Circuits and the speed of light
Suppose we had a simple one-battery,
one-lamp circuit controlled by a switch. When the switch is
closed, the lamp immediately lights. When the switch is
opened, the lamp immediately darkens:
Actually, an incandescent lamp takes a short
time for its filament to warm up and emit light after
receiving an electric current of sufficient magnitude to
power it, so the effect is not instant. However, what I'd
like to focus on is the immediacy of the electric current
itself, not the response time of the lamp filament. For all
practical purposes, the effect of switch action is instant
at the lamp's location. Although electrons move through
wires very slowly, the overall effect of electrons pushing
against each other happens at the speed of light
(approximately 186,000 miles per second!).
What would happen, though, if the wires
carrying power to the lamp were 186,000 miles long? Since we
know the effects of electricity do have a finite speed
(albeit very fast), a set of very long wires should
introduce a time delay into the circuit, delaying the
switch's action on the lamp:
Assuming no warm-up time for the lamp
filament, and no resistance along the 372,000 mile length of
both wires, the lamp would light up approximately one second
after the switch closure. Although the construction and
operation of superconducting wires 372,000 miles in length
would pose enormous practical problems, it is theoretically
possible, and so this "thought experiment" is valid. When
the switch is opened again, the lamp will continue to
receive power for one second of time after the switch opens,
then it will de-energize.
One way of envisioning this is to imagine
the electrons within a conductor as rail cars in a train:
linked together with a small amount of "slack" or "play" in
the couplings. When one rail car (electron) begins to move,
it pushes on the one ahead of it and pulls on the one behind
it, but not before the slack is relieved from the couplings.
Thus, motion is transferred from car to car (from electron
to electron) at a maximum velocity limited by the coupling
slack, resulting in a much faster transfer of motion from
the left end of the train (circuit) to the right end than
the actual speed of the cars (electrons):
Another analogy, perhaps more fitting for
the subject of transmission lines, is that of waves in
water. Suppose a flat, wall-shaped object is suddenly moved
horizontally along the surface of water, so as to produce a
wave ahead of it. The wave will travel as water molecules
bump into each other, transferring wave motion along the
water's surface far faster than the water molecules
themselves are actually traveling:
Likewise, electron motion "coupling" travels
approximately at the speed of light, although the electrons
themselves don't move that quickly. In a very long circuit,
this "coupling" speed would become noticeable to a human
observer in the form of a short time delay between switch
action and lamp action.
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