You're not supposed to do line voltage with that board at all.
They didn't design it for that sort of high voltage (it's totally notUL.)
It has no agency approvals for anything of the kind.
[Especially since the traces for the terminals and relay traces are so close to the Arduino USB connector shell.]
Yes, you can use voltages lower than the rated voltages on the relay labels.
You bring the voltage that you want to switch into one of the relay terminals (COM) and look for it at that relay's NC (normally closed) or NO (normally open) contact.
You can use it for 12 V AC.
But as stated, be real sure it doesn't touch any parts ofthe Arduino.
You could consider to extend the headers of the Arduino to be sure.
I've seen some shields that get too close to the USB connector shell to my taste, but haven't acutally seen these shields.
Runaway Pancake has as you can see in his link.
Cut 1 line and connect it through the relay.
PSU side to COM and lamp side to NO.
3A is your maximal current.
The difference between the AC and DC voltages is due to AC is alternating and will go through 0 volts 100 - 120 times per second.
A switch off spark will be stopped at that moment, and this will not occur when using DC current.
So a DC voltage will generate sparks for a longer time, damaging the contacts more.
The switch gets opened or closed depending on if there's a built up magnetic field (an electromagnetic) you power the electromagnetic
with your arduino (or transistor in this case), once the magnetic field occurs, it will repel off a perm magnetic which pushes the metal
I think the power supply is more than it's capable of.
If it does 3A @ 24VAC, how would I know what amperage it could handle at 12VAC?
If I had to guess I'd say in the neighborhood of 6A, but I have a feeling that's wrong.
3A is the maximum current it can handle. Period. There is a certain amount of contact resistance, so there is a certain amount of heat generated. That rating has little to nothing to do with the maximum voltage the relay can switch.
When it says 120Vac and 24Vdc max, that is the maximum voltage that the contacts can interrupt at 3A. When you open switch or relay contacts, an arc forms. How long it can get depends on the amount of current flowing through it, and the voltage driving it. More current means a hotter arc and therefore lower resistance, so it takes less voltage to sustain it. A higher voltage means the arc can get longer before the resistance rises high enough that the current through it can no longer keep it hot enough.
As someone else pointed out, AC is interrupted 100 or 120 times a second (depending on if your power is 50Hz or 60Hz), so a higher voltage can be interrupted by the same switch. DC, however, makes a continuous arc, so a lower voltage can sustain an arc at the same current.