# I Voltage across two different circuits

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1. Mar 5, 2017

### Luke0034

I have a question regarding the voltage of two different circuits. In the first circuit there is a 75 volt battery with just one 4 ohm resistor. In a separate second circuit there is a 75 volt battery again, but this time there is a 4 ohm resistor and 9 ohm resistor in series. My question is this: Why is the potential difference across the 4 ohm resistor in the first circuit 75 volts, but not in the second circuit. In the second circuit, according to ohms law, the potential difference across the 4 ohm resistor is 23.08 volts, and the potential difference across the 9 ohm resistor is 51.93 volts, so the total voltage adds up to 75 volts, BUT WHY? I'm wondering how the system as a whole can tell how many resistors are in the circuit. Because the way I am seeing it right now, there is a potential that comes out of the positive terminal of the battery and reaches the 4 ohm resistor the same in both circuits, so why would it take more energy to cross the 4 ohm resistor in the first circuit, but less in the second circuit when the electrons are crossing the same resistor? Is it because of less current flow? Because according to ohm's law, the current flow across the 4 ohm resistor in the second circuit would be less. Can someone explain to why this is? Why does more total resistance in a circuit mean less current flow? I guess big picture: Why is ohm's law the way it is? Why does current * resistance = voltage?

2. Mar 5, 2017

3. Mar 5, 2017

### John Morrell

I get your question, because it does seem like information (e.g. the number of resistors in the circuit) is somehow being transmitted instantly to the electrons in the circuit, which would be a problem. But I also think I can see why it's actually not doing that, though you'd be well off checking my idea with someone else first in case I'm wrong.

First of all, if you use the analogy of water (which always works surprisingly well) in this same situation it might be a bit more obvious. There's a pipe, with a pump that puts pressure on the water, and narrow sections that resist flow. The pressure on the water is like the potential. The water is pretty in-compressible, so when the pump is turned on all the water at the beginning of the pipe starts pushing on the water further on, sending a pressure wave that propagates through the water at the speed of sound and getting all the water flowing. The water at those narrow portions pushes back a bit, meaning that the pressure wave that moves past each narrow section has a smaller magnitude than when it reached the narrow section. The greater the current, or in other words the more water is flowing past any part of the pipe at any moment, the more back-pressure is generated by each narrow section, because the water has to be pushed faster and faster to maintain a current through that narrow part of pipe.

When you first turn on the pump, there really isn't any way to know how many narrow sections are in the pipe, right? You can't tell until the pressure wave has propagated all the way through and the current is flowing at the same rate in the whole pipe. The speed of sound is pretty fast, so it'd be hard to notice the flow rate or pressure differentials adjusting. In a circuit, the electrons flowing are also extremely in-compressible, and their "pressure wave" travels at the speed of light, so within fractions of a millisecond the whole circuit has adjusted.

4. Mar 5, 2017

### John Morrell

While I do love the sentiment in this video I'd say the questioner counts as a student of physics who wants to know one level deeper than just ohm's law.

5. Mar 5, 2017

### cnh1995

It would be better if you wrote current=voltage/resistance. You apply voltage, current is decided by the resistance of the circuit. Naturally, more resistance means less current and the voltage drops should add up to the supply voltage.
This is Kirchhoff's voltage law. The sum of potential drops in a loop should be equal to the sum of potential gains in that loop, which means the total of potential changes should be zero in a loop.
Think about it. If this weren't true, where would the extra volts go?

See if this picture helps.

6. Mar 5, 2017

### Luke0034

I guess what I'm not understanding about this analogy and my big question in general is why the voltage drops all the way to zero after the last resistor. So let's just use your water analogy. The voltage starts out in a pipe and travels through a resistor (pipe with smaller radius), so shouldn't there be water coming out on the other side of smaller pipe (resistor)? But this doesn't make sense when measuring the potential difference before and after the resistor. Because before the resistor it is has the potential of the battery, and after the resistor it has 0 potential, so the difference would be the voltage of the battery. If the potential after the resister is 0, that essentially means there's no pressure after the resistor, which would mean nothing to move the electrons from the end of the resistor to the negative terminal of the battery. Oh wait I just answered my own question and had a eureka moment. The water coming out the other side is the current, and there doesn't need to be voltage after the resistor because the wire connecting the end of the resistor to the negative terminal of the battery requires no energy to move along, well almost nothing.

