Author Topic: REALLY why is current same through a series circuit?  (Read 17583 times)

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Offline FenderBender

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REALLY why is current same through a series circuit?
« on: January 23, 2013, 01:27:34 am »
I'm going a bit crazy. If you thought electronics is hard, well trying to figure out the physics behind it is another thing. I apologize in advance for not being a very competent physicist.

We all know that in a circuit consisting of a battery, some connecting wires, and a resistor has the same current throughout the circuit. It makes sense logically, but if you get down to the nitty gritty, you notice that as electrons move through a circuit, they loose energy, and though charge stays constant, the electrons loose voltage because V = J(energy)/ C(charge).

If we are talking about electron flow, (from - to +), then when the electrons get near the positive terminal of a battery, the voltage between the terminal and the electrons is very small, (close to 0). So if the voltage at that point in the circuit is close to 0, if we were to look at Ohm's law, it would say that I = VR, so if V approached 0, then I would also approach 0. But that is certainly incorrect, since we know the current is the same throughout the circuit.

I've read up a bit and I've heard the term gradient of voltage used. Sorry to bug you guys again for a physics question, but I'm trying to solidify the under-workings a bit.

Thank you.
« Last Edit: January 23, 2013, 01:40:30 am by FenderBender »
 

Offline tom66

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Re: REALLY why is current same through a series circuit?
« Reply #1 on: January 23, 2013, 01:43:26 am »
Just because a water pipe may loose pressure along the way does not mean that the rate or amount of water flowing changes through it.

Indeed, you can think of it as a charge model: the same charge must exit the battery per second, as must enter it again (of course, minus lost energy.)  If there was a difference, where are these mystery electrons either coming from or going to?
 

Offline FenderBender

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Re: REALLY why is current same through a series circuit?
« Reply #2 on: January 23, 2013, 01:48:15 am »
Right. Well it makes sense, conservation of charge at least.

Just wondering why the reduction in energy on the electrons would not correspond to a reduction in rate. I know it's not physically possible. And your analogy makes sense as do many others.

Is the rate the same because the electrons are all pushing on each other? Not like that makes too much sense for my caveman mind anyway.
 

Offline fbs

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Re: REALLY why is current same through a series circuit?
« Reply #3 on: January 23, 2013, 01:55:35 am »
So if the voltage at that point in the circuit is close to 0, if we were to look at Ohm's law, it would say that I = VR,

I = V/R!

V is small, but R is also small. So the V/R ratio stays just the same.
 

Offline FenderBender

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Re: REALLY why is current same through a series circuit?
« Reply #4 on: January 23, 2013, 02:18:37 am »
Wow mind just was blown.

All comes back to ohm's law now doesn't it.

Thanks. Sometimes you guys just make me feel dumb. Haha.
 

Offline raymohi

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Re: REALLY why is current same through a series circuit?
« Reply #5 on: January 23, 2013, 02:24:19 am »
It helps to remember that current is a rate of Coulombs per second. Just in my mind.

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Re: REALLY why is current same through a series circuit?
« Reply #6 on: January 23, 2013, 03:14:40 am »
With an AC circuit, the current will not be the same at different points in the circuit! Further away from the source, some current goes into cyclically charging and discharging the lines. It's negligible at low frequencies, but it can be very significant at RF.
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Offline FenderBender

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Re: REALLY why is current same through a series circuit?
« Reply #7 on: January 23, 2013, 04:22:54 am »
Tricky tricky
 

Offline AndyC_772

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Re: REALLY why is current same through a series circuit?
« Reply #8 on: January 23, 2013, 07:06:57 am »
With an AC circuit, the current will not be the same at different points in the circuit! Further away from the source, some current goes into cyclically charging and discharging the lines. It's negligible at low frequencies, but it can be very significant at RF.
Some energy may well be dissipated this way, but not charge. To suggest that current is not conserved is to say that charge is also not conserved, and that means electrons being either created or destroyed. This doesn't happen.

In the rf case, the problem is in creating a simple series circuit to analyse in the first place, because the small parasitic elements become significant and must be included in the circuit analysis.

Offline Kremmen

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Re: REALLY why is current same through a series circuit?
« Reply #9 on: January 23, 2013, 08:39:31 am »
I'm going a bit crazy. If you thought electronics is hard, well trying to figure out the physics behind it is another thing. I apologize in advance for not being a very competent physicist.

We all know that in a circuit consisting of a battery, some connecting wires, and a resistor has the same current throughout the circuit. It makes sense logically, but if you get down to the nitty gritty, you notice that as electrons move through a circuit, they loose energy, and though charge stays constant, the electrons loose voltage because V = J(energy)/ C(charge).

