I * V = W
1A of current @ 1V is: 1W
1A of current @ 10V is: 10W
I understand that 1A is 1C-per-second, which is some amount of electrons. Intuitive so far.
How can I get more power if I use the same amount of electrons-per-second flowing through?
Using the water analogy, where voltage is the pressure of the water and current is the amount of water that flows through, using more pressure also gives us more water flow, so they aren't independent variables. Using another water analogy, where voltage is the height of a waterfall, this one seems to work because the water has some time to accelerate and have a bigger impact on the ground (more power), but I can't find where is the equivalent effect in electricity - what causes the acceleration, and what are the velocity * mass here?
What exactly happens when you increase the voltage in a circuit, without changing the number of electrons passing though per second?
Another analogy to voltage is how much the electrons want to move. But if they only want to move (Voltage) but aren't actually moving (Current stays the same), how can this affect something? (power)