Also I think someone else in this thread said the current in the circuit is determined by the resistors present, so I think that explains why voltage across the 4 ohm resistor in the first circuit differs from the voltage across the 4 ohm resistor in the 2nd circuit.

So should I generally think of circuits already being adjusted l, because like you said, it hapens very quickly?

Another quick question, why does the pressure (voltage) drop in the water analogy when going onto the smaller pipe (resistor)? Doesn't pressure increase when forced through a smaller space, shouldn't the pipe get larger to decrease the pressure (drop the potential)?

Thanks guys, correct me where I might have said something wrong, but I THINK I'M FINALLY STARTING TO UNDERSTAND :)

7. Mar 5, 2017

### Luke0034

So if I'm understanding correctly, does this mean that according to Ohm's Law, the amount current flowing in a circuit will always change to a quantity that coincides with the potential dropping to zero after the last resistor in the circuit?

8. Mar 6, 2017

### CWatters

There is no first and last resistor in a circuit. You can analyse the circuit starting anywhere around the loop.

KVL just says that the voltages sum to zero. It doesn't say you have to "start" anywhere in particular.

9. Mar 6, 2017

### sophiecentaur

The Ohm's relationship applies to each resistor separately. The potential drop across each resistor is responsible for the current that flows. There is no need to consider what happens immediately after switch on; that is much more complex and involves an EM wave passing over the circuit. Once a steady state has been reached, each resistor has its appropriate share of the available PD from the voltage sources (batteries). Kirchoff's Laws give you a way to determine what the steady state gives you. They give you a set of simultaneous equation which you can solve. They are based on Energy Conservation around any loops in the circuit and Charge conservation at any node. Kirchoff supplies the 'knowledge' that each component has about what all the others are doing.
Feinman gets understandable tetchy when asked the question "WHY?" because there is no universal reason for any phenomenon. Someone earlier used the term "deeper than Ohm's Law" but Ohm's Law and the definition of Volts and Current are just one shell in the onion of understanding. It's self consistent within its gamut and will give you the 'right answers'. If you want details of a model of conduction within a substance, that's another issue. Stacking both models together can introduce confusion rather than clarity and, after all, you could say that QM ( and Nuclear Physics should be included in any circuit analysis. But why?
PS I often wonder if the desire to 'look deeper' into the Physics of electrical circuit analysis can actually be a reluctance to get ones hands dirty and go to the trouble of doing the Maths that's involved in the exercises. Understanding will never be acquired (or extended) until one is familiar with the nuts and bolts of the business. Worked examples may be a pain but they certainly give you an ability to progress where arm waving will let you down.

10. Mar 6, 2017

### Jony130

I think that you should start to use "black box" approach. Don't go too deep into the subject.
In the first circuit, we have one voltage source and one resistor. This one resistor is connected directly across the voltage source terminals ( two terminals A and B).
From point B to A the voltage is equal to VB and the resistor is also connected between point B and A, So the resistor will also see the same voltage across his terminals and this is why Vb = V1 (Vbattery = the voltage across resistor).

For the second case, we have one voltage source, but this time we have two resistors connected in series.
And again the voltage Vab = Vb. And notice that this two resistors are connected between terminal A and B, so the sum of V1 and V2 must be equal to VB.

And some water analogy

And some water analogy for parallel connection.

Notice that this time all resistor will see the same voltage (VB)

11. Mar 6, 2017

### rumborak

Yes, for anything we're discussing here, you can assume instantaneous steady state. And "steady" here means steady flow of current.

