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Re: [Phys-l] RC Disharge Analysis



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