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So I am a 10th grade student and my teacher told me that the current is the same at every point in a series circuit. It does split up in parallel circuit but it then recombines and the current flowing out of the battery is the same as the current flowing back into it.

My question is - Why does the current remain the same?

I mean let's say that there is a light bulb somewhere in a series circuit. Now, current(or electrical energy) will flow into it and then convert into light energy.

But if the amount of current flowing into the filament of the bulb = the amount of current flowing out of the filament and at the same time it is producing photons(light energy) [and some heat energy too] then aren't we creating energy ? Which is not possible.

I am really confused and can't seem to grasp this idea. Please help.

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    $\begingroup$ Current is charge per time. Since charge is conserved, the same charge that flows into a circuit has to flow out, again. The energy in a circuit, on the other hand, is not represented by the current but by the electric potential. A current that flows into one part of the circuit at a higher potential and that leaves at a point of lower potential will perform work on that part of the circuit. If the potential was the same, no work would be performed. $\endgroup$ – CuriousOne Jul 24 '16 at 6:50
  • $\begingroup$ Good question. As you could see from the example with water or sliding blocks the gravitational potential is responsible for energy release in mechanical systems. For a battery this can't be the reason of energy storage. Kinetic energy can't be the reason too. At the end an electromagnetic interaction rearrange the electrons into different chemical bonds. And pushing electrons some part of the EM radiation over goes to the electrons. So beside the potential (gravitational) and kinetic energy there is storage of EM energy. You feel it right. $\endgroup$ – HolgerFiedler Jul 24 '16 at 8:41
  • $\begingroup$ Your mistake is equating current with energy. Energy and current aren't the same. $\endgroup$ – user2520938 Jul 24 '16 at 11:20
  • $\begingroup$ Because the electrons don't pile up in the lightbulb. Every time an electron goes into the lightbulb another one comes out the other side. $\endgroup$ – user253751 Jul 24 '16 at 20:44
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    $\begingroup$ Energy is simply a scalar value representing the change in state of the object (battery). In the realm of electricity, the change in state is the change in where the charge particles (electrons) are positioned. Taking this into the entropy formula with the the probability of finding electron in a cell space inside the battery as basic event, after electrons move from one polar end to another you have more evenly distributed probability of finding electrons in all cells. This means an increase in entropy with that encoding (cell and electron's position). This is where light/energy comes from. $\endgroup$ – user124111 Jul 25 '16 at 6:02
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I'm surprised that no one has yet mentioned the hydraulic analogy for electricity to help the OP understand better. A brief summary of this analogy is:

Electricity is like water flowing through pipes.
Current = amount of water flowing through pipe
Voltage = pressure of water
Power = water pressure x water flow (voltage x current)
Resistors = constrictions in pipe. Pressure (voltage) drops occur across them.

Any point in a (series circuit) pipe has the same amount of water flowing past that point as any other.

Any split in a pipe (parallel circuit) shares all water flowing into the split (the current of all legs equals the current before the split)

There are also water analogies for other electrical components like coils and capacitors; visit the link if you are interested.

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    $\begingroup$ Probably because the tired old hydraulic analogy only works well if you're already a plumber, and it leads to a couple of misconceptions that we have to handle over at electronics.SE. $\endgroup$ – pipe Jul 25 '16 at 10:23
  • $\begingroup$ Water in a full pipe flows uniformly because of water incompressibility. But why is flow of electrons "incompressible" ? $\endgroup$ – James Well Aug 18 '17 at 23:55
  • $\begingroup$ @JamesWell: liquids do compress, just not very much (for a given amount of pressure) as compared to, for example, gasses. In the same way, electrons (current) doesn't compress well because electrons repel each other due to their charge. $\endgroup$ – Mark Ripley May 25 at 11:19
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Imagine a block sliding down a slope and that there is an amount of friction between the slope and the block such that the block slides down the slope at constant speed.

As the block slides down the slope it loses gravitational potential energy and an equal amount of heat is generated due to the friction between the slope and block.
The block does not change but is part of the mechanism by which gravitational potential energy is converted into heat.

