Re: [Phys-l] RC Disharge Analysis

[John Denker <jsd@av8n.com>]

Michael Edmiston wrote:

> I still maintain that if you apply the loop theorem correctly, you must 
> choose i = -dq/dt for this problem, and that bugs students.

That's what separates fundamentalists from physicists.

-- Fundamentalists see i = dq/dt in a yellow box in the Book,
  and they assume it must be literally, eternally, and universally
  true.  They memorize the formula, not what it means.
++ Physicists don't need to memorize the formula.  The learn the
  meaning of a few physics principles.  The formula i = dq/dt
  is an obvious consequence of conservation of charge.
  Similarly i = -dq/dt is an equally obvious consequence of the
  same principle, if the charge is flowing the other way.

Similar remarks apply to the sign of V = ± I R.  The sign is nontrivial,
and depends either on how you choose the polarity of the terminals and
the direction of the current.  There are conventions on this, but the
conventions are non-binding.  If you apply even the teensiest bit of
physics understanding, you don't need to memorize the conventions;
positive power dissipation demands that the direction of forward
current correspond to the direction of voltage _drop_.

As I said in my previous note, it's not magic, it's not willy-nilly,
it's just physics.

We can agree that it's often not explained well in the texts.  I'll
say more about that in a later message.

Also let me re-re-reemphasize the importance of drawing the diagram.
Arguing about the "literal" interpretation of the formulas is just
playing the fundamentalist game.  Drawing the diagrams is usually
the easiest way to assign _meaning_ to the quantities of interest.

And I don't mean just a diagram showing the components;  it is vital
to assign meaning to the _variables_ by showing what they mean on
the diagram.  This includes showing what the voltages are measured
relative to (notice the ground symbol on my the diagrams I provided
yesterday) and it also includes showing the location and direction
of the currents (notice the >>> tag on each diagram).
   https://carnot.physics.buffalo.edu/archives/2006/02_2006/msg00362.html
   https://carnot.physics.buffalo.edu/archives/2006/02_2006/msg00363.html

===========

I wish I got paid a dollar every time I told a kid not to memorize the
form of a formula, but rather to learn the meaning behind the formula.
The latter is a far better foundation for further learning, i.e. it
generalizes far better to new situations.

BTW the distinction is easy to check for by asking questions and seeing
what type of mistakes are made.
 -- The fundamentalists tend to make "typographic" mistakes in the form
  of the formula;  for instance I = V/R looks about the same as I = R/V
  to them.
 ++ Physicists tend to make a whole different type of mistakes;  they
  tend to get "close" in the sense that the dimensions are right and
  the scaling laws are satisfied, but they blow off factors of two and
  factors of pi.

Once upon a time when I was a junior I had an oral final exam in general
relativity.
  (The fact that I was even *in* the course is a funny story;  it was a
  graduate-level course and I didn't have any of the prerequisites, but
  it was reputed to be a reeeally good course and it was only taught
  during even-numbered years, so I signed up.)

The exam was at 8:00am.  I was really tired, having stayed up all night
printing 1.2 million sweepstakes entries.  The professor began by asking
what I would like to be examined on.  I said "Huh?".  He said "everybody
gets to choose the topic of their exam;  if you'd been to class recently
you'd know that."  Oh.  "So tell me, what do you find most interesting
about the course?"  I replied that I found the recent discussion of
symmetries and Killing vectors to be deeply fascinating, but not suitable
for an exam because I didn't really understand it.  He said he found it
confusing also.  (I couldn't help suspecting he was confused on a much
higher plane than I was.)  At this point I decided the topic should be
gravitational waves and mechanical detectors.

After getting the first two questions completely and categorically wrong,
the third question went like this:  "Suppose a little green man on Mars
is shaking his fist.  Calculate the intensity of the resulting gravitational
waves received on earth."

I knew there was a formula for that, but I couldn't remember it.  I also
supposed any other student in the class could work out the formula by
analogy to the electromagnetic radiation formula ... but I didn't remember
that, either.  So I noodled out the formula by applying a series of scaling
laws and symmetry arguments, and then threw in a factor of c^5 to make the
units come out right.

At that point the professor said "you forgot this factor of two" and reached
over my shoulder and corrected the formula I was working on.  Then he smiled
and told me the exam was over.

I got a better grade in that course than I was expecting;  I figured the
professor felt that somebody who could work out the radiation formula
from general principles wasn't all bad.  Later I came to realize that he
undoubtedly _preferred_ it that way ... preferred it to memorizing the
form of the formula without understanding why it had to be that way.