My apologies for a typographical error in my late night typing. I
should have known better than to fall asleep, wake up, and make a post
before going back to bed.
Of course when I wrote q/C - IV = 0 for the loop theorem, I had intended
to write q/C - IR = 0. Worse, I typed the wrong thing more than once.
I think John and I are talking past each other on drawing
diagrams/circuits. I am talking about only one circuit; that is, only
one way of organizing the resistor, capacitor, switch in a single-loop
circuit. All ways of constructing the circuit yield either the
identical circuit or the mirror image of the circuit, and the circuit
and mirror-image circuits are analyzed in an identical procedure. John
is talking about the annotated circuit diagram in which the analysis has
already begun (the current direction is noted and +/- signs are placed
on the diagram). I agree there are two conventional ways to draw the
annotated diagram because it is arbitrary which capacitor plate is
chosen as the positive plate.
When you apply the loop theorem to a single loop, you have only two
choices, CW or CCW. I hope we agree on that. And the reason I said you
can apply the loop theorem after choosing the current direction is
because if you apply the loop theorem before choosing the a current
direction you don't know whether there is a voltage increase or decrease
as you traverse the resistor. Assuming we are defining current as
positive charge flow, the loop theorem either yields q/C - IR = 0 or it
yields -q/C + IR depending on which way we navigate the loop. Serway
says -q/R -IR = 0. Can anyone explain how that could be correct? The
only way I can get that is to draw the current through the resistor in a
direction that would result in charging the capacitor rather than
discharging it.
Bob Sciamanda says that properly written loop equations will be valid
whatever the signs. Of course, because a valid loop can be traversed
the opposite direction, or the algebraic equation can have both sides
multiplied by -1.
I still maintain that if you apply the loop theorem correctly, you must
choose i = -dq/dt for this problem, and that bugs students.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu