Why must current loop in a circuit?

Question

This is a problem that's bothering me for a while, and I'm going off accepting other people's claims rather than figuring out the first principles of circuits.

Consider this circuit right here. From my understand, when an electron/current from the 5mA source goes to the ground, it can't go to the 0.01Vo source because it would violate the circuit law of going back to a node without looping.

But from a physics standpoint, I know charge moves from high to low potential, and voltage sources need to produce some sort of electromotive force to bring a looped electron back to high potential. And in this circuit, once an electron goes to the ground, why can't it be stolen by another source and brought back to high energy? Said differently, why does current have to loop when the only thing an electron knows is to move in the direction of the direction of an electric field and not that it needs to travel to each node only once per loop?

Answer 1

You are confusing electrons and current.

Current is a macro-scale phenonenon that is the mass movement of electrons. Even "small" currents for electronics mean that many many electrons (or other charge carriers) are moving around. For example, just 1 µA flowing thru a wire means that, on average, there are 6.24x10¹² electrons flowing past any one point every second. With that many electrons to average over, the average is quite reliable.

However, individual electrons behave probabilistically. You never know where any one electron is or what it's doing. One electron in your left current loop could have diffused over to the right side after getting to the ground conductor, and from there got swept into the right current loop. There could be 100s of electrons doing this every second. However, there would then be, on average, a equal number that go the other way every second.

Trying to follow individual electrons is pretty much impossible, and not useful anyway. You don't care that 100 electrons went one way, while at the same time 100 other electrons went the opposite way. At the higher level, you have 0 current, and that's all you care about.

Another point is that individual electrons don't actually go far or fast, on average. 5 mA isn't a steady stream of electrons all whizzing around at the speed of light thru the loop. It's local electrons moving a little, which push on their neighbors, which cause them to move, which push on their neighbors, etc. The propagation of electron motion one place causing electron motion further down the wire proceeds at a good fraction of the speed of light, but individual electrons don't need to move fast or far for that to happen.

The 5 mA thru the left loop means that in the aggregate 31,207,500,000,000,000 electrons are heading one way every second past any one point in the loop. Note that this says nothing about how fast any of the electrons were moving, or how far individual electrons moved.

Suppose I told you that a particular river has a flow of 1,000,000 liters/second. What is the speed of the water? How many liters are in a small snippet of the river? If I put a drop of dye in the river upstream, where exactly will it go?

The point is you don't know any of these things from just the flow rate. Likewise, you don't know what individual electrons are doing just from knowing the current.

Answer 2

When solving problems one builds mathematical models. Those models are necessarily approximations of reality. We explicitly or implicitly decide what things we are going to consider and what things we are going to ignore.

An important thing to remember is that current flow caused by an electric field will change the charge distribution in such a way as to reduce that electric field.

So yes if two charged objects are connected together there will initially be a current flow between them but very quickly the potential will equalise and the current will drop away. For a sustained current flow a circuit is needed.

Most of the time we model our circuits as a group of "components" and work under the assumption that the net charge on components is zero and that charge only enters or exits a component through it's terminals. It's not a perfect model but it's good enough most of the time and it's simple enough that we actually stand a chance of solving it.

Answer 3

Electricity is the movement of electrons and what goes in must come out (or what goes out must come in).

When you take a transformer the current is induced so only the free electrons of the atoms that make the cable are used. No electrons are added or removed thru the transformer only the free electron of the conducting metal is pushed. If no electron was given back the conducting metal would not have any free electron to keep the current going and the current would stop.

This is roughly what happens when you charge a battery (or capacitor). You move electrons to one side and create "holes" on the other side. When it is fully charged no more current can flow. In the reality, if you force too much electrons in the whole thing will go BAM! ("electrons and holes meet each other violently"). But you have to force it, they will never do it by themselves unless something goes wrong.

It's like having piped filled with water. A circulation pump is like a power source (pressure is voltage and flow rate is current). A battery is a double ended reservoir with a center diaphragm (you can push water in but water has to come out the other side and if you try to push past it's maximum it's blow)

Now if you take your example and build it with water pipes you will see that nothing is lost from one side to the other but both side can exchange water but the sum of the currents is 0.