If we are talking about electron flow, (from - to +), then when the electrons get near the positive terminal of a battery, the voltage between the terminal and the electrons is very small, (close to 0). So if the voltage at that point in the circuit is close to 0, if we were to look at Ohm's law, it would say that I = VR, so if V approached 0, then I would also approach 0. But that is certainly incorrect, since we know the current is the same throughout the circuit.

I've read up a bit and I've heard the term gradient of voltage used. Sorry to bug you guys again for a physics question, but I'm trying to solidify the under-workings a bit.

Thank you.
Think of it this way: In a battery there is a chemical redox (reduction/oxygenation) reaction taking place. These reactions can be fearfully complex but the end result is always the same: a reduction reaction in one plate is absorbing electrons into bonds in the molecules of the plate substance. In the opposite plate, an oxygenation reaction is taking place, liberating electrons into the plate. The plate, being metallic i.e. conductive, permits the electrons to move.
Now there is an imbalance: an excess of electrons in the negative plate and a deficiency of electrons in the positive one. The mutual repulsion between similar sign charges distributes those charges in the plates so as to minimize the potential energy of the whole system. If you then connect the 2 plates with a conductor (i.e. substance that also allows electrons to move semi-freely between the molecules) this repulsion between similar charges / attraction between opposite charges will cause electrons to flow from the negatively charged plate to the conductor (in order to minimize the potential energy in the new situation). All along the conductor the similar charges behave similarly, causing the effect to ripple almost instantaneously to the other end of said conductor. That in turn is connected to the opposite plate of the battery, where the electrons meet the reducing reaction and are absorbed into the plates. So it is like the analogy with marbles that someone quoted: fill a hose with marbles, push the last one and the first one pops out from the other end. Same force - electromagnetic repulsion.
You can replace the battery with a generator as we do in the power grid and the result will be the same. In the first case the potential imbalance is created by a chemical reaction, in the second by pumping action with a magnetic field.

Now, on a macroscopic level this is put into Ohm's law and Kirchoff's current law - that the sum of currents entering and leaving a network node always equals zero.
The resistance of a circuit, and resulting power loss are explained straightforward by transformation of the potential energy in the electric field into heat. That potential energy in turn is created by the chemical reaction in a battery or by mechanical energy input to a generator.

So, an electron charge ("energy") of course is constant. The "pressure" or electric field, i.e. electron concentration in a (DC) circuit varies based on the properties of the material and affects the field strength (voltage) measurable at each point along the circuit. In AC circuits new rules come into play in the form of magnetic fields in inductors and electric field concentrations in capacitors. Combinations of these effects create the time-varying effects you see in AC circuits. Since those effects are the consequence of an electron "feeling" the magnetic and electric fields, the same phenomena are present also in DC circuits although to a far lesser degree. But that also explains the concept of distributed inductances and capacitances.

Hope it makes some sense.

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Offline JuKu

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Re: REALLY why is current same through a series circuit?
« Reply #10 on: January 23, 2013, 04:56:49 pm »
...when the electrons get near the positive terminal of a battery, the voltage between the terminal and the electrons is very small, (close to 0). So if the voltage at that point in the circuit is close to 0, if we were to look at Ohm's law, it would say that I = VR, so if V approached 0, then I would also approach 0. But that is certainly incorrect, since we know the current is the same throughout the circuit.
You forgot that at that point R approaches 0, too.
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Offline Gall

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Re: REALLY why is current same through a series circuit?
« Reply #11 on: January 23, 2013, 05:01:13 pm »
The answer is simple: generally the current is not the same.

When the electrical process gets stationary, there are no more changes of potential in any single point of the circuit. This means that every point has its elecron income and loss equal. We call it "current is the same".

In AC processes if the frequency is low enough we could count each moment as being stationary. This is true for most circuits up to 10s of MHz and sometimes even in GHz range. The above consideration still makes sense here.

99.9% of all electrical circuits fall into one of these two categories. The rest should be calculated carefully taking speed of light and EMI losses into account. In  0.1% cases there is no such thing as Kirchhoff's circuit laws anymore.
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Offline G7PSK

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Re: REALLY why is current same through a series circuit?
« Reply #12 on: January 23, 2013, 05:25:38 pm »
The current in a series circuit has to be equal at all points because it has to comply to the lowest denominator, Imagine a crowd of people all jostling to get to the other end of a que but there are doors in the way some will allow several people through at a time but one door only allows one person to pass at a time, the crowd can only go at the rate or speed allowed by the single door or highest resistance to the flow.   
« Last Edit: January 24, 2013, 11:32:42 am by G7PSK »
 

