Phase difference in long runs of wire

[elegysix]

Hi so I am wondering about potential phase difference in some 110v 60 hz household wiring... Say I have two switches to control one light and am too cheap to buy 3 way switches. If I were to run power from switch 1 to switch 2 (bypassing switch 1), so that they both had power at the switch, if I were to turn both switches on, would the difference in phase at the light cause a problem? (granted at such small distances it will be a small fraction of a degree out of phase)

From a theory standpoint, if the voltage propagates at .5c, then .5c/60hz = 2,500,000 m, so for 90 deg out of phase we would need 625,000 m of cable... think of a single long wire which is hot loops around and touches itself, from the point of contact to the end of the wire is 625,000 m (90 deg out). While it is touching what is going on in the wire? lots of current? superposition? something bad? lol

Lets go a step further and make it 180 out of phase... what then? no voltage on the line? what's the current doing? does my generator explode? XD

thanks

BTW i am NOT actually going to wire my house like that, just curious

 

[anorlunda]

Remember that single phase wiring is a closed loop. A switch or a load is inserted by cutting the loop at some point, then inserting the two terminal device across the gap. You are asking if there is a problem because the distance from the supply to one terminal of the gap is longer than the distance from the supply to the other terminal.

If you cut the closed loop at any point and insert a small resistance, what would the voltage magnitude and phase difference be between the two resistor terminals?Given that way of looking at it, I'm sure that you can answer your question yourself.

I'll let the mentors decide if this discussion of DIY home wiring is OK.

 

[elegysix]

Welllll, not exactly. See, in your scenario there is a single loop going back to the source. Mine is a little different. In my wiring example, the hots connected together would be connected to a resistor and the neutral. But forget about that. Here's a simplified picture. When you have a large length of wire to span, because the voltage has a propagation speed, we get a difference in phase along a single wire, which is what this question is focused on. What's going on in the loop?

 

[anorlunda]

I don't understand your pictures. The second one shows a short circuited loop closing on itself.

 

[elegysix]

Yes, it is shorted on itself. And there is a phase difference between where it is shorted, before shorting it. so what happens? that is the question.

 

[anorlunda]

OK, now I got your question better. Wave propagation in the context of house wiring, with a 625 km long loop in your house. Will that short the generator? No.

In fact you can eliminate the hot leg of the circuit and consider just the short loop. Open the loop, put a pulse in one end, then close the circuit before the pulse can propagate around the loop. Won't the pulse just circulate and decay?

I suspect that RF engineers might answer this question better than power engineers,

 

[anorlunda]

By the way, you should not have used 60 hz in the OP. Wave propagation speed is 0.5c or about 150,000,000 m/s.

In the context of your question things happen so fast that 60 hz power is DC for all practical purposes.

 

[Baluncore]

Your circuit and scenario are sufficiently divorced from reality that there cannot really be a real answer.

You show no return wire. A neutral would need to be bundled with the active in the loop or you would have an antenna radiating the energy you wanted to use in your light.

If we assume there is a ground plane or that the line is actually a transmission line then; where you short circuit the loop you have a 3 way junction. The energy of a wave reaching that junction will be split in three, one going each way around the loop, there will also be energy reflected back down the feed line. Those waves in the loop are traveling in different directions so they will pass on the far side of the loop without interacting, to meet again after one trip round the loop when they get back to the junction. They will sum at that point to be split three ways again due to the impedance mismatch. It will continue to go round in circles.

 

[elegysix]

to be clear I've made a better picture. What I'd like to know is what kind of power would be going through such a circuit, and what would be happening when S3 is closed (when S1 and S2 closed). What would happen with a 90 degree phase difference across S3? or 180?

 

[Baluncore]

You show one Earth connection. Is that the MEN link or a connection to a ground plane?
Building wiring codes require the active and neutral travel together and pass through the same holes. That reduces radiation. You need to redraw your circuit with wires in bundles that have sum-zero currents. Only then can you consider the phase at different points in the circuit.

Your circuit seems to be something a bit like a 3/2 wavelength hybrid ring coupler.
https://en.wikipedia.org/wiki/Power_dividers_and_directional_couplers#Hybrid_ring_coupler

 

[elegysix]

Tell me more. this is fascinating. I don't know what difference the MEN link or ground plane would make. Nor had I considered radiation. I was simply wondering if the phase difference might act like a short, or whether something more complex would happen. Please, elaborate. What would be the difference in running bundles vs single wire as shown?

 

[Baluncore]

Consider two parallel wires, one is the active, the other the neutral return wire. The currents are equal and opposite. Outside the wire the electric fields cancel and the magnetic fields due to the currents cancel.

Between the wires is an electric field determined by the difference in voltage between the wires. Between the wires the magnetic fields due to the equal and opposite currents do not cancel, they sum to double. So between the wires is a strong electric and magnetic field. That is where the energy travels towards the load. When you keep the active and return wires together you prevent loss by radiation of that energy.

Study transmission lines; https://en.wikipedia.org/wiki/Transmission_line
Once you understand impedance matching take a look at the Smith chart. https://en.wikipedia.org/wiki/Smith_chart