# Speed of propagation of electric current and displacement travelled during a period

1. I read that "In general, the speed of propagation of electric current in a typical copper cable is about 70% to 90% of the speed of light, or about 210,000 km/s to 270,000 km/s"
2. Let's say we have an electrical signal of 100 Hz. The period is 10ms.

Let's say the speed of propagation is 250,000km/s, at this speed in 10ms the distance travelled is 2,500km. So in one period the signal moved 2,500 km?

Sounds weird to me, I don't know how to link those data's.

• doesn't sound weird to me, the math checks out. What's the question here? (by the way, "speed of current propagation" is… a kind of strange term; but we can work with it. In the end, this is just a shorthand for "group velocity in a waveguide of sorts") Mar 7, 2023 at 22:37
• "Weird" how? Too much, too little? Mar 7, 2023 at 22:43
• @EugeneSh. Too much .. I'm working with a circuit (a M.P.P.T. for a photovoltaic system) in which a signal will switch from in-phase to out-of-phase indicating that we need to increase or decrease (respectively) the voltage to reach optimal power. But then when I am at that optimum I will have a very fast oscillation between decreasing and increasing around that optimum so the change in phase will create random behaviour since it will change many many times inside one period ! Mar 7, 2023 at 23:07
• that's a problem that got essentially nothing to do with the speed of your current. It's "how do I dampen my control system"! Also, you are probably ignoring that your plant has limited bandwidth. Mar 7, 2023 at 23:20
• Again, I don't think the speed of electromagnetic waves in your system is of any relevance at all for your control problem. The phase of your 100 Hz current changes by $2\pi$, 100 times a second. That's what what phase does... Mar 8, 2023 at 1:11

In your application, the electrical signal propagation through wires is practically instantaneous. You don't have to worry about it at all.

Propagation through everything else but the wires, though, is another story - and that's where control theory and feedback circuit design comes into play. Typically you shape the frequency response of various parts of the circuit so that the control loop remains stable.

Well, I basically thought (wrongly) that each "loop of the current" in my circuit would contain many periods. So changing the phase every xx periods would have worked as I wanted (I thought to vary the command of a buck converter from a state to another accordingly to that information of phase, with that variation damped by a low pass filter

You seem to think that the only way to store state in an electric circuit is by having a long wire that propagates state. In your case this would be a serious limitation and require extremely long wires :)

Instead of storing state in a wire, it can be stored in a low-pass filter directly! The filter - even the simplest first order R-C filter - imposes its own response on how the signals propagate through it.

• Great to hear that its probably not a problem. However so far when I'm trying to simulate a change of phase every 1ms , it does produce garbage in my circuit. I'm already using a low pass filter but I'm probably still missing something. I'll write a new post of its own about it when I'm back home. Mar 8, 2023 at 7:06
• @c.leblanc Ask with a circuit schematic included, and tell us what is the application, i.e. why you're doing it. Mar 8, 2023 at 18:48
• @'Kuba hasn't forgotten' I just found the solution to my problem with an assistant at uni. Your answers paved the way for me though, thank you ! Mar 9, 2023 at 16:48