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.
- REVIEW:
- In an electric circuit, the effects of
electron motion travel approximately at the speed of light, although
electrons within the conductors do not travel anywhere near that
velocity.
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