,
it's more practical to ride my bike. Riding a
bike requires more skill and strength than riding
a tricycle ... but I can manage it. The bike
outperforms even the best tricycle by some huge
factor.
*) In the exceedingly rare situations where I might
actually want a tricycle, the wooden thing is no
good; if I actually sat on it, it would collapse.

I mention this because it seems to me that Kirchhoff's
circuit «laws» are pretty much like a wooden tricycle.
Maybe I'm exaggerating a little, but not as much as
you might initially think. Let me explain:

In my experience, in the last 1000 situations where
Kirchoff's «laws» might apply:
*) About 900 of those cases could be solved more
easily just using Ohm's law for impedances in series
and impedances in parallel. This is as easy as
walking to the bathroom. You don't need Kirchhoff's
«laws».
*) In the remaining 100 cases, you can't use series
/ parallel reduction, because of some messy mesh
structure.
-- However, in 96 of those cases, you can't use
Kirchhoff's «laws» either, because they would get
the wrong answer.
-- A couple of cases such as the Y-Δ transformation
can be solved by appeal to linearity.
-- Otherwise, mostly you wind up using relaxation
methods rather than closed-form solutions.
-- Maybe I'm overlooking something, but the only
cases where I can remember actually using Kirchoff's
«laws» are contrived end-of-chapter exercises, not
real-world situations.

Kirchhoff's laws appeal more to physics teachers than
they do to electrical engineers ... and even that is being
generous. Paul Horowitz is a card-carrying physicist, yet
the esteemed Horowitz and Hill text drops Kirchhoff's name
in passing on page 3 and never mentions it again.

I reckon that teaching Kirchhoff's «laws» ... especially
if they are touted as /laws/ ... is more likely to spread
misconceptions than anything else.

Real-world engineers think in terms of impedances in
series and impedances in parallel -- even in situations
where Kirchhoff's laws «laws» do not apply. They handle
the latter by sticking in notional "parasitic impedances"
to account for the stray current and/or stray voltage.
Reference: any of Morrison's books.

The students who are EE majors have essentially zero need
for Kirchhoff's «laws», and the others have even less.

All too often, people suggest «reforms» that make life
more complicated for teachers and students. In contrast,
this seems like a golden opportunity to make things simpler
and better.

So I leave it as a question, partly rhetorical but partly
not: In the introductory physics course, why do we give
Kirchhoff's «laws» even one minute of class time, or even
one inch of space in the textbooks? Why not skip it and
go directly to impedances in parallel and impedances in
series?
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