A one light-year circuit of christmas lights

[Jetro]

I have a bit of a puzzle I'm trying to answer.

A K2 civ decides to celebrate Christmas, so they build a circuit of trillions of Christmas lights 1 LY in circumference.

When they flip the on switch, what happens? Do the lights come turn on one after the other in response to the electrical field as it passes each light? Do they turn on all at once one year later when the field has made an entire loop around the circuit? Or do they need two years; one for the electrical field to make a full loop around the circuit, followed by another year for the information that the each light needs to turn on to travel down the circuit?​

 

[Dale]

When they flip the on switch, what happens?

Making the completely absurd assumptions that the fuse doesn’t blow and that all of the bulbs are intact then they will light up starting from the switch as fast as the fields can travel.

 

[fresh_42]

Making the completely absurd assumptions that the fuse doesn’t blow and that all of the bulbs are intact then they will light up starting from the switch as fast as the fields can travel.

I found the question interesting: Do the bulbs glow the moment the circuit is closed (first one after 1 year), the moment the field travels along them (first one suddenly), or after the information of the closed circuit has arrived at each point (all at once after 1 year). In other words: When will the potential difference at a single bulb manifest?

 

[Delta2]

This question is perfect to illustrate the subject of the "secret starting transient state" of every DC or AC circuit. Even in a DC circuit that has only resistors, there is a transient state at the very start from the very moment we close the switch, the current can't instantaneously go to $V/R_{total}$ from 0. It takes some time (which in my opinion is a multiple of the total circuit length divided by the speed of light , so in this case it will be a multiple of 1 LY) for the current to increase to $V/R_{total}$ from zero, though the current starts increasing from the very moment the field passes from there.
So my answer is that each bulb will start glowing from the moment the field passes it, but will reach maximum glow after time that is some multiple of 1LY.

A simple model to analyse the transient state is to view the circuit as having inductance and capacitance due to the huge loop, so it will be an RLC circuit, but I believe a more accurate model is to view it as a huge transmission line, with resistive loads placed in regular intervals inside this transmission line.

 

[256bits]

Do we have a SPST at each terminal of the power source? Say a battery.supplying a DC voltage, of potential E.
When one switch is thrown, nothing too much spectacular happens - some little bit of current flows through the terminal and wire.
( does it take a whole year for the wire to become equalized at the same potential as the terminal - something to think about )
Throw the other terminal switch and current can now flow through the battery.
Both wire ends are conducting current and thus bulbs start glowing in succession from each end of the battery outwards.

Or perhaps the terminals are connected and the SPST switch is located at the far end of the loop of lights.
Of course, since the terminals are already connected, some of the lights ( beginning from the terminals ) are already glowing before the switch is thrown.

If before we throw the switch, we had waited long enough for the transients to die out and both wires become at the potential of each terminal, all bulbs are out.
Now throw the switch - One would suspect that the bulbs would begin to light up starting from the switch, since we have terminal voltage.
But a wire has a only a small capacitance, and that point now being at potential E/2 spreads out from the switch along the wire, with bulbs hardly showing any sign of a glow from switch to battery terminals.

So perhaps the first paragraph is incorrect, and the bulbs in succession glow only briefly if the switches are at the battery terminals.
A long single wire transmission line with reflections traveling back and forth from terminals to far end and back again as a wave lighting up some bulbs along the way and then having them extinguished as the wave passes.. All bulbs being light only after a long long time as the transient dies out
similar to @Delta² post.

 

[CWatters]

Are the bulbs in series or parallel? Does it make a difference?

 

[Delta2]

Are the bulbs in series or parallel? Does it make a difference?

Ah good question, originally I thought the OP meant they were in series, but if they are in parallel then they get the full glow as the wave of current travels through the transmission line at the same speed as the field does. No need to wait for 1LY.

But if they are in series, then the lumped model of transmission line fails (I think). What sort of transmission line model can we use for this case?

 

[256bits]

Low C, low L, what's R?
Low R and it is similar to just a loop of wire.
High R and we just about get infinite resistance.

