I had always been troubled by this equation: Power equals Volt times Ampere.
Because P also = I^2 X R.
Given the analogy of water fall. Power is the effect/work (wheel rotate) of current "I" (stream) under the resistence "R" (tap) after the voltage "V" (water level), I just couldn't imagine how IxIxR and VxR would change P without changing I.
I believe the key is there are two ingredients in a current. I'd always seen current in the quantity context but I've forgotten that speed is involved too. Thus with magnitudes of speed and quantity increasing and decreasing or vice versa correspondingly, current I could remain constant. Although, I have yet to consider the force of the current, only assuming that the speed or quantity of electrons could affect the P (power) independently.