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For simple stuff such as those lights, polarity is usually not a problem when using AC.
In case of AC (Alternating Current), instead of having a + and - pole, you have a Line and a Neutral terminal.
The Line terminal goes + ... - ... + ... - ... + ... - with time and the Neutral stays at 0.
When connecting to LEDs and such, you have an AC to DC converter, which tends to be fine no matter which pin you put in which hole.
Edit for clarity: I am talking only about the specific appliance in this case, having a 2 pin plug. When doing home wiring, polarity matters a lot.
Anti Commercial-AI license
Ah, so that's why it's half power compared to DC, makes sense.
Kinda, it's half the power because the power goes like the temporal average of the current squared, the current oscillates like sine or cosine, and the temporal average of a sine or cosine squared is 1/2.
Unless the AC is a square wave, in which case stuff becomes different.
Not really.
Where on earth would Mains be a square wave?
Low quality UPS Inverter
That's not what Mains means.
As far as the appliance cares, it is the only input power it gets at that time.
In household wiring polarity does matter, especially if you are assembling plugs. Only one of the three wires is carrying live current (hot), the other two are the neutral return path, and ground which is for safety. If you accidentally switch polarity, you can cross hot to neutral and cause a short circuit.
Switching the neutral and hot pins doesn't matter except for appliances with exposed metal tied to the neutral pin, which is pretty much exclusive Edison screw lamps. This is why many plugs (especially those that immediately go to a rectifier) don't bother with polarization.
Swtching hot and ground is a problem
My bad. I wasn't clear enough.
I was talking about 2 pin plugs, as shown in the post and how it is usually for those cheap lighting thingies.