12. Mar 6, 2017

### sophiecentaur

My problem with your water analogy pictures is that they assume there is a gain in Kinetic Energy during each fall. This waterfall doesn't help at all because there is a great amount of energy transfer during the fall but none at all in a perfect wire. When someone is fed with a questionable analogy they are very apt to pick it up and run with it in totally the wrong direction. If you really feel that you have to use a water analogy, you have to have extremely slow flow of water through pipes (= wires) with no KE gained and hydraulic type motors (loads of pressure and no appreciable flow) in place of electrical loads. So which bits are you going to tell them are OK and which bits do they have to ignore?
To my mind, if someone is not prepared to think 'abstract' and use some Maths then they will have serious problems in understanding to a high enough level where they can take it further on their own and come to correct conclusions. Just what is wrong with the half dozen simple equations that we learn in early EE?

13. Mar 16, 2017

### John Morrell

I think for most people and most subjects, there is a difference in how we use equations to solve a problem and how we conceptualize the problem. I totally agree that analogies, which are never perfect, can be very misleading. But only knowing an equation and not understanding what you're really doing while using it can also be misleading.

If you find yourself having trouble with where an analogy breaks down, sometimes the answer is to go even more literally. A lot of circuit problems can be better understood conceptually by not thinking of them as "circuit" problems, but by thinking of them as what they really are; huge numbers of individual electrons pushing on each other and being pushed around by other things.

14. Mar 16, 2017

### Staff: Mentor

There is a name for doing that correctly. It is called QED (quantum electro dynamics).

The analogy of rubber balls pushing each other ignores the wave-like aspects of charged particle behavior. It ignores the crystal lattice of solids

The famous Drude model treats conduction like a pachinko game analogy. I hate that

I oppose analogies at any level in physics (even if I share the guilt in past posts ). They are pop science which is supposed to be forbidden on PF because they are not mainstream science. They lead to misunderstandings such as, "when the ball arrives at the other end, that is energy."

There are three valid and internally consistent levels to study electricity.
1. QED
2. Maxwells Equations
3. Circuits
We do a disservice to readers when we encourage fractional level reasoning, such as the water analogy 2.5 and the Drude Model 2.3.

I know that there is tremendous pressure from those who think circuits are too simple and Maxwells too difficult, but we should not encourage that.

:End Rant:

15. Mar 16, 2017

### sophiecentaur

Up to a point, I agree but people tend to have a hard cutoff about maths at a certain level. Possibly as a defence, they say that they need to know 'more' than the maths tells them. But they will all be quite prepared to use the maths at their level of competence and that very much goes to support their 'feel' (intuition) about stuff that they feel they understand. Maths isn't magic; it's just a model that can be applied to things. But the point is that it works extremely well- much better than a half baked analogy, and there are many analogies that are so full of holes that they are really false friends. Take, for instance, the flowing water model.Our intuition about that model uses Kinetic Energy of the moving water.** Applying that to explaining electricity is just plain wrong - really wrong - and takes you down totally wrong paths. So we end up with analogies that need to have a page and a half of caveats and exceptions but those are all ignored when someone tries to apply the analogy to a further step in understanding. I have to ask myself "why bother?", when all that's needed is to go through some easy worked examples in simple circuit theory and the 'rules' become as intuitive as all the other rules which we learned. And, in any case, those rules were not actually intuitive before we got familiar with them. Fact is that there are very many concepts in Science that just cannot be appreciated at the 'Concrete Level" of thought. It's Abstract stuff.
**There's a good example where things are not always as they might seem, intuitively. At the bottom of the feed pipe to a hydro turbine, which energy accounts for most of the Electrical Power that's generated - is it the KE of the fast moving water or is is the Force against the blades (pressure times area) times the speed they are rotating? You could produce the same amount of power if you increased the area of the blades and had more water flowing slower( tidal energy schemes), for instance. Where does all that fit in with electrical ideas?

