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Imagine a long circuit that goes around the Earth, or just spans a large enough distance to measure the effect, say 100'000 km.

The circuit has efficient light bulbs installed at each 10km mark. There is a power source connected which powers all the light bulbs.

Time N = all light bulbs are lit.

(+.................-)

Time N+1 = the circuit is cut in the middle point, equidistant from the power supply terminals.

(+......./ /.......-)

Question is, how do the light bulbs shut down along the timeline, starting with N+1.

  1. Do they turn off one by one starting from the middle point, or does it start from the terminals moving towards the middle point?
  2. Is the speed of propagation the same for both halves of the circuit?
  3. What is the propagation speed?

Thanks and sorry for stupidity if this question is trivial :)

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A circuit of this scale can no longer be analyzed with the lumped element model and must, instead, be analyzed with a transmission line model.

When the circuit is cut, that information (the voltage and current waves) propagates at some speed less than $c$ outward from the cut in both directions.

Thus, the lights will not turn off simultaneously and, if the two halves are identical, the turn off should be symmetric.

The actual details of the turn off transient requires more information and would likely best be found via numerical simulation.

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  • $\begingroup$ Is it correct to understand from the second sentence, that the lights will turn off one by one starting from the cut ends of the circuit? $\endgroup$
    – PhyIk
    May 29 '14 at 23:11

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