Offline Kremmen

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Re: REALLY why is current same through a series circuit?
« Reply #13 on: January 23, 2013, 05:27:37 pm »
Just 1 comment to your last sentence; I fail to see where Kirchhoff's laws would not apply. Please don't confuse a _point_ and a _region_. If there is an electric charge density gradient over a region, then equalization currents may very well flow in that region and the sum may not be zero. But for points the rule always applies.
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Offline Smokey

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Re: REALLY why is current same through a series circuit?
« Reply #14 on: January 23, 2013, 11:39:00 pm »
This discussion reminds me of this video.  I'm surprised no one posted it yet.  I would love to take classes from this guy.  Too bad he's mostly retired I guess.
 

alm

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Re: REALLY why is current same through a series circuit?
« Reply #15 on: January 23, 2013, 11:52:38 pm »
The closest you might get to taking a class from Walter Lewin:
MIT 8.02x on edX
 

Offline Smokey

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Re: REALLY why is current same through a series circuit?
« Reply #16 on: January 23, 2013, 11:59:11 pm »
Ya, but that's like reading the Feynman lectures.  Still awesome, but not as awesome as being there.  Talk about happening to be in the right place at the right time.  Those were some lucky undergrads.

~edit~
Sorry to get a little offtrack, but that makes me think about what happened to all those Caltech physics students that got to see the lectures live since he only did it for one class of students (2 years).  I wonder how many of them ended up doing something completely unrelated to physics or the sciences?
« Last Edit: January 24, 2013, 12:59:45 am by Smokey »
 

Offline IanB

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Re: REALLY why is current same through a series circuit?
« Reply #17 on: January 24, 2013, 03:58:40 am »
Some energy may well be dissipated this way, but not charge. To suggest that current is not conserved is to say that charge is also not conserved, and that means electrons being either created or destroyed. This doesn't happen.

Charge is conserved of course, but it is not correct to say that current is conserved. Conservation of charge is a general law, but conservation of current is not so. You must remember the general balance equation,

  input - output = accumulation

In flow terms, this becomes

  input flow - output flow = rate of accumulation

Relating this to current specifically, we have

  input current - output current = rate of accumulation of charge

Only when the system is (or can be assumed to be) in steady state can we say that the current everywhere in a series circuit is the same. For most practical purposes this is the case, but we must not assume it is a physical law. It is only an assumption that usually holds.

(Kirchhoff's current law does not contradict this. It applies to balances around a point, and since a point has no volume there is no possibility of accumulation. In all real world examples the conducting medium has volume and KCL is an idealization that is not exactly satisfied--but the error may be negligible, just as we may ignore relativistic errors when applying Newton's laws of motion to terrestrial engineering problems.)

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Offline IanB

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Re: REALLY why is current same through a series circuit?
« Reply #18 on: January 24, 2013, 04:06:37 am »
The current in a series circuit has to be equal at all points because it has to comply to the lowest denominator, Imagine a crowd of people all jostling to get to the other end of a que but there are doors in the way some will allow several people through at a time but one door only allows one person to pass at a time, the crown can only go at the rate or speed allowed by the single door or highest resistance to the flow.

There is a very simple real world example where the current is not equal at all points, and that is the Van de Graaff generator. When the generator is running there is a current of several microamps flowing into (or out of) the accumulation sphere at the top, but this is a dead end flow. The current flowing into the sphere is being accumulated there and is not flowing out again. There is a jam where the people cannot get out of the door and they are all piling up in the lobby! Eventually the pressure builds up beyond breaking point and all the people burst out of the door in a large mass--this is what happens when a spark leaves the dome of the generator and finds its way back to earth.

So the Van de Graaff generator is a series circuit where the current is not equal at all points (although it is on average). The current flows up into the dome from the ground electrode, but for considerable periods no current flows out of the dome back to ground. Only when the voltage reaches the breakdown voltage and a spark happens is there a momentary surge of current back to ground to balance things out.
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Offline Kremmen

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Re: REALLY why is current same through a series circuit?
« Reply #19 on: January 24, 2013, 06:39:33 am »
Ahh, maybe this is verging on sophistry, but before discharge the van de Graaf is not a _circuit_. Rather it is an artificially induced charge density gradient - the motor and belt acting as the charge pumps. Exactly the same thing happens in  a "normal" generator based on magnetic induction, should it feed a storage ball. The voltage would presumably be much lower but the same thing in principle. So, while Kirchhoff does not directly apply due to the (un)equalization current, i think it would be fair to say that the current is more or less equal along the generator. The charge storage ball of course is a macroscopic object and when the charge distributes in it, the moving charges (i.e. current)  of course separate over a region. So yes, if you want to concentrate on that part then of course you can select a subregion and say that the current is not equal to the total charging current. But the sum total entering the whole ball is. That's where it breaks down since as i noted, this is not a true closed circuit. So obviously the charges cannot continue to the opposite pole of the source.
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Offline FenderBender

