So I plug in a circuit 299,792,458 meters long into my wall outlet

Hope the subject caught your attention, I just wanted to clarify my some things about ac current...

Ok, for our "circuit" we're going to have copper wire for simplicity's sake. Also, we're going to say that our Electric force travels at c on the wire. Just a big loop, no sharp turns, nothing crazy. Ignore the obscene Ohmic losses we would have unless our voltage was in the google range. (wow, can you imagine that?) And the circumfrence is 299,792,458 meters long.

Now, with the 60 Hz current coming out of my wall, and the circuit an entire light second long:

1. Does the signal travel from positive to negative, taking an entire second to circle the circuit or does the signal leave both terminals simultaneously and "meet in the middle" taking 1/2 a second to effectively traverse the entire circuit?

2. At any given instant, if you freeze the circuit in time, is the current changing direction 120 times along the entire circuit? (2 direction changes per hertz on a sinosoidial wave).

3. Since the whole circuit is just one big loop with a current, is it a solenoid? Or, if question 2 is "yes," how does this affect things?

4. Assuming copper is about .75 per meter, does anyone have about 225 million dollars I can borrow to build it? I'm sure the U.S. Government could just write a check, right?

Thanks!

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jambaugh
Gold Member
The paradigm for your example as an AC circuit with long length relative to the wavelength of the AC signal. When you switch on the current the two ends of the circuit will behave like independent wave-guides. They will have a large capacitance and impedance at the given ac frequency and so the 60Hz waves will propagate down each end meeting at the far point a half second later. Given it is exactly 1 light-second in length and given the AC signal is exactly 60Hz you'll get constructive interference at the far end and after one second the current should settle down to approximately the long term cyclic behavior.

Now this is a gross simplification. The actual propagation will initially follow the Telegrapher's equation, propagating more like a series of diffusive waves until it settles down to long term "steady" state. Even with no pure resistance you'll get radiative losses.

What you have is basically a loop antenna for ELF (Extremely Low Frequency) radio.

after one second the current should settle down to approximately the long term cyclic behavior.

Now this is a gross simplification. The actual propagation will initially follow the Telegrapher's equation, propagating more like a series of diffusive waves until it settles down to long term "steady" state.

So, basically, the entire loop will be changing polarity in unison? Not as waves running down the loop?

Oh, and thank you very much for the answer to the 1 second / .5 second question.

f95toli
Gold Member
You need to remember that there is no such thing as "suddenly" turning on a 60Hz signal; try drawing the waveform (in the time-domain) and you will see why.
I guess what you have in mind is a sinusodial waveform modulated by a step function (which obviously won't be a real step-function in a real circuit).
However, a waveform like that will contain a LOT of high-frequency information meaning it is not really a "steady state" 60 Hz sine until everything has settled down which can take quite a while. As jambaugh has already suggested you need to solve a telegraph equation in order to see how thing really evolve in time (not really difficult, but quite messy).

If you are interested in this I would suggest you download e.g. LTSpice (free from www.linear.com) and play with some simple circuits.

If you had two parallel wires, one for positive and one for negative, or one for hot AC and one for neutral AC, you would have both electric and magnetic fields between the two conductors. The pair would be about 1.5 x 10^8 meters long, and a TEM (transverse electric magnetic) wave would take about 1/2 second to get to the end, and another 1/2 second to get back. If you had a single turn coil (solenoid) you still need time to charge up the magnetic field in the center of the loop, and the time would be similar. If there are no losses, and the coil did not radiate (like a loop antenna), it would just oscillate, using the permeability and permittivity of free space as the resonant inductance and capacitance.

If you have access to a 1Ghz DSO, a signal source, and a hundred meter or longer section of wire not in a tight coil, but looped back gently on itself, you have a very instructive experiment.

Several reasons why Fast-Ethernet doesn't work well beyond about 200m are visible.