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



On 08/27/2015 11:31 AM, Diego Saravia wrote:

I agree that you will not operate a lot off
times directly with k laws.

OK. That was my main point.

is not obious to erase them from the
framework of thought.

I'm not saying you have to entirely erase them from your
thoughts. (I'm not saying anybody has to do anything.)

However, often the way /you/ think about it differs from
the way /students/ think about it, especially on first
exposure. See below for more on this.

It seems to me that the range of usefulness of
Kirchhoff's «laws» is getting squeezed from both sides.
It is getting squeezed from below by things that are
more convenient, and squeezed from above by things that
are more reliable. In particular, when I'm doing it,
a direct appeal to conservation of charge strikes me as
simultaneously easier /and/ more reliable than a two-step
process that derives Kirchhoff's «laws» and then applies
them.

But how can you deduce the parallel fórmula without asuming that node
dont hace self capacitance?

Beware that I'm arguing three different sides of the
argument:
1a) Bad: squeezed from below
1b) Bad: squeezed from above
2) Not so bad: Kirchhoff's «laws» have "some" value;
otherwise they never would have been mentioned,
and we wouldn't be having this conversation.
I'm not taking an extreme position. As usual,
all the extremes are wrong.

In any case: You don't have to /derive/ the parallel and
series formulas at all.
By way of analogy, early in the introductory course, it
is standard practice to introduce the gravitational law
F=mg as a thing unto itself. As an expert, *you* could
derive it from the law of universal gravitation +
centrifugal force + some sort of model of the figure of
the earth etc. etc. etc.... but on first exposure, the
students don't need to see the derivation. My point
is: A bogus derivation, simply setting mg = GMm/r^2,
strikes me as worse than no derivation at all.

The fact is, /if/ you decide to derive the parallel-impedance
formula and/or the Kirchoff node «law», you need to make
a boatload of assumptions. For example, in the case of
a battery, it is conventional to model it as a capacitor
where the mutual capacitance is infinite and the self-
capacitance is zero.

I guess what I'm saying is that if-and-when I want to
derive something -- other things being equal -- I prefer
to see all the assumptions on center stage, not wrapped
up in some opaque bundle called such-and-such «law».
The opacity all-too-often hides the fact that the «law»
was wrongly derived to begin with ... wrongly derived
and then wrongly remembered to boot.

On the other hand, in all fairness, sometimes there
is value in wrapping up what you know into a bundle,
such as F=mg. So there is no issue of principle here.
We're just haggling over the price. In that spirit, I
find F=mg to be worth the trouble in ways that Kirchhoff's
«laws» are not. It's just too easy to directly apply
the more-fundamental laws, such as conservation of charge
or voltage = flux dot.

I mentioned the assumption about zero self-capacitance
because it is the one most often neglected in discussions
of the topic. Without it, no derivation is possible.

-----------------------------------

On 08/27/2015 01:53 PM, Richard Tarara wrote:

For the bio and pre-med courses, the problem with dropping Kirchoff
is that the MCAT test (the main reason these students take physics)
likes to include at least some simple K-problems.

Correct me if I'm overlooking something, but the MCAT examples
I've seen can be solved by practical, sensible methods such
as series/parallel reduction, with no need for Kirchhoff's
«laws» ... so (for once) I'm not seeing any trouble with the
MCAT, narrowly speaking.
http://www.varsitytutors.com/mcat_physical-help/electricity-and-magnetism/zphysics/circuits

OTOH if there really are MCAT questions that require rote
regurgitation of scripture, or require direct application of
Kirchhoff's «laws» to the exclusion of other methods, that's
trouble. Do you know of any such?

That kind of trouble is certainly a possibility to watch
out for: On 08/27/2015 01:32 PM, Philip Keller wrote:

JD won't like this, but one of the things that the AP people want
students to parrot back is that the node law is based on conservation
of charge and the loop law is based on conservation of energy.

SsSsSsSsSsSsSsSsSsSsSsSsSsSsSsSsSsSsSsSsSsSsSsSs
(The sound of steam coming out of my ears.)

++ I like conservation of charge.
++ I like conservation of energy.
++ I like parrots, when they're birds.
-- I don't like parrots, when they're selling mandatory tests.
-- The oft-repeated claim that Kirchhoff's «laws» are equally as
valid as conservation of charge and energy really offends me.
Anybody with a brain bigger than a lorikeet's knows it's not
true. Anybody who knows what an electrical transformer is
knows it's not true. Anybody who has the slightest idea what
a "ground loop" is knows it's not true. Anybody who has the
slightest idea what the Maxwell equations are saying knows
it's not true.

Over-reliance on these $#!+ tests is destroying the educational system.