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Re: REALLY why is current same through a series circuit?
« Reply #20 on: January 24, 2013, 01:21:41 pm »
What doesn't make sense to me is how an electron loses the same amounont of energy going through a 1ohm resistor as it loses going throgh a 1Mohm resistor. I know that a resistor only limits the rate of flow of electrons, but surely an electron would bounce around more in a 1Mohm resistor  than it does in a 1ohm resistor. So if it bounces around more, wouldn't it lose more energy? Where is my concept faulted here? How can the energy it takes to go between two points the same even if there is different resistances. Again I know that resistance only limits the rate of flow but I'm still uncertain?
 

Offline FenderBender

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Re: REALLY why is current same through a series circuit?
« Reply #21 on: January 24, 2013, 01:24:23 pm »
The way I'm thinking abput it is that the electron is doing the same amount of work, but the rate of that work is limted to the value of the resistor. So the resistor WOULD affect power since power is rate/time.

Am I wrong?
 

Offline G7PSK

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Re: REALLY why is current same through a series circuit?
« Reply #22 on: January 24, 2013, 03:29:04 pm »
The current in a series circuit has to be equal at all points because it has to comply to the lowest denominator, Imagine a crowd of people all jostling to get to the other end of a que but there are doors in the way some will allow several people through at a time but one door only allows one person to pass at a time, the crown can only go at the rate or speed allowed by the single door or highest resistance to the flow.

There is a very simple real world example where the current is not equal at all points, and that is the Van de Graaff generator. When the generator is running there is a current of several microamps flowing into (or out of) the accumulation sphere at the top, but this is a dead end flow. The current flowing into the sphere is being accumulated there and is not flowing out again. There is a jam where the people cannot get out of the door and they are all piling up in the lobby! Eventually the pressure builds up beyond breaking point and all the people burst out of the door in a large mass--this is what happens when a spark leaves the dome of the generator and finds its way back to earth.

So the Van de Graaff generator is a series circuit where the current is not equal at all points (although it is on average). The current flows up into the dome from the ground electrode, but for considerable periods no current flows out of the dome back to ground. Only when the voltage reaches the breakdown voltage and a spark happens is there a momentary surge of current back to ground to balance things out.

With the Van De Graf surely we are no longer talking about a purely resistive circuit, Capacitance has been introduced, the capacitance between the two spheres on the one hand the top of the Van De Graf and the other the one we call Earth. There fore it takes time for a charge to accumulate to a sufficient point that there is a dielectric breakdown. In a straight resistive circuit the current has to be equal at all points (the PD might alter) conservation of energy will tell you that the current has to be the same 
 

Offline IanB

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Re: REALLY why is current same through a series circuit?
« Reply #23 on: January 24, 2013, 04:06:14 pm »
What doesn't make sense to me is how an electron loses the same amounont of energy going through a 1ohm resistor as it loses going throgh a 1Mohm resistor.

Before we discuss whether this is right or wrong, I'm curious, what caused you to think this? Did you read it somewhere, did someone tell it to you, or did you conclude it from other facts? You are stating something as a fact--"an electron loses the same amount of energy going through a 1 ohm resistor as it loses going throgh a 1 Mohm resistor"--and asking why it is, when your supposed fact may not be a fact at all.
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Offline Kremmen

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Re: REALLY why is current same through a series circuit?
« Reply #24 on: January 24, 2013, 04:07:13 pm »
What doesn't make sense to me is how an electron loses the same amounont of energy going through a 1ohm resistor as it loses going throgh a 1Mohm resistor. I know that a resistor only limits the rate of flow of electrons, but surely an electron would bounce around more in a 1Mohm resistor  than it does in a 1ohm resistor. So if it bounces around more, wouldn't it lose more energy? Where is my concept faulted here? How can the energy it takes to go between two points the same even if there is different resistances. Again I know that resistance only limits the rate of flow but I'm still uncertain?

and

The way I'm thinking abput it is that the electron is doing the same amount of work, but the rate of that work is limted to the value of the resistor. So the resistor WOULD affect power since power is rate/time.

Am I wrong?

Think of it this way: the electron does not do any work - it is only the medium by which work is done. It is the source of electrons that is doing the work. E.g. a battery converts chemical energy into electric field by liberating electrons in a redox reaction. Or a generator that converts mechanical work into an electric field by pumping the electrons. It is this field that pushes the current through the circuit. The electrons stay as they are, not gaining or losing energy (let's ignore kinetic energy here).
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