Last edited: Mar 16, 2017
16. Mar 16, 2017

### John Morrell

Look, any analogy is obviously going to be unrepresentative at some level. That's what we mean by an analogy. But frankly speaking, isn't it a bit arrogant to assume that we've figured out the "way it all really works"? QED is the most direct way of looking at interactions between electrons and photons and the like, but when Gauss was looking at flux lines he thought the same thing.

Until we have a system that 100% accurately predicts everything in all realms of science harmoniously, we obviously haven't gotten to the bottom of it yet.

17. Mar 16, 2017

### John Morrell

It'd be great if we could just teach QED to everyone but frankly I don't really understand it well at all despite hours and hours spent researching it. It's hard stuff to understand. If you want more people, who don't necessarily have such good mathematical intuition, to understand this stuff, you've got to use some sort of analogies. It's just being realistic.

18. Mar 16, 2017

### rumborak

Entirely agree. I find these tirades against analogies a bit strange, since in a lot of ways, scientific theories are themselves mathematical analogies to what might, or might not, be reality.

The water analogy explains a lot of aspects of circuits correctly. Is it better to give all people an intuitive understanding that might not explain everything correctly, or is it better to have 2% of those people understand the true nature, and the remaining 98% not understand anything at all? As an engineer myself, whose professional life is essentially the art of using half-knowledge, I think the former is the better way. As long as the analogy is followed by "this is just an analogy, it's incorrect in certain ways", you can leave it up to the interested listener to maybe learn more.

19. Mar 16, 2017

### sophiecentaur

Normal circuit theory is perfectly self consistent you could say it's more a set of axioms which have been arrived at from experience. It works in the majority of cases and, where it doesn't, that's recognised and some extra factors are introduced. No Science pretends to be 100% accurate and it is only non-Scientists who claim that it should be.
The "true nature" of Electricity is never going to be known, even by the 2% - as with all Science. We try to follow a convergent path and that's a much as we should ever expect. There are 'rules' about how circuits work and they work in most cases and those rules are often all you need. If someone cannot handle them then they are just fooling themselves that there should be another arm waving analogy that will do as well. If it's too hard for someone then that's fair enough and there's no shame in it. Trying to give someone an analogy to explain how those rules apply is not helping them - except that it may make them feel better about it.
There are many topics in Science that are beyond average ability; it's a very difficult field. You should ask yourself what the purpose of an inadequate analogy is if it can't be applied to a problem and produce the 'right' answer. It's little more than a PR exercise for a system that likes to think it's 'educating' people in Science when in fact it's not.
Take the parallel situation in Maths education. Every step, from integer arithmetic (one sheep plus one sheep makes two sheep) to advanced Calculus, involves a steady increase in demand for the student. No one would attempt to describe the process of Autocorrelation in terms of sheep and goats. That would be daft. So why is it assumed that you can describe Electrical Theory in terms of other, more tangible things? Who is fooling who? I think it shows a lack of suitable respect for the subject when it's assumed to be simpler than it actually is.

20. Mar 16, 2017

### sophiecentaur

That would be a really bad idea because it's just too hard (as you have found). Of course Maths is an analogy but, when it has been show to model a system well, it is very robust and copes with most situations, allowing you to take things further. At the sort of level that circuit theory operates (or basic dynamics and static mechanics) we can be fairly sure that the Maths will not let us down because, if you start with a valid statement, the answer will (should) fall out in the end. There is no such assurance when you try to extend a physical analogy that the answer will be valid-EXCEPT when the maths of the two situations are the same (SHM, for instance).
But Maths can never tell you 'Why" and that is absolutely fine because it only does what it says on the tin. Unfortunately, people take a loose analogy and somehow believe that the 'Why' question is being answered. That is my basic problem with all but the best analogies.
My Maths packs up fairly soon along the way but, nonetheless, I have faith in it as a system and I 'trust' the answers of those who are better at it than I.

