Re: [Phys-l] RC Disharge Analysis

[John Denker <jsd@av8n.com>]

Michael Edmiston wrote:
> 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.

That is just plain false as stated.  I'll let you choose which plate
of the capacitor is positive.  I'll bet you $1000 I can draw two
different diagrams, one of which has the discharge current flowing
clockwise, and one of which has it flowing counterclockwise.

> 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.  

That embodies the same wrong idea.

> 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.  

I very much doubt I can get either of those equations from the
loop law.  Using the near-universal terminology, I*V is power,
while q/C is voltage.  I assume IV is a typo for IR.

> 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.

It is entirely within the reasonable envelope, although it is
not the _only_ way of doing it.

> 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.

Seeing it in a yellow box does not relieve you of the responsibility
to know what it _means_.

> 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.

I can sympathize with that!

> 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.  

I agree that there are changeable conventions, and I agree that
the changes might _appear_ to be willy-nilly, but actually the
changes are well-founded ... just hard to explain, and often not
explained well.

> That is, they don't understand how we know a 
> sign has to be changed. 

If you try to express things in terms of "the" current in "the"
circuit, you will run afoul of conflicting conventions.  There
are two solutions to this:
  *) Experts know this instinctively and use unconventional
   directions of current flow sometimes ... remembering to
   stick a minus sign into the associated equation.  The
   rationale for this is hard to explain to non-experts, but
   the procedure is rigorously correct, if done right.  If
   the equation for current _into_ a capacitor has a plus sign,
   the equation for current _out of_ a capacitor will have a
   minus sign.  It's not magic, it's not willy-nilly;  it's just
   physics.  You have to know what the equation _means_.
  *) The other procedure is more tedious, but is more transparent
   to non-experts, and is used even by experts when the circuits
   become more complex.  That is to systematically write lots of
   different current variables
     I1 = current _into_ the top of the capacitor
     I2 = current _into_ the top of the resistor
     et cetera
    and systematically determine the relationships between the
    various variables.  Using blissful ignorance to set them
    all equal is not recommended.