Resistors - Current equal in Series

[mk9898]

Hello,

I've been googling about this topic and have read from a number of different books but I still haven't found an exact answer to my question.

It is known that the current is equal when the resistors are in a series. But the resistors per definition reduce current flow. If there are 2 resistors R1 and R2 with different values, then the current flow in both of them will be different. The electrons will perhaps hit more atoms etc. If that is the case, then dQ/dt will in fact not be constant throughout the circuit and will be different when going through R1 and R2. Yes, the charges have nowhere else to go since there is only one path but still I am not convinced that "I" is the same through out the current circuit. I would speculate, that there would be some build up since the electric potential difference from the beginning of the circuit on the positive side to the very start of R1 will be higher than that of the electric potential from the beginning of R1 to the end of R1. Therefore there should be some time of build up of charge and the current will not be equal overall.

Can someone explain to me why this is false? I would really appreciate understanding why the current is the same throughout the entire circuit.

 

[Dale]

But the resistors per definition reduce current flow.

This is not correct. Per definition V=IR, so resistors make current proportional to voltage.

That I is equal for all elements in series is a consequence of Kirchoff's current law, and is not dependent on what types of components are placed in series. So being in series requires that the resistors share the same current, and the definition of the resistors (Ohm's law) requires that the voltage across each resistor be proportional to the shared current.

 

[mk9898]

"In electronic circuits, resistors are used to reduce current flow, adjust signal levels..." per Wikipedia.

 

[Dale]

What they are used to do is not the same as how they are defined. Ohm's law defines a resistor, and it simply establishes a proportionality between voltage and current.

Again, the more important fact is Kirchoff’s current law. Because of KCL all circuit elements in series must have the same current regardless of the details.

 

[CWatters]

If the current wasn't the same everywhere in a series circuit then charge would indeed build up and the voltage at that point would increase. However there would be nothing to stop it continuing to increase.

The water analogy isn't very good but... if you keep pouring water into a bucket the level keeps rising. It will only stop rising if you make a hole in the bucket so water can escape at the same rate.

 

[berkeman]

If there are 2 resistors R1 and R2 with different values, then the current flow in both of them will be different.

When they are in parallel branches of a circuit, that is correct. But not when they are in series. When two different value resistors are in series, the current through both is the same (because they are in series), but the voltage drop across each will be different according to V=IR as others have been saying. Hope that helps to clear it up for you. If you still are confused, please post an example schematic that we can all talk through with you.

 

[sophiecentaur]

But the resistors per definition reduce current flow.

Adding a resistor into a chain of resistors will just INCREASE the total resistance in the chain. This will reduce the current flowing through the WHOLE chain. Resistors are not like a leaky hosepipe which 'wastes' some water as it flows through. The same current enters at one end of the chain as leaves at the other end.
And, before you ask 'how the circuit knows about the resistors further along the chain', the initial process at switch on is that an electromagnetic pulse travels around a circuit and things eventually settle down to a steady state. The time taken for this to happen may only be a matter of nanoseconds.

 

[Integral]

The current source cannot know what individual resistor values are, It sees a NET or Total resistance which determines the total current. In conductive metals the current carrier is electrons. The number of electrons flowing past a point in the circuit in a second is the current. In order for different resistors in a series circuit to have different currents you would have to add or remove electrons this cannot happen.

 

[sophiecentaur]

The current source cannot know what individual resistor values are, It sees a NET or Total resistance which determines the total current. In conductive metals the current carrier is electrons. The number of electrons flowing past a point in the circuit in a second is the current. In order for different resistors in a series circuit to have different currents you would have to add or remove electrons this cannot happen.

I have no problem with the logic here, of course, but why bring electrons into it? So far in the thread we have used V, I and R and they were good enough for this sort of discussion before 1897. I just feel that you are opening up a whole new idea for people to be grappling with.
I realize that it may 'feel as if it's making it more mechanical and tangible but electrons are actually fit neither of those descriptions.

 

[mk9898]

Thanks everyone. After reading through the posts and more googling, I understand my error.

 

[Integral]

I have no problem with the logic here, of course, but why bring electrons into it? So far in the thread we have used V, I and R and they were good enough for this sort of discussion before 1897. I just feel that you are opening up a whole new idea for people to be grappling with.
I realize that it may 'feel as if it's making it more mechanical and tangible but electrons are actually fit neither of those descriptions.

Because they are the real phenomenon that is the source of all of this. To ignore them is a over complication.

 

[Dale]

To ignore them is a over complication.

Personally, I disagree (although I do recognize it is a matter of opinion and there is considerable variation).

To treat electrons correctly requires quantum electrodynamics, which seems excessively complicated to me. The question here is a question of circuit theory, it doesn’t even require Maxwell’s equations, let alone quantum electrodynamics.