 

[sophiecentaur]

Einstein had a 'dream' about this sort of think happening. There was a line of cows, resting their heads on the wire of an unpowered electric fence. The farmer turned on the power. This link discusses what Einstein and the Farmer saw and how it relates to Relativity.

 

[Jetro]

Einstein had a 'dream' about this sort of think happening. There was a line of cows, resting their heads on the wire of an unpowered electric fence. The farmer turned on the power. This link discusses what Einstein and the Farmer saw and how it relates to Relativity.

I see how that would work in that particular example, but since the light bulbs in this case are in a circle, I wouldn't expect all photons from the lightbulbs to arrive at the same time as the electrical wave. Photons from a light bulb across the diameter of the circle from the power source, for example would arrive before the Electrical wave if they were lit, since the Electrical wave has to travel the circumference of the circle but the photons traveling the diameter would take a shorter path.

 

[Jetro]

Low C, low L, what's R?
Low R and it is similar to just a loop of wire.
High R and we just about get infinite resistance.

Let's just assume the wire is super conducting for the sake of simplicity.

 

[sophiecentaur]

e, I wouldn't expect all photons from the lightbulbs to arrive at the same time as the electrical wave.

I can't find any mention of where the observer is. Transit times to the centre would be equal but not to anywhere else. We are plagued with Relativity so any of these sorts of problems must be specified tightly (including all the assumptions of ideal behaviour) or the conversation can never end.

 

[Delta2]

well, @Jetro you didn't answer if they are in series or in parallel.

If they are in parallel, then the setup can be modeled by a conventional transmission line https://en.wikipedia.org/wiki/Transmission_line#Telegrapher's_equations
with resistive loads (the bulbs) placed at regular intervals. If we ignore relativity, then the bulbs glow after time $l/c$ where l is their distance from the source along the circumference path.

If they are in series, then I believe the bulbs will need multiple of light years in order to glow fully. It is some sort of transmission line again but the conventional model of transmission line that uses the lumped elements R,L,C,G per unit length I believe it fails here, it is not adequate to describe what's happening.

 

[Dale]

If we ignore relativity, then the bulbs glow after time l/c where l is their distance from the source along the circumference path.

I agree with this except that l should be the distance to the switch. The EM wave starts at the switch, not the source.

 

[sophiecentaur]

I agree with this except that l should be the distance to the switch. The EM wave starts at the switch, not the source.

I think the problem is passing from the totally ideal to the partly practical, in which case there should be an agreed 'equivalent circuit'.

 

[bob012345]

There are so many interesting issues with this problem. Given a voltage source large enough to light trillions of bulbs, as the pulse propagated even one light microsecond, the voltage across each of the first lit bulbs would begin to melt them since the circuit can't yet sense the total resistance making the current too high. One would have to design a power source to match the increasing load as the signals propagated. A limited scale model of the circuit could be designed in modern simulator and one could study the signals as they propagate given different power source configurations.

 

[sophiecentaur]

There are so many interesting issues with this problem. Given a voltage source large enough to light trillions of bulbs, as the pulse propagated even one light microsecond, the voltage across each of the first lit bulbs would begin to melt them since the circuit can't yet sense the total resistance making the current too high. One would have to design a power source to match the increasing load as the signals propagated. A limited scale model of the circuit could be designed in modern simulator and one could study the signals as they propagate given different power source configurations.

There is a perfectly reasonable solution to the problem as long as the impedances of the bulbs are chosen right and the coupling to the transmission line is low enough.
Just don’t ask me to build the thing!

 

[Nik_2213]

Slightly OT but, given the 'Blackpool Illuminations' season has just begun, I'm reminded of a former colleague's student-era tale. For 'beer money', he replaced blown 'incandescent' lamps on their VERY LONG festoon runs.

The many lamp fittings were wired in parallel so that one failure would not darken an entire run. Such festoon runs were long enough, with sufficient line resistance, that each festoon was divided into sections, and replacement lamps were coded with the voltage applicable to that section...

This provided both optimal life for each filament and fair brightness matching.

All such have now gone LED etc for economy...