Comments on How long does it take for energy to propagate in a circuit?
Parent
How long does it take for energy to propagate in a circuit?
The premise
In a recent video by the pop-sci channel Veritasium, the concept of the flow of electricity and energy transmission in a circuit was discussed. In that video a thought experiment is presented:
The video concludes that, after the switch is flipped, the lightbulb will turn on after 1/c seconds (1 meter divided by the speed of light), since the lamp and the battery are 1 meter apart. This is explained by showing that, in an electrical circuit, energy is transmitted through an EM field, which propagates at the speed of light, and not through movement of particles in a conductor.
This explanation did not sit right with me, for mainly two reasons:
- Clearly, the conductor plays a role in the transmission of energy. This is actually pointed out in the video as well, by saying that after a connection in a circuit is made, the EM field will propagate along the conductor at the speed of light. To me, this would mean that the field would take 1s to propagate through the cables in the thought experiment, and the lamp will turn on after 1s.
- For the lamp to turn on, current must flow through it, heating the filament. Simply being in an EM field generated by the battery would not work, there needs to be some potential difference at the lamp's terminals. The signal doesn't "know" what happens at the load until it reaches it. This is a big part of reflection in signal and transmission lines, yet seems to be ignored here. Therefore, the voltage will take 1s to arrive at the lamp in this case.
The question
Is the answer of 1/c seconds correct, or should the answer be something else? If the answer is not 1/c, where does the mistake in the video's reasoning lie?
Try this out for size: - Image alt text Hope it's clear. Maybe a little simulation of 10 km 600 Ω line might h …
3y ago
Is the answer of 1/c seconds correct It can't possibly be. The question is looking for a time value. "C" is a speed …
3y ago
I add my answer here because I think the other answers are incorrect or irrelevant: namely, the answer of Andy is nice a …
3y ago
This is someone trying to rehash a Light experiment with circuits, however I do not think it holds up. Inside a medium, …
3y ago
So here's the thing. Energy doesn't "propagate" as the video suggests. Energy is used. A voltage potential may propagate …
3y ago
Post
Is the answer of 1/c seconds correct
It can't possibly be. The question is looking for a time value. "C" is a speed, which has units of distance/time. "1/c" therefore has units of time/distance.
In this case, 1 is 1 meter
"1" is never one meter. "1 m" or "1 meter" is one meter.
Added: I guess a discussion of the physics has been delayed long enough so that there have been enough consequences for the sloppy use of units.
One answer discussed propagation of current down the wire and radio propagation from the switch to the light bulb. There is another possibility, which is the transmission line effect.
If each out-and-back segment at left and right were a transmission line, then current would be induced in the far conductor very quickly. Another way to think of the same thing is that the near wire is the primary of a transformer, and the far wire the secondary. When current changes in the primary, there will be an induced voltage in the secondary.
In this case, with the near and far wires being 1 m apart, that coupling is rather weak. Most of the magnetic field produced by the current in the near wire won't wrap around the far wire. The energy transfer between the two will therefore be minimal. Another way to put this is that the transformer has large leakage inductance, and small coupled inductance.
If the two wires were right next to each other, then this effect could be significant. With perfect coupling and 0 wire resistance, any current in the primary wire would immediately cause an equal and opposite current in the secondary wire, which causes the magnetic field to stay at 0. In that case, the light bulb would light almost instantly. In the case actually presented, a tiny voltage could be detected after the magnetic field propagated from the front to the back wire. The bulb lighting would have to wait until the current propagates in the wire to the bulb.
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