Re: RC circuit and oscilloscopes

[William Beaty <billb@ESKIMO.COM>]

On Thu, 13 May 1999, Yanai Krutman wrote:

> Anybody has a way to explain to first year students ( only mech
> theory they have ), how a capacitor is charged and discharged,
> in terms of I(t) or Q(t)??
> I need to talk on this may be 5 min!?
> Suggestions are wellcome.

Here is an analogy which helped me immensely:

               _________
            _ /   | |   \ _
          /  _____| |_____  \
       /    /     | |     \    \     THICK IRON SPHERE, RUBBER WALL
      |   |       | |       |   |    DOWN THE MIDDLE, BOTH SIDES FULL
     |  |         | |         |  |   OF WATER, w/CONNECTING HOSES
     |  |         | |         |  |
      |   |       | |       |   |
        \// \_____| |_____/ \\/
       //\ _      | |      _ /\\
  ___//      \____|_|____/      \\____
  ----                            ----

When water is injected into the above device through one hose, an equal
amount of water is forced out through the other hose.  Yet the rubber wall
prevents any water from flowing through this "capacitor".

In a real capacitor, the path for current SEEMS to be through the device,
and charge SEEMS to flow through it.  As an engineer, I treat capacitors
as special kinds of conductors; where the potential difference across the
device depends on how much charge has been forced to flow THROUGH it.  Or
conversely, the amount of charge flowing through the capacitor depends
on how fast we are forcing the potential difference to change.

No charges actually flow through a capacitor, even though an ammeter
appears to show that they do.  If one bit of charge is placed on one plate
of a capacitor, its repulsion force causes an equal bit of charge to flow
out of the other capacitor plate and out of the other terminal.  If the
other terminal is disconnected, then this prevents charges from leaving
the other plate, and this also prevents us us from forcing charges into
the first plate unless we can apply a really large voltage with respect
to some external "ground." (large = many KVolts).

To get a "feel" for this phenomena, refer to the water analogy above.  If
we try to force some water in through one hose, this causes the rubber
wall to bend, and it immediately forces an equal amount of water out
through the other hose.  If that other hose is blocked, then we won't be
able to force any water into the first hose unless we can apply a really
immense pressure.

The two volumes of water are directly coupled together because they are
enclosed within a solid tank, and they can "feel" each other via the
flexible wall.  Capacitors are similar.  We could say it like this:
capacitor plates don't behave as individual charged objects, instead they
are electrically coupled together very "solidly."  This is also similar to
the near-100% coupling between the primary and secondary coils of a power
transformer.


How does this analogy work in terms of voltage and capacitance?  Well, if
the rubber wall took the form of a thin membrane, then that device would
be analogous to a LARGE capacitance.  With a thin membrane, it only takes
a small change in voltage to drive a fairly large current through the
device, and the "capacitor" behaves almost like a conductor.  If the
rubber wall was inches thick of hard rubber, that would be equivalent to a
SMALL capacitance.  It would take a huge voltage change to drive even a
tiny flow of charge "through" the device, and the capacitor behaves almost
like an insulator.


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William J. Beaty                                  SCIENCE HOBBYIST website
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