Do AC Circuits Combine Coherently at 60Hz?

[Idea04]

Homework Statement

my question is when you connect let's say many ac circuits into one circuit and the cycle is 60Hz. Do the cycles stay coherent to one another or do the pulses of the alternating current get mixed once they all combine into one circuit.

Homework Equations

The Attempt at a Solution

 

[mgb_phys]

If the lengths of the wires are similair they cycles will all be in phase.
If you have an experiment with very long wires, such that it takes more than 1/60s to travel down different parts of the circuit it gets more complicated.

 

[Idea04]

well the ac current comes from many individual circuits and the wires are all different lengths. So to get them all on the same phase do you have to put the current through a capacitor or something like that. I really don't know , or does the pulses automatically align them selves.