An ampere is a measure of how many electrons move past a point every second (though technically, it's movement of any charged particles, but for metal wires it's always electrons). 1 ampere = 6,241,510,000,000,000,000 electrons per second. A pipe with water moving through it could be measured in gallons per second. Same idea.
Watts are not just used in electronics. They're a measure of the rate at which energy is used or transferred. A stick of dynamite and a candle have similar amounts of stored chemical energy, but the dynamite releases it much faster than the candle, so the dynamite has a higher power output (for a shorter time). Likewise you could use two identical batteries in different ways. If one way uses more power, the battery will not last as long.
1 horsepower is about 750 watts, if you're familiar with cars. Just different ways to measure the same thing.
watts = volts * amps. So a 60 W bulb plugged into a 120 V socket will be drawing 1/2 an amp.
60 W = 120 V * 0.5 A
In AC circuits, the electrons are vibrating back and forth instead of going in a continuous loop. The frequency is just the number of vibrations per second. 50 Hz means they move back and forth 50 times per second.
It's important to understand the difference between current flow and energy flow, though. The actual electrons in a wire don't move very fast. In a DC circuit, the actual electron flow around the loop might be at the speed of molasses. The reason flipping a switch causes the light to turn on very quickly is because the energy flow is very fast. The energy is carried by waves in the electrons, not the electrons themselves. They are constantly repelling each other, so when you push some extra electrons onto one end of a wire, the others nearby jump away, which causes more near them to jump away, and so on, creating a wave of "push" that travels down the wire and then pushes on things at the other end. This wave travels from one end of the wire to the other at maybe 2/3 the speed of light, while the electrons themselves barely move.
Just to make things simple, I'm going to assume that everything in your consumer electronics is designed properly (reasonable assumption) and is still operating to it's designed standards.
Another assumption I am going to make is that at least one of these units and perhaps both has only a 2 pronged plug that receives mains voltage.
The power transported and converted in the wall wart/power plug is transported in an AC waveform. There should be no direct DC connection, unless there is, in which case there will be a third prong (called safety) on your plug into the mains current. And even then that ground/safety may not be carried through the USB port of controller line.
Basically one or both of the DC sides of the power brick has no ground reference with the AC side. The DC is "floating", there is no assumed ground.
The solution for you is that you need to establish that ground, by connecting all of the grounds on all of the devices together.
For proof you simply need to measure the differences in grounds between the controller and the USB based FPGA ground. Do so with both DC and AC and you'll find that it is drifting around.
If there is a fault, or things have failed you'll notice it by circuit breaker going.
Have you ever noticed that when you plugin a USB port from one computer to another that there is sparks? but everything works once connected? It's the same thing happening here.
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The 0V is relative to earth, in theory. When the neutral wire carries some current from devices, the resistance causes a small voltage between neutral and earth.
Besides, RMS does not mean "relative to hot wire". It just tells how voltage is expressed.
HYPOTHETICALLY, yes. Though, don't to this!
Some outlets have a distinct orientation, some have not, like this Type-F used in Germany:
There is absolutely no rule which one is neutral and which is hot. It is sometimes said to connect neutral to the left when the outlet is mounted with the holes aligned horizontally, since then it's the same as Type-E, which is used in France, for example: