Why current in series circuit is the same?

I have read in the internet that the charges do not have any other path to go and they must go through the same in a series circuit,hence the current is same.

It was quite convincing but what confused me was: "A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. Resistors act to reduce current flow..."(according to the Wikipedia). This means that the resistors slow down the rate of flow of charges. By definition, electric current is the rate of flow of charges. Then must not the current be reduced in a resistor even when the amount of charge is same?

• A case of what is pushed out at one terminal of the battery (namely electric charge), returns to the other terminal (there are no leaks). Even more than this, since charge doesn't pile up anywhere, the rate of charge that leaves one terminal is the same as returns to the other terminal, and "rate of moving charge" is called current. – jim Apr 24 '16 at 19:06

Consider the following analogy to water pipes: Wires are like pipes already filled with water; the water resembles the movable charge, in case of metal electrons. Voltage is a pressure difference between two points, e.g. because one is higher up than the other. The pipes are really broad in comparison to the slow flow of water in it, so one can ignore friction/turbulence. Resistors are like chokes, simply a very narrow passage.

From this point of view it should be clear that the $$\frac{volume\space of\space water}{time \space interval}$$ is the same everywhere in the pipe. If you leave the pressure constant and enlarge the choke point, there will be more flow of water. If you squeeze it almost tight, there will be almost no flow of water, even though the pipes are nice and wide everywhere else.

From this point of view it should be really intuitive and trivial how simple circuits involving Rs and voltage sources behave.

My guess is that you confused current (which is $$\frac{charge}{time \space interval}$$ ) with the speed the charges move, which is called [drift velocity](see wikipedia).

This site has correct and very intuitive explanations of related concepts, and Ohm's Law and parallel circuits are very important but also easily understood given the analogy I gave above.

Yes, but where is the problem? :)

If you have a resistor in your series circuit, then the current is reduced - in the whole circuit, of course, not just in the resistor. The current is the amount of charges per time. There are just less, in a certain time, but they still have to pass through all the other elements of the circuit too.

• I thought the current is reduced only in the resistor and that is where my confusion was. – Gayatri Apr 24 '16 at 1:01
• If you have a resistor in your series circuit, then the current is reduced" - This isn't necessarily true. For example, adding a resistor in series with a current source will not reduce the series current. – Alfred Centauri Apr 24 '16 at 1:16

What this means is that the resistor reduces the current compared to a circuit that didn't have the resistor in it.

Say you have circuit with a bulb and a battery in which 0.5 A of current flows. If you then introduce a resistor in series with the bulb the current everywhere in the circuit will be less than 0.5 A. The current entering and leaving the reistor will always be equal.

Resistors act to reduce current flow...

I will give a counter-example to the claim that resistors "act to reduce current". Consider a $9V$ battery connected across a $100\Omega$ resistor; the battery current is $90mA$.

Now, connect another $100\Omega$ resistor in parallel with the first. The battery current increases to $180mA$.

Here's another counter-example. Adding a resistor in series with a current source will not reduce the current but will, instead, increase the voltage across the current source.

So, a blanket statement like "resistors act to reduce current" is as misleading as the ubiquitous "current takes the path of least resistance".

That fact is that a resistor has a voltage across that is proportional to the current through. You must apply this to your particular circuit arrangement to determine if adding a resistor will decrease, increase, or leave unchanged, a particular current.

I have edited the Wikipedia article to read "may be used to reduce current..." however, edits on electronic articles typically have a short half-life.

Your confusion can be met with a practical scenario. You know that it'e the electrical energy that is carried from the battery to the load by the electrons. A connection wire has very good conductivity. A resistor obstructs the flow of current. Inside the resistor, the electrons lose their energy in the form of heat due to collisions with the atoms and only the remaining energy is passed through the load. This is why some potential drop occurs across a resistor. Now let's go to the everyday scenario.

Imagine the flow of water through a small river that has many branches. the water is flowing with some energy, which can be accounted as it's kinetic energy. Now, let there be some obstacles in it's way. The same amount of water passes through it, but the flow of water get reduced as the water loses it's kinetic energy due to collisions. Now there are two branches of the river. The amount of water flowing through branch 1 will depend on how much resistance the water has to face through branch 2. (It's the potential divider rule). If more resistance is at branch 2, then only a little water flows through there and more of it flows through branch 1.

This is the case that happens in an electric circuit. The battery is the electrical energy source. The resistor is used to cut off some energy from it. In each details explained below, think in analogy about the flow of water in the river illustrated above.

When you connect two resistors in series, then the same current flows through them. Current is the no. of charges (not the amount of charges) flowing through a point in unit time. Since the electrons have no other way to go, they go through the resistors. The resistors could slow down the electrons. But it cannot block some of the electrons. So the current is the same. But due to the presence of resistors, the electron loses some of it's energy gained from the battery there which appears as heat in the resistor. So, at the first resistor, the electrons lose some energy and the remaining energy goes to the second resistor. There also, it loses some energy again.

Now, if you connect the resistors in parallel, the path of the electrons on reaching a point get split into two paths and then again meet at some other point. As in the case of river, now the current has got two paths for flowing. The splitting up of current depends on the value of the the resistances. The amount of current flowing through resistance 1 will be determined by the resistance 2. If resistance 2 has more resistance than the first, then more electrons will go through first and vice versa. So the potential difference between the two points will be the same, but the current will be different and it has to be so as per Ohm's law.