How can I physically interpret voltage and current?

My understanding of an electrical current is that it is the flow of electrons through a material. The only magnitude I can fathom for this process is the number of electrons which are flowing.

I know ohms law, and how some of the basic components of a circuit work (resistors and capacitors, specifically). If there is a circuit attached to a 120V power source, the voltage at the beginning of the circuit will be 120V, and at the end of it will be 0V. When the current experiences resistance, voltage is lost, so more current has to be supplied to the circuit so that exactly all of the voltage is lost by the end of the circuit.

My question is: what is happening when voltage is lost? When current is increased? When learning about capacitors in university, I understood that voltage is built up on each plate by electrons flowing in and spreading out across the surface of the plate. But if voltage is the number of electrons in a circuit, what is current? And if all voltage is dropped at the end of a circuit, where do the electrons go? I figured that since electrons won't build up ad infinitum throughout the circuit (obviously since everything would build up an increasingly negative charge), the magnitude of the current must be the number of the electrons. But then what is voltage? What is lost? How should I interpret the stored charge on a capacitor?

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One way of viewing it that you may find useful is as a fluid comparison; the rate of flow is analagous to amount of electrical current, while the fluid pressure is analagous to electrical voltage. –  Michael Luciuk May 31 '11 at 22:34
As David Zaslavsky says in his answer, flow of electrons is common but not the only current. In any battery or accumulator or electrolysis cell there is no electron flow, but ions! –  Georg Jun 1 '11 at 8:54

Current is defined as the total amount of charge that passes through a surface per unit time, and voltage is defined as the electrical potential energy per unit charge. So, for the usual case in which electrons are the charge carriers, the amount of current corresponds to the number of electrons, and the voltage corresponds to the potential energy that each electron has.

When voltage is lost (by which I presume you're talking about the voltage decrease as you move along a circuit), it just means that the electrons lose potential energy as they move through the circuit. By the time they get to the end of the circuit (the positive terminal of the battery), they've lost all their potential energy to collisions with atoms in the wire. Then they go through the battery and get their energy replenished, so they can start the cycle over. Keep in mind that the same electrons keep cycling through the circuit over and over again - they don't go anywhere when they reach the end.

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I think my difficulty stems from not being able to wrap my head around electric potential. I've used it, done math with it... But I don't quite get what it "is," compared to gravitational potential or the like. –  Carson Myers May 31 '11 at 22:48
@Carson: physically, potential is just the potential energy per unit charge. For a given electric field, a particle with twice the charge will have twice the potential energy if you put it in the same place, but the ratio of energy to charge, the potential, is the same (so it depends only on the field, not on the charge you put in it). The closest equivalent for gravity would be the product $gh$ (gravitational acceleration times height), but for whatever reason we don't give that its own name. –  David Z Jun 1 '11 at 1:12
@david okay, I think I understand. Thank you for clarifying. –  Carson Myers Jun 1 '11 at 4:13
@Carson: glad that helped. It also just occurred to me that I misspoke slightly: the closest equivalent to potential for gravity in general would be $GM/r$ (Newton's constant, times the mass of the gravitating body e.g. Earth, divided by the distance from its center). $gh$ is just an approximation that applies near the Earth's surface. And the quantity $GM/r$ is occasionally called "gravitational potential." –  David Z Jun 1 '11 at 4:18
Oh, and just in case it wasn't clear, "potential" (or "electrical potential") is essentially the same thing as "voltage," but not the same as "potential energy." –  David Z Jun 1 '11 at 4:20

Without going into the depths of things like displacement current and semiconductors (which is when we learn that everything we were taught in Electricity 101 was a lie), you have it basically right: Current is the flow of electrons. More quantitatively: 1 Amp = a charge flow of 1 Coulomb/second = 6.25 x 10^18 electrons/second.

Voltage is the force with which the electrons are forced through a circuit. Voltage can be thought of as an electromotive force.

Voltage is NOT the number of electrons in a circuit nor on a capacitor. However, the number of electrons on a plate of a capacitor can produce a voltage which (typically) resists current flow. That is: the electrons in a capacitor create a voltage which opposes the voltage which forced the electrons onto the capacitor plate.

When an electron gets to the end of a circuit, it really hasn't gotten to the end of the circuit. It has only gotten to the part of the circuit you see on the schematic in your text book. After that it has a long journey back to the power plant, where generators pump it back out to somebody else's hair dryer or toaster oven. Or, in the case of battery powered electronics, it fuels a chemical reaction.

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I like most of this, except "Voltage is the force..." Voltage is a potential, so a force would be charge multiplied by the gradient of voltage. –  Mark Eichenlaub May 31 '11 at 21:45
okay I see, I have a hard time imagining this though. I think of potential as lifting something, compressing a spring, etc. Maybe I'm digging too deep here, but what properties of an electron change when it is given potential? –  Carson Myers May 31 '11 at 22:46
Carson: No physical properties change, more how much the electron wants to go from a to b increases or decreases with its potential (or better, the potential of the position the elctron is at). If I lift a weight against gravity I am doing work and the energy is going into the potential of the object, same with a stretched spring, same with an electron and proton. They 'want to be together' and so moving them apart is just like lifting a weight above the earth... –  Nic Jun 1 '11 at 9:32
@ Mark --> Agreed, my choice of words was sloppy. Voltage is a potential. It needs something upon which to act to create a force. Just like gravity is a potential, but it needs a mass upon which to act in order to create a force. –  Vintage Jun 1 '11 at 21:46

electrons dont go through the ac cicuit. they just vibrate around (50Hz), almost steady

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There is some truth to this statement, but it is far to sparse to be of much value. –  dmckee Jun 3 '11 at 14:22