I'm a little confused about "voltage". We learned that voltage is somewhat similar to electric field: a way to refer to the potential energy of a charge A when put near charge B without actually knowing the charge of charge A. That made sense to me, but then suddenly in class (this is college physics by the way) we're refering to the voltage in a battery as a source of current... and i guess i didn't really get the transition from the voltage of a point in relation to a point charge, and voltage as some abstract value of a circuit thats equal to the current times the resistance. I mean i can do the math and solve circuit problems, the whole E=IR thing is simple enough to use, but i don't get how "voltage" applies to the situation. I kind of see circuits being similar to a river with a mill in it- as the water flows by the mill some of it's kinetic energy is transfered to the wheel. While the current of the water is the same before and after the water interacts with the wheel, the velocity(and energy) of the water changes. Is this a good way to think of it or is this a horrible comparison? And if it's a sound comparison, what would the "voltage" be, the difference in gravitational potential energy between the source and mouth of the river?