Malcolm wrote:
Ummm,
On Fri, 2008-09-12 at 15:36 -0005, M. G. Devour wrote:
Dear Neville,
You write:
[The actual linear velocity of the electrons within the wire is
proportional to the current: Zero with the switch off, and limited by
ohm's law, ie. total circuit resistance and voltage, when on.]
As a simple example...the higher the current, the quicker the 'flow',
(forgetting ohms law for the moment)... yes?
The higher the voltage or lower the resistance, then yes, the current
will be higher, which means the electrons are moving faster in the
wire.
well not really, though more of them will be moving in the (roughly)
same direction past a given point; that is, after all, what "Current"
is.
It's not that the electrons run faster from end to end, hence increasing
the current; it's that higher voltage crowds them in more densely: for
yet another very imperfect analogy, more get stuffed into the subway
train, but the train doesn't go any faster, and so more get out at their
destination, per unit of time (hours if you live in New York!)
The number of electrons inside a wire is constant, and independent of
any voltage on the wire, it will be equal to the number of protons in
the nucleus, always. Now if you put high voltage on a wire, the number
of electrons on the surface will vary due to the capacitance effects on
the surface, but this is trivial compared to the number of electrons
inside the wire. If what you were saying were true, then applying a
positive voltage to a wire that is grounded would result in a reduction
of current as the voltage is increased, since that would result in fewer
electrons in the wire. Ohms law is correct whether the wire has a
positive voltage or negative voltage on it since the voltage on a wire
has no effect on the number of carriers inside the wire. It only
affects their average velocity. Think in terms of a pipe with water.
Adding pressure does not change the amount of water in the pipe, except
by any little amount the pipe stretches, but adding pressure drop from
one end of the pipe to the other changes the velocity of the water in
the pipe, thus the flow increases. Voltage equals pressure, current
equals flow.
It is actually pretty simply to do the math. An electron experiences a
pull when in an electric field. This pull is the vector product of the
voltage gradient and the charge on the electron. The electron
experiences an acceleration which is mathematically equal to this force
divided by the mass of the electron. However before it has gone far, it
bumps into an atom, and loses it's velocity, and the kinetic energy is
converted to heat. This is what give wire resistance. Now if you can
couple the electrons together into pairs, they can actually flow without
bumping into the atoms, and that is how a superconductor, which has no
resistance, works.
Marshall
Marshall
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