Re: [Phys-l] RC Disharge Analysis

[Jack Uretsky <jlu@hep.anl.gov>]

Hi all-
	The point that everyone seems to be missing is that the direction 
of I is determined by the fact that Q is a conserved quantity, and I is 
the flow of Q.  The choice is whether I is the outward flow or the inward 
flow from the region where Q is accumulated.  Given any conserved 
quantity, call it K, in a region, there is an expression of the 
conservation dK/dt+F=0, where F is the outward flow of "stuff" from the 
region.  In the electrical case we must choose F so that the net voltage 
around the circuit vanishes, and the voltage drop along a resistor is in 
the direction of flow of F.  You check for consistency in an RC circuit
by replacing the capacitor with a battery having the same polarity, and 
insisting that the current direction from the battery is the same as the 
initial current from the charged capacitor.
					Regards,
						Jack



On Sun, 19 Feb 2006, Bob Sciamanda wrote:

> I might have added that it follows from the choice 1) that there is a
> potential DROP of V = iR across the resistor in the direction chosen for
> positive i.  Likewise, it follows from the choice 2) that there is a
> potential DROP of V = q/C from the capacitor plate chosen in 2) to carry q,
> to the other capacitor plate.   These signed potential differences must be
> heeded in writing the loop equation.
>
> I also add that in making the choices 1) and 2) you are NOT forecasting the
> direction of i, or the sign of q; you are simply DEFINING the meaning
> (including sign) of these quantities.  Properly written loop equations will
> be valid whatever circumstances dictate to be the actual signs of these
> quantities.
> Bob Sciamanda
> Physics, Edinboro Univ of PA (Em)
> http://www.winbeam.com/~trebor/
> trebor@winbeam.com
> ----- Original Message -----
> From: "Bob Sciamanda" <trebor@winbeam.com>
> To: "PHYS-L Maillist" <phys-l@carnot.physics.buffalo.edu>
> Sent: Sunday, February 19, 2006 9:04 AM
> Subject: Re: [Phys-l] RC Disharge Analysis
>
>
> | One must always DEFINE the positive sense of all signed quantities and
> stick
> | with those definitions in writing equation models and in interpreting
> | results of calculations.  Just as this applies to coordinates (eg: x,y,z)
> in
> | kinematics, it applies no less in this capacitor discharge situation:
> |
> | 1) One must specify the positive direction of the current i. You may
> choose
> | either direction as positive;
> | 2) One must specify which capacitor plate carries the signed quantity q.
> | You may choose either plate for this purpose; the other plate then carries
> | the charge (-q).
> | If you are faithful to your specifications, and interpret your results
> | accordingly, you may then traverse the circuit in either direction and
> your
> | "loop theorem" statement will be valid.
> |
> | Note if one chooses positive i in 1) to be the direction INTO the
> capacitor
> | plate chosen to carry q in 2), then it follows that i = dq/dt.  If instead
> | one chooses positive i in 1) to be the direction OUT OF the capacitor
> plate
> | chosen to carry q in 2), then it follows that i = - dq/dt.
> |
> | Note here the unspoken convention that the positive direction of i refers
> to
> | the flow of POSITIVE charge carriers.
> |
> | Bob Sciamanda
> | Physics, Edinboro Univ of PA (Em)
> | http://www.winbeam.com/~trebor/
> | trebor@winbeam.com
>
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