You can think of the electrons as being charged blocks which are losing electrical potential energy (sliding along a potential gradient at the drift velocity) and this energy is converted into heat and light in a light bulb.
When the electrons reach the positive terminal of the voltage source they are then given more electrical potential energy by the voltage source and so can again slide along the potential gradient.
The electrons do not change and are not created or destroyed rather they are part of the mechanism by which electrical potential energy is converted into heat and light.

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    $\begingroup$ So in the analogy, the battery is like a winch that pulls the electron/blocks back up to the top of the slope? You know a very similar analogy might be a roller coaster. The same number of cars are always going by in the (series) circuit. The winch that pulls the cars up to the top of the hill is the battery. The noise made by the cars as they go around curves, etc. is the light from the lightbulb (or whatever). The cars just have energy added to them by the winch and they give up that energy during the ride (more or less). $\endgroup$ – Todd Wilcox Jul 24 '16 at 16:27
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Why does the current remain the same?

Interesting question. As you could see from the examples with falling water or sliding blocks the gravitational potential is responsible for energy release in mechanical storage systems. For a battery this can't be the reason of energy storage. Kinetic energy inside the a battery can't be the reason too. At the end in the battery an electromagnetic interaction re-arrange the electrons into different chemical bonds. And pushing electrons into re-arrangements some part of the EM radiation over goes to the electrons. Electrons are able to store EM radiation or more precise to store photons. Mostly some part of the energy will be released again in the form if longer wavelength photons and this is why the storage of energy in accumulators is inefficient.

So beside the potential (gravitational) energy and the kinetic energy there is a storage of EM energy. You feel it right with our question. The electrons at the end of the circuit are of the same amount and of course of the same charge. The release of energy in a bulb as well as in the wire due to the Ohm resistance is only possible because before the electrons are charged with EM energy.

Note, that such an explanation, if you could not find in literature, should not be wrong but could be new. So your question touches an interesting point of the interaction between electrons and EM radiation.

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If the amount of electrons remain the same, where does the energy come from?

Batteries have energy stored inside. The energy inside a battery could accelerate electrons to a very high velocity. However, this doesn't happen in a circuit. Just as the battery speeds up an electron, the electron hits to another one and remains constant speed. So the battery constantly pushes the electron but in the end it comes back to it with the same velocity. It's like shooting a ball downward from a high place with speed of $10$ and it gets to the ground at the same speed; though we expect it to hit the ground with a greater speed (due to the force of gravitation).

The battery is constantly pushing but the electron remains in the same velocity, now it makes sense. The energy released by the battery gets used in the circuit and becomes heat which can later become light.

A good example of what I'm describing would be water turbines. When a water turbine is set, say along a waterfall, the amount of water came in equals the amount of water that flows away. So where does the energy come from? Like the electron and circuit case, it's all about velocities and electrons and water are only energy carriers.

(Note that this answer is based on free-electrons model which is now replaced by more accurate ones which are taught in university level.)

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But if the amount of current flowing into the filament of the bulb = the amount of current flowing out of the filament and at the same time it is producing photons(light energy) [and some heat energy too] then aren't we creating energy ? Which is not possible.

Current is the flow of charge over time , Q/t. It can be larger of smaller depending on the resistance in the circuit. Suppose you have a battery with a voltage drop Delta(V), it is related to the current by

Delta(V) = R*I

Where R is the resistance in the circuit. If there is less resistance, removing the lamp for example, the current will be higher.

It is the battery that is supplying the energy to the charged electrons which will scatter in the light bulb and create light and heat. So it is a total solution of the circuit which determines how much light the bulb gives. The current is the carrier.

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Current is a measure of how many electrons go past a particular point in the circuit every second. So there are electrons rushing into one side of the light bulb, and rushing out of the other side. The number rushing IN each second is equal to the number rushing OUT each second. If that wasn't the case, then there'd be a build-up of electrons inside the light bulb; which would hinder the flow of further current.

Although the number of electrons rushing into the light bulb each second is equal to the number rushing out of it, each electron loses a little bit of energy on its way through the light bulb; and that's where the light comes from.

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