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Re: [Phys-L] big circuit

Here are a few points that people seem to be missing.

1) The video mentioned problems with early transatlantic
communication cables. However, it didn't really explain
the problem, didn't quantify the problem, and didn't say
how the problem was overcome.

The short answer is that in addition to problems like
gross short circuits that had obvious solutions, there
were some subtler problems, including dispersion. Hint:
It was mentioned that the cable could be operated "slowly".

Details here:

Early solution:

In the introductory class it is traditional to assume that
every wave equation is non-dispersive, but in reality lots
of things are dispersive. Ocean waves are dispersive. Even
ripple tank waves are dispersive. Gravitational waves are
dispersive. The Schrödinger wave equation is dispersive.

Intoning the words "Poynting vector" will not make the
dispersion go away.

2) The "big circuit" experiment is underspecified. In order
to proceed, we must make assumptions. I assume the circuit
is made of copper wire with a generous 1 cm² cross section.
Plugging in the length of the wire, the resistivity of the
copper, and the impedance of the twin-lead transmission line,
I estimate that the signal will be attenuated by a factor
of exp(-100) or so. That's a lot.

Details here:

especially the part where it says
signal strength will decay over distance as exp(− α x)
3) Even if we assume perfect zero-resistivity wires, there
are still causality issues.
— The voltage source is not clearly specified, but it
looks like a car battery, so I assume the output
impedance is much less than 1 Ω.
— The light bulb was not clearly specified, but I assume
it resembles a car headlight, with an impedance of 2 Ω
or so.
— The geometry of the twin-lead transmission line is not
clearly specified, but I assume the impedance Z is somewhere
in the neighborhood of 377 Ω (the impedance of the vacuum).

The details are not important. Ballpark estimates suffice.
Here is the sequence of events:

a) Since the battery impedance is small compared to Z, the
battery clamps the waveguide voltage to the battery
voltage, almost.

b) Some time later, the pulse arrives at the light bulb.
Since the bulb impedance is small, it clamps the waveguide
voltage to zero, almost. This causes a tremendous reflected

c) Some time later, the reflected pulse arrives at the
battery. The battery says oh-no-you-don't and shorts the
signal back up to the battery voltage, almost. This sends
a re-reflected signal into the waveguide.

*) Over the course of N round trips, the voltage settles
exponentially to the steady-state voltage.

I think of this as "shuttle diplomacy". The two principals
are talking to a third party (the waveguide) instead of
talking directly to each other. The shuttle has to make
N round trips to reach agreement.

Let's be clear: the time it takes for the light bulb to
come on is N times the speed-of-light round-trip time.

Bottom line: In the video, all the options on the multiple-
guess question are wrong. By a lot. For multiple reasons.
Quantitatively wrong as well as conceptually wrong.

Appendix: Funny(?) story:
Back when I was a sorcerer's apprentice I built a circuit
that failed for physics reasons. The first model worked
OK. For the second model, I wired up twice as much memory
capacity, and it failed miserably. It took me a while
to figure out that the address bus and the data bus
were acting like unterminated transmission lines.
To fix it I had to add termination resistors to every
single bus line, which was a pain. Also I had to
replace all the memory chips, because the reflections
caused an overvoltage that damaged the chips.

You may say "Well, duh" ... but it wasn't so obvious
at the time. I had formed the habit of wiring up chips
and expecting them to just work. I got complacent. I
treated the chips as well-behaved black boxes. I did
electronics with one part of my brain and physics
with another part. I'm not proud of this, but it's
what happened. I swore it would never happen again.

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