An interesting question from Veritasium on YouTube

  • #1
Veritasium on YouTube https://www.youtube.com/c/veritasium/community has posted this problem, inviting viewers to say what would happen:
NtduIWUZ7iWg=s1024-c-fcrop64=1,00000000e97dffff-nd.jpg


Is the following answer correct?
In series with the battery, switch and lamp are two transmission lines. At ##t = 0^+##, we will have twice the characteristic impedance ##2Z_0## of the line in series with the lamp. Since the wire spacing is 1 meter, ##2Z_0## would be quite large, which will limit the current and won't let the lamp glow. Once the voltage steps make one round trip (simultaneously) though the left and right lines, the series impedance will drop to zero and the lamp will light up.

But if we replace the lamp with a neon lamp or an LED, and use a high enough voltage, then the lamp would light up instantly because then the ##2Z_0## would be less than the lamp resistance.
 
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  • #2
jbriggs444
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Is the following answer correct?
Coupled lines, I've seen myself. I'd crimped a DB25 onto a 300 foot RS232 cable - shielded 6 strand twisted pair. Keyboard input transmitted out the transmit lead (pin 2) would result in matching characters being received as terminal output (pin 3) despite there being nothing plugged in at the far end and no physical connection between the strands.
 
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  • #3
anorlunda
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But if we replace the lamp with a neon lamp or an LED, and use a high enough voltage, then the lamp would light up instantly because then the 2Z0 would be less than the lamp resistance.
Wouldn't that mean that you can send a signal faster than the speed of light?
 
  • #4
jbriggs444
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Wouldn't that mean that you can send a signal faster than the speed of light?
One assumes that a few nanoseconds to get a field across the one meter air gap counts as "instant".

I'm not smart enough to know whether this thing works like a capacitor or a transformer, but it is clear that the connected ends of the wire 1/2 light year away are irrelevant in the near term.
 
  • #5
anorlunda
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but it is clear that the connected ends of the wire 1/2 light year away are irrelevant in the near term.
Not irrelevant. You need Maxwell's Equations to solve that problem, not circuit analysis.
 
  • #6
Baluncore
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The question is a mares nest, made up of unspecified parameters;

1. The voltage of the battery. It may be 1 V or 1 kV.
2. The impedance of the transmission line. (What diameter are the wires?) 1 m = short circuit.
3. The DC resistance of the very long transmission lines.
4. The cold resistance of bulb B.
5. What is actually meant by “will light up”, a momentary flash, or a continuous dull red glow.

You can get any answer you want by setting different parameters.
 
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  • #7
PeroK
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Is it safe to say that from a practical point of view, a circuit with the dimensions of several light years is impossible?

What if the circuit is of more modest proportions? Doesn't the current flow generally at something short of the speed of light in vacuum?
 
  • #8
Baluncore
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Doesn't the current flow generally at something short of the speed of light in vacuum?
That sub-luminal velocity would be along the transmission line if there was a dielectric insulation rather than only vacuum. vf = √ Er .

The near end of the line will appear to be a small capacitance with ½ m long leads, in parallel with the characteristic impedance of the line. Closing the switch might light the lamp for a couple of nanoseconds.
 
  • #9
PeroK
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That sub-luminal velocity would be along the transmission line if there was a dielectric insulation rather than only vacuum. vf = √ Er .

The near end of the line will appear to be a small capacitance with ½ m long leads, in parallel with the characteristic impedance of the line. Closing the switch might light the lamp for a couple of nanoseconds.
Forgive my ignorance of EE, but isn't that a basic DC circuit diagram?
 
  • #10
Baluncore
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Forgive my ignorance of EE, but isn't that a basic DC circuit diagram?
Not if it has a switch that is flipped every 100 years.
 
  • #11
PeroK
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Not if it has a switch that is flipped every 100 years.
What's this about every hundred years?
 
  • #12
Baluncore
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The turn on transient is clearly an AC signal.
How long ago was the electrical equipment manufactured and turned on for the first time ?
DC is just very low frequency AC.
 
  • #13
PeroK
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The turn on transient is clearly an AC signal.
How long ago was the electrical equipment manufactured and turned on for the first time ?
DC is just very low frequency AC.
I find that post less than enlightening!
 
  • #14
Baluncore
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I find that post less than enlightening!
If you wait for a year, the reflection from the far end of the two short-circuited transmission lines will get back, then the status of the filament in "bulb B" will be illuminating.
 
  • #15
anorlunda
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The question smokes out two principles.
  1. One of the base assumptions of CA (Circuit Analysis) is "The time scales of interest in CA are much larger than the end-to-end propagation delay of electromagnetic waves in the conductors.
    Source https://www.physicsforums.com/insights/circuit-analysis-assumptions/"

    Typical EM propagation speeds in wires is of the order 0.7-0.8 c.

  2. Forget electricity and circuits. Basic relativity tells us that we can't propagate information faster than light. So you can't have a switch that triggers a bulb 0.5 light years away with less than 0.5 years delay. Drawing circuitry in this question is a diversion. The mechanism is irrelevant. Signals can't travel faster than light.
 
  • #16
pbuk
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So you can't have a switch that triggers a bulb 0.5 light years away with less than 0.5 years delay.
The bulb is only 1m away.
 
  • #17
anorlunda
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The bulb is only 1m away.
Not following the path of propagation. Not unless we say that free space radio transmissions cross the 1m to light the bulb.
 
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  • #18
Baluncore
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Drawing circuitry in this question is a diversion. The mechanism is irrelevant. Signals can't travel faster than light.
The input impedance of a transmission line is immediate and not related to the length of the line.
 
  • #19
pbuk
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You can get any answer you want by setting different parameters.
This - so not a very interesting question.

There is obviously some capacitance > 0 between the wires, and the more ideal we make all the components the more likely it is that enough current flows for long enough to light the bulb.
 
  • #20
pbuk
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Not following the path of propagation. Not unless we say that free space radio transmissions cross the 1m to light the bulb.
Your aerial [edit: antenna to some] pair is my capacitor :-p
 
  • #22
PeroK
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Did no one read #2 by @jbriggs444 ????
When I first read it, I just assumed he'd been drinking. Now, I think I understand it.
 
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  • #23
Bandersnatch
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Lol. This thread is an unexpected gold mine of humorous nuggets. Do carry on.
 
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  • #24
Baluncore
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Here is a simulation of lines matched to the global load. For time, treat the seconds as years.
The two 1G0 resistors are needed to satisfy the initial DC bias of the transmission line model.

When V1 first rises to 100 V, the 100 ohm globe receives half current because the circuit resistance is 50+100+50=200 ohms. When the reflection of the short circuit finally gets back, the resistance falls to 0+100+0=100 ohms, so the full current flows from then on.

Lowering the line impedance will brighten the globe initially, but reflections will go on forever.

Verit_plot.png
Verit_schematic.png
 
  • #25
Baluncore
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Here it is with 10 ohm transmission lines and immediate visible light.
Will a filament bulb survive the second year with more than 10% over-voltage ?

Zo=10.png
 

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