Wiring – Precautions in connecting high voltage source to a relay

This seems like the neutral cable in a split 120-N-120 service is not handling the full current. A small gain in brightness of a lamp on one side of the circuit, when a 30 or 50 A load is applied to the other side, is not unusual, but measure the voltage if it's more than a barely-noticeable increase in brightness. The maximum voltage should be no more than ~127 V.

In the extreme case of a neutral wire breaking (which happened to my service after a tree fell on the entrance cable), the voltage across each half of the circuit becomes 240V split by the resistance for the circuit. E.G. with a 40 A designed load (3 ohms) on one side, and a 1 A designed load (just a 120 W lamp, 120 ohms) on the other side, the actual voltage across the lamp would be ~234 V, and the 40 A water heater would get only ~6V. The lamp would be very bright for a very short while. (In my case, I was lucky -- a few lamp ballasts burned out, but over-voltage protection varistors on outlets blew circuit breakers before a fire started).

EEK! Kill it with fire, before it kills you with fire!

I'm referring to the breakable Edison screw base bulb that is on the floor and underfoot, ready to be tripped over, tearing the porcelain base socket off and exposing you to 120V. UGH. Remember, if you bust that bulb, you will have live 120V inside broken glass right next to grounds, and there you are groping around in the pitch black! Unacceptable!

Here's what I would do.

1. Get a modern transformer that's built into a junction-box lid, like this one. Not for this junction box - this box gets a blank lid, so you can climb across it without touching anything electrical.

2. In the (illegal) hole the transformer wiring went through, I'd get some EMT conduit and extend it along that joist, toward the eave, as far as practical before the clearances get too close to work. I'd install another junction box there, screw it to the joist with 2 screws. I'd fasten the EMT to the joist rather firmly with lots of clamps so you can climb/step across it or put stuff on it. There'll be a 1/4" or so gap between EMT and joist, the usual practice is 4 subtle bends, I'd just put shims under it.

3. In that new box I'd install the new "in the lid" transformer.

4. Out of the side of that junction box, I'd go EMT, flexible conduit or armored cable to a suitable location for LED lights. I'd put two there, selecting models unlikely to be damaged from rough handling of boxes etc. in the attic. Two, so I can use cheapies and still have light to fix one when it fails.

Ground wires needed also, I'm not showing the grounds since wherever you use metal EMT, that can be the ground. I also overlooked a light switch, I don't know how the attic light turns on now. If needed you can run some flexible armored cable over to a convenient location for a switch.

You could also relocate the existing box to be on the sides of the rafters instead of the top, but that's more than I wanted to get into here.

By the way, the transformer is the "ridiculously easy" part of this. The REAL work, and real win, is fixing that dangerous lighting situation and making your attic space a lot more usable. Besides, wireless doorbells look cheap IMO and hurt your resale. If you've got a real one, it's not hard to keep it.