> Volts is the number of electrons sitting there on the negative rail of a battery
No, Volts is how hard they "want" to move. Do they have a great urge to move, or are they apathetic about the idea of moving?
Volts has no meaning for a single point. Volts is always between TWO points. In the real world we often have some large sorta-conducting object around, such as a chassis or the dirt, so sometimes we simplify by making that large object one of the two points, and then forget to mention it.
Say you stand across the street from a bar with $4 Miller beer, and you are not very thirsty. You feel very little "voltage" pushing you across the street. Now say you stand across the street from a bankrupt studio, and the landlord is throwing vintage Neve modules in the trash. You feel a very large voltage urging you across the street.
> One amp equals the movement of a certain number of electrons from a negative place to a positive place in one second
Current could be seen that way, but it is usually best to draw a line across a conductor and count the electrons which cross the line. Same as the rubber hose across a highway used to get traffic-count. Main St carries 4,321 cars per hour. 1 Amp is one zillion electrons crossing the line in one second. The exact big-number is not used in practice.
Going back to the dumpstered Neves: if many geeks have easy access, there will be a large current of geeks moving toward that dumpster. If it is way out in Allice Springs behind a 10 foot wire fence with guard dogs, very few geeks will overcome the resistance in the way.
> Watts on the other hand is hard for me to grasp
The root definition is the work one horse can do. This concept comes from coal mines under the sea: to lift water out as fast as it came in, a mine might need 1, 2, 3 or however many horses working the pump, and Jimmy Watt sold engines on the basis of how many horses could be replaced. Watts are the same thing, except defined in terms of the arbitrary non-horse units Volts and Amp. A Watt is about a 1/750th of a Horse, or say a horse about 1 hand tall.
The gut-level definition of Watt always comes down to HEAT. A small car can cruise the highway with 10 horsepower or ~7,500 Watts. This power goes to move the air the car hits so it goes around the side of the car, mechanical energy. But power always ultimately appears as heat. At 60MPH, the air heat is small, but at 2,000MPH it melts metals.
Watts, Power, Horses, is always two factors. Lifting water out of a mine, you can lift 33,000 pounds one foot in one minute, or 1 pound 33,000 feet in one minute. Conversely, you could get 1 horsepower from a water-wheel if you had 1 pound per minute falling down a 33,000 foot pipe or 33,000 pounds a minute falling 1 foot over a low dam, or 330 poinds/min falling 100 feet. They are different wheel designs, but you can get the same work done.
In electricity, if you need 1,000 watts to warm a cold room, you could use 100 Amps from a 10V supply or 1 Amp from a 1,000V supply. You need different resistances, but you get the same power and the same heat. Likewise you could burn a big pile of damp wood, or a small pile of oxy-hydrogen: temperature times size is heating power.
> The trippy thing is that these three things are so related.
How big is your farm? It is so-wide times so-long and so many acres.
Perhaps a better analogy: how powerful is your farm? It is the area times the sun+rain that falls on it. Sun and rain are the "voltage" that makes plants grow: an acre in Siberia or Nevada won't grow as fast as an acre in Brazil or Florida. Even with big sun and rain, plants don't grow instantly: there is "resistance". But Volts divided by resistance gives a "current" like one foot of growth per week, or one acre-foot of produce going out your gate to market each week.