21. Mar 17, 2017

### Staff: Mentor

I agree! Also, anyone who has actually done fluid flow problems will realize that the circuit equations are much simpler. It would make more sense to use the simple electrical circuits to explain the complicated fluid flow than the other way around.

22. Mar 17, 2017

### Staff: Mentor

We have a model which accurately predicts all EM phenomena observed to date. That isn't arrogance, it is good science.

23. Mar 17, 2017

### Staff: Mentor

Because that is the only voltage and current which satisfies Kirchhoff's laws and Ohm's law.

Circuit theory is governed by Kirchoff's laws. Those laws are the answer to all "why" questions within circuit theory. Kirchoff's are taken as a given within circuit theory, but students should be aware that they are only valid in certain limits.

In addition to Kirchoff's laws there are a variety of constitutive relationships such as Ohm's law, which are used to constrain the voltage and current relationships. Those are not determined by circuit theory, but by experiment (this component behaves this way, call it a 1000 ohm resistor, that component behaves that way, call it a 1 farad capacitor).

24. Mar 17, 2017

### Staff: Mentor

Understanding and using circuit theory is not nothing. I studied Maxwells and QED, but my mastery of those subjects is tenuous at best. However, I built a 45 year career based on V=IR and P=VI (mostly in complex form because my field is power, and throwing in spoonfuls of thermo, nuclear, diffeq, and economics into the recipe). It is insulting to suggest that those who master only V=IR and P=VI are the 98% who understand nothing at all.

QED aside, I think Maxwells Equations are too difficult for many students (curls and integrals intimidate). The correct thing for them to do is to learn circuit theory well, and to practice its application the best they can. That is good education and useful education. The problem comes when students try to imagine "what is really happening" or "conceptualizing" on their own, inventing personal theories that their teachers did not teach. Then they spend their efforts doing that instead of becoming more proficient at circuit theory. They may feel better because they think they understand deeper because of pop sci, but in reality they are learning false lessons and do not understand actual physics. They dismiss V=IR and P=VI as being too trivial to be a place to stop before mastering all that V=IR has to offer.

My advice to those who feel math challenged is to stick with V=IR and P=VI and then try to go broader rather than deeper. If your math and physics is good enough for Maxwells equations, go for it. If your math and physics is good enough for QED, go for it. If not, then don't use pop sci to substitute for math and physics.

In most of the PF forums, such as QM, cosmology and relativity, personal theories, analogies, and conceptualizing are treated more harshly than here. They are likely to be shut down quickly by the mentors. Strict reading of the PF guidelines forbids personal theories and things that are not mainstream science. But I like it the way it is here on the EE forum. The mentors here are not harsh with those who try to use electrical analogies. Fear of the math and yearning for deeper understanding is quite human and something we all share to some extent. But that does not mean than we shouldn't rant and condemn the practice often, even if we allow it. We should try to steer people in the right direction which is choose to study electricity 3, 2 or 1 as a study subject. Don't try to invent, imagine, conceptualize, or propose fractional levels here on PF.

Edit: mangled quote repaired

Last edited: Mar 17, 2017
25. Mar 17, 2017

### Staff: Mentor

Let me try a different way: science may be on an endless quest to attain perfection in its explanations (and to the best of our knowledge, some are...even if that has been simultaneously true and wrong before), but most people never reach a level where perfection is even attempted. The problem of the thread - as most small scale circuit problems do - contains the simplifying assumption that the resistance in the wires is zero; The perfection is out the window from the start.

So while the theory here may be "perfect" it certainly isn't used in a way that attempts to harness the level of perfection it is capable of. As an engineer, I see little difference between simplifying assumptions, simplified models (Newton vs Einstein) and analogies.

In some ways, engineering is the art of knowing how to apply "perfect" theory to imperfect reality and still get a useful result. It seems to me like scientists don't like to admit they do that too, but they do it a lot, particularly at the levels of the problems usually seen here. At the same time, I do think they don't do it enough and overwhelm people with answers that are at a higher level than necessary, which the user is then unable to learn.

/rant