The reason I described a specific way to draw the circuit is because I
am criticizing a particular textbook. But in reality there is only one
way to draw the circuit (capacitor, resistor, switch, all in a single
loop). Whether the capacitor is on the left, right, top, bottom doesn't
matter. Likewise for the resistor and switch. The only circuit
analysis difference comes when you state which capacitor plate is
positive, and that determines whether the current through the resistor
will be headed in a clockwise sense around the loop or in a
counterclockwise sense around the loop.
Once you state which plate is positive, and from that determine which
way the current goes through the resistor, you can apply the loop
theorem. You can navigate your loop in the same direction as the
current through the resistor and get -IV + q/C = 0 or you go the
opposite direction and get IV-q/C = 0. In either case, when writing the
loop equation in this manner (zero on one side, voltages on the other
side) the signs of IV and q/C must be different. But Serway/Jewitt
has -q/C-IV = 0. That just seems wrong.
The reason I say current is defined as I = dq/dt is because that is the
way every textbook on my shelf defines it, generally inside a
yellow-highlighted box. Indeed, the next step in Serway/Jewitt is to
remind the student that I = dq/dt.
I have often exclaimed my frustration that students don't read the
textbook, and others on this list have stated the same frustration.
However, often the students can fight back by saying they have read the
textbook and it didn't make any sense.... and I have to agree with them.
Indeed, the reason why I created this thread is because my son (who is
using Serway/Jewitt at a different institution than where I teach)
called me Saturday afternoon and asked me to turn to page 876 in
Serway/Jewitt and see if I thought equation 28.16 was correct. I do not
think it is correct. Bob LaMontagne has looked at Serway/Jewitt and he
also agrees equation 28.16 has a problem. In the case of Serway/Jewitt
I think it is just an outright error in the application of the loop
theorem.... but they still get the right answer by using I = dq/dt
rather than I = -dq/dt.
On the other hand, the book I am using (Tipler/Mosca) gets the loop
theorem correct, but then uses I = -dq/dt and *my* students complain
about that. They say, "That's not how current is defined in equation
26-1" and they are correct. Tipler/Mosca says "Electric current is
defined as the rate of flow of electric charge through a cross-sectional
area." But then in the capacitor section Tipler/Mosca says "the current
is the rate of decrease of [the capacitor plate] charge." Students who
read the book say, "Which is it? Is current the rate of flow of charge
through a cross-sectional area, or is it an increase/decrease of charge
on a capacitor plate?
John Denker is correct that this one manifestation of the plug-and-chug
mentality of the students. But I give them some sympathy on this one.
Getting the plus/minus signs correct in circuit analysis is crucial, and
students view it as something not learnable because it appears the
professor and the textbook change definitions or conventions willy-nilly
to get the right answer. That is, they don't understand how we know a
sign has to be changed. If current is the rate of flow of electric
charge through a cross sectional area, and is written as I = dq/dt, how
do we know that sometimes this must be written as I = -dq/dt?
Along similar lines to what Bob M said, the substitution of I = -dq/dt
is being done in the resistor term, not the capacitor term. So why do
we need to look at the capacitor to determine a plus/minus sign on the
basis of its charge increasing or decreasing when the dq/dt is being
substituted for I in the IV portion (the resistor portion) of the
analysis? That's where the students are coming from.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu