electricaljunction-boxwiring
I want to connect the wiring from my shed into a junction box on the ceiling in the basement. I opened the box to see what I was dealing with, I figured it should be simple, there is only 2 wires going in. but i am confused- black to black, and both white wires just loose on their own. How do I connect my new wire into this box?
This is a single circuit, and the neutral is common to all branches of this circuit. In this case, all neutral wires in this box must be connected together.
Similarly (and this is regardless of single or multiple circuits/breakers) all grounds must be connected to each other, as well as to the box itself.
In the case of your switches, they simply need a neutral to operate the electronics in the switch itself. All you need to do is wire the neutral to each switch. You'll probably have to add pigtails, and probably additional wire nuts (purely for convenience).
Just to illustrate, using your schematic, I added the neutral lines (my changes highlighted in yellow):
The number and placement of wire nuts is not important, other than you need to pay attention to the number and size of wires when choosing wire nuts (they have a rating that will say how many wires of a given gauge they support).
It looks like a standard "power on the end, lamp in the middle" 3-way arrangement. However (for whatever reason) they chose to make the travelers black and white on both segments.
Travelers can be quite a dog's breakfast, I've seen 3-way circuits where the travelers change colors on every segment. Choosing the same colors thru makes some sense -- however white should not be one of the chosen colors. though the far, far better way is to pick a colored tape color such as yellow, and mark both travelers yellow (they are interchangeable, they can be the same color).
That's because white is special in Code rules. Colored wires (hots) cannot be remarked to be neutral. But white wires can be remarked to be a hot wire. The last guy should've made red and black the travelers and tagged white with colored tape in the segment where it served as switched-hot. That would've been reasonable.
Best Answer
This looks like it used to hold a light fixture that was controlled by a switch. One white conductor is a grounded (neutral) conductor, the other is a switched ungrounded (hot) conductor (presumably).
To verify, follow the cable in both directions (one direction at a time, unless you have a split personality) and see if it eventually runs to another light fixture or a switch.
Alternatively, you could carefully connect a multimeter to the two wires. Then run about wildly flipping switches until either a reading is displayed, or the reading goes to 0.