John D. wrote:
|Similarly the words are technically correct because they
|mention the "Q" plate ... but they are perhaps open to
|misinterpretation because they also mention the plate
|"with the positive charge".
Nowhere do I mention the plate "with the positive charge"
John D. also wrote:
|Bob's diagrams neither disclose nor solve the full range of
|notational problems, because all of his examples show positive
|absolute charge on the chosen "Q" plate. . . To say the same thing in
|different words, do *NOT* use a + sign to indicate "Q lives here" |because
Q might be negative.
The + sign does not imply that this plate will be positively charged. The +
and - charge signs merely serve to define the charge configuration to be
represented by a positive value of Q, even though Q can be + or -. This is
the same approach that we use when we draw a directed arrow to define the
direction of a current to be represented by a positive value of i, even
though i can be + or -.
In the general, complex circuit case one does not know ahead of time the
directions of currents or the charge configurations of capacitors. This is
true even in simple, one-loop circuits if one does not yet know the initial
conditions. The equations should be written for the general case: as a
computer algorithm applicable to any and all initial conditions. One
therefore needs a general set of defining conventions for correlating
current directions and capacitor charge configurations with the algebraic
signs of the quantities i and q, respectively.
One safe way to do this is to:
1) For each current, choose (and indicate) a definite direction to be
represented by a positive value of the signed variable i(t).
2) For each capacitor, choose (and indicate) one of its two plates to be
that whose absolute charge is represented by the (signed) value of a
variable q(t). The other plate of this capacitor will carry the absolute
charge - q(t).
All of these choices are completely arbitrary. However, once chosen, they
will force one or the other of the relations i=dq/dt or i=-dq/dt in the
wires directly connected to each capacitor.
Bob Sciamanda
Physics, Edinboro Univ of PA (Em) http://www.winbeam.com/~trebor/
trebor@winbeam.com
----- Original Message -----
From: "John Denker" <jsd@av8n.com>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Sunday, February 19, 2006 8:13 PM
Subject: Re: [Phys-l] RC Discharge
|I am worried about recent references to the capacitor plate
| "with the positive charge".
|
| The diagrams Bob posted at
| http://www.winbeam.com/~trebor/RC%20discharge.jpg
| are absolutely correct because he labels the "Q" plate.
|
| Similarly the words are technically correct because they
| mention the "Q" plate ... but they are perhaps open to
| misinterpretation because they also mention the plate
| "with the positive charge".
|
| The problem is that "positive charge" means something very
| specific in electrostatics, and identifying something as
| positively charged is nowhere near synonymous with identifying
| it as the plate on which the capacitor's nominal charge is
| stored.
|
| Electrical engineers don't bother to label one of the plates
| with a "Q" as Bob has done. Instead they just choose a direction
| and speak about the voltage drop across the capacitor in the
| chosen direction, and the current flowing in the chosen
| direction.
|
| In the fairly-common case where one terminal of the capacitor
| is tied to ground (or at least AC ground), the other terminal
| obviously becomes "the" terminal of interest. In this case
| (and not otherwise) it is unambiguous to talk about current
| flowing into (or out of) "the" capacitor.
|
| More generally, it is necessary to speak of current flowing
| into (or out of) a particular specified leg of the capacitor.
|
| Bob's diagrams neither disclose nor solve the full range of
| notational problems, because all of his examples show positive
| absolute charge on the chosen "Q" plate.
|
| It must be emphasized that in the context of capacitors, + and -
| undoubtedly refer to absolute charge, not to what happens if
| you draw charge out of "the" capacitor. This is important in
| connection with electrolytic capacitors. If you get it wrong,
| the capacitor won't work, and it might explode. Guess how I
| know.
|
| Suppose I take 1 milliamp out of terminal "A" of a 1 microfarad
| capacitor for 1 millisecond. Then the voltage across the
| capacitor (V := V_A - V_B) will decrease by one volt during
| that time. Note that I did not say anything about whether
| plate "A" was positively charged at the beginning only, at
| the end, or neither.
|
| To say the same thing in different words, do *NOT* use a +
| sign to indicate "Q lives here" because Q might be negative.
| Instead, it is permissible (but unconventional) to use an
| explicit "Q" as Bob has done ... and it is more conventional
| to just pick one of the leads and label it as to current-in
| or current-out.
|
| Michael Edmiston wrote:
|
| >> If we agree that Bob's analysis of his third circuit is correct, then
| >> the Serway/Jewitt analysis would certainly seem incorrect. Can anyone
| >> look at Bob's third diagram and legitimize the Serway/Jewitt analysis?
|
| I can, as follows:
|
| Consider the + and - markings on the capacitor as _obiter dicta_ since
| they don't have any real bearing on what follows. This is a linear
| circuit, and the polarity of the initial charge doesn't really matter.
| That is, I am assuming a non-polar (non-electrolytic) capacitor.
| This is an entirely appropriate simplification for beginning students.
|
| Tie the bottom of the diagram to ground. This is consistent (in the
| weak sense) with standard practice when drawing circuit diagrams ...
| i.e. not necessary, but common and completely unsurprising.
|
| At this point our diagram is the same as Bob's #3, except that the Q
| symbol has migrated to the top plate. Equivalently it is the same
| as #2 except that the capacitor was initially charged to a negative
| voltage with respect to ground, so that we need to reverse the + and -
| signs in #2 (or erase them completely, since they don't matter to
| what follows).
|
| Note that the current arrow into the top terminal of the capacitor is
| consistent with the foregoing decisions, and consistent with conventional
| notions of current "into" the capacitor.
|
| This is consistent with Tim's notion of charge on the *"upper"* plate on
| the capacitor ... but diametrically opposite to his choice of I being
| the current *"out"* of the upper plate.
|
| At this point, the equations are identical to Bob's equations for case #2.
|
| I still haven't seen Serway's diagram, so I won't comment on whether
| there might be ways of improving it. But I see no evidence that it
| is provably wrong, or inconsistent with his equations.
|
| ====================================================
|
| I find Tim's suggestions to be a major step in the right direction:
|
| > Let's explicitly write
| > q(U) = Net charge on upper plate
| > I = current out of the upper plate
| > dq(U) = change in the charge of the upper plate in time dt.
| > dq(W) = charge moving past a point in the wire in the positive
direction in time dt
|
| However, they don't go quite far enough. We still need a labelled
| diagram in order to define what is "the positive direction" in the
| wire.
|
| Furthermore, although the ideas are sound and are adequate for the
| ultra-simple circuit being discussed in this thread, stronger methods
| are needed for more-complex circuits.
|
| Therefore I (yet again) recommend DRAWING THE DIAGRAM and labelling
| the things you care about ... not just the components, but the
| current and voltage variables you intend to use in your equations.
|
| This upholds the cherished principle of mean what you say, and say
| what you mean.
|
| If you want (I) to be the "current out of the upper plate", just draw
| a little arrow on the wire coming out of the upper plate and label
| it (I). Then we know what (I) is, and we no longer even need to know
| what is the "upper plate" ... indeed we can rotate to the capacitor
| so that it doesn't even have an upper plate.
|
|
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