I have been extremely confused about exactly how to think about voltage (and power) when it comes to circuit analysis. In physics, voltage is just described as the energy required to move a unit charge a specific distance across an electric field, but that seems to be in free space and my physics teacher didn't really apply it to a circuit. For a circuit, he described it as a difference in electric potential energy per unit charge between two points, which "pushes" charges. I am a bit confused as to why increasing the difference in potential energy per unit charge manages to push more current. If I am dumping a bottle of water out into a sink, moving the water bottle up and down as I am dumping it won't make the water come out of the bottle any faster or slower, even though I am technically changing its gravitational potential.
I am also confused when we talked about power. Power is described as $P = VI$, but if we have a circuit with three resistors, and, without changing the voltage of the source, have 1 resistor with the equivalent resistance, it obviously dissipates more power as heat, despite the constant current through the circuit. But why? Why does potential energy per charge between two points translate to thermal energy? I thought that if voltage was a push, the potential energy would just get converted to kinetic energy in the electrons, so where did the thermal energy come from?
So, what is the best way I should conceptualize what's happening here? I can analyze a circuit and do KVL and KCL and Ohm's law and all that, but I want to actually know what I'm doing when I do that, so can someone please give me a good way to think about everything?