# I Conceptual Understanding for Voltage in a Circuit

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1. Mar 21, 2017

### Blissed

I'm having trouble understanding circuits, particularly voltage. So my question is more of a conceptual dilemma. Please correct my definitions and relations if it is incorrect. Voltage is the energy provided per charge, and this energy is converted to KE once the circuit is closed, or in other words it influences the velocity of the electrons, and in effect influences the current.

For instance, in a simple circuit made up of a battery and a resistor, the voltage drops to 0 once the electrons pass through the resistor, or the energy provided by the battery is all dissipated. Then why is the current still constant? If the voltage drops, doesn't that imply a drop in velocity of the electrons? So shouldn't it lead to a decrease in current as it leaves the resistor?

A follow up question is, why is the voltage drop the same in a resistor as the voltage provided by battery? How does a resistor "know" that it should use up the same amount of voltage provided by the battery?

2. Mar 21, 2017

### .Scott

Voltage is not energy - it is a difference in charge. If you think of water levels, it is a difference in water levels - but the size of the body of water is not relevant.
So, an electrostatic charge may give you a 20Kv voltage compared to you environment, but the energy involved may be slight.

When voltage is applied to a resistor, the current will be proportional to the voltage and inversely proportional to the resistance. So if a battery is connected to a resistor, the current will decay as the voltage provided by the battery decays.

Since the battery and the resistor have both ends tied to each other, they will always have the same voltage across them.

3. Mar 21, 2017

### sophiecentaur

I think you should do some homework before you try to 'explain' something to someone.
Voltage and charge are different quantities entirely. (You would not say that a head of water in metres is the same as the difference in volume between two tanks of water.)
Voltage is Energy per Unit Charge and it represents the Energy that is available or used up as units of charge move round a circuit. One volt is One Joule per Coulomb.
That's more like it. 20kV gives 20kJ to every Coulomb it supplies but, often, a very tiny charge is involved (say 1milliCoulomb) so the actual Energy would only be 20J.
That confuses everyone. The current that flows through a Resistor is determined by its Resistance Value but that is true, only after a certain (short) amount of settling time. Initially, an Electric Pulse flows along the wires and the steady current flowing is given by I=V/r. Things in Science don't "know" whats happening or what part they play in a system - they just behave according to the rules. Those rules have been formulated as a result of many measurements. Resistors behave 'as if they knew' about the rest of the circuit. Does the idea of a settling time satisfy you? It deals with the 'knowing' problem.

4. Mar 21, 2017

### Blissed

So I should just take that it's a given that the voltage will be the same? It's just the current that changes depending on the resistor. I mean I can understand this from the formulas itself, but I'm trying to visually and conceptually understand why this occurs. I imagine an electron moving through a resistor with a certain amount of KE provided by the battery. Once it collides with the molecules in the resistor, the KE provided by battery can drop to 0. However, in a different scenario, what if that electron leaves the resistor with a portion of KE provided by the battery intact, doesn't that imply the voltage drop for that electron isn't exactly equal to the voltage of the battery? So that's where my two questions come from. Why can we comfortably say that the voltage drop in a resistor is equal to the voltage in the battery?

As for my first question, why is the current consistent as it exits and enters the resistor? If the current is affected by the velocity of the electron, and the velocity of the electron correlates with the voltage provided by the battery, doesn't this imply that the current changes since the KE of the electron changes as it traverses through the resistor? So the KE of the electrons just before it enters the resistor is higher than the KE of the electrons as it exits the resistor.

5. Mar 21, 2017

### sophiecentaur

A battery will provide the same voltage whatever load you hang on it (that's the ideal battery we use in problems - a Voltage Source)
A voltage source has no internal resistance but a real battery has a small series resistance which will lose you some of the nominal battery volts as soon as you take current through it (same as a long connecting wire resistance will do).
Ignore the KE of electrons. It is not a significant quantity in the transfer of the energy. Electrons have an average speed of only around 1mm per second and their mass is a tiny proportion of the metal (much less than 1/10,.00th) so KE is not part of things. Also, the electrons are travelling through the resistor at a constant (very low) average speed.
Think in terms of the links in a bicycle chain. They can be going quite slowly and the same number are being pulled from the back sprocket as are going round the chain wheel every second. Their KE of the links is not very relevant - it's the tension in the chain and the speed it's going over the wheels (Force times speed = Power). In the case of electrons, the KE is an even smaller proportion of the energy transferred and the same number enter at the - end and leave at the + end of the resistor. If the numbers didn't balance, there would be IMMENSE forces of mutual repulsion or attraction.
Again NO.

6. Mar 21, 2017

### Staff: Mentor

That is a very incorrect way to think. KE plays no significant role, and it is not helpful to think of electrons like billiard balls filled with energy. Accept V=IR as it is and forget completely about electrons.

@sophiecentaur , Remember the recent thread where I ranted about levels 1 QED, 2 Maxwells, 3 Circuits, and how it was wrong to make fractional level metaphors?. I thought you supported that.

I'm sure it is inadvertent, but when you say that current in the resistor starts after "a short time" that is mixing the metaphor, and providing an explanation not 2 and not 3.
• In circuit analysis (3), V=IR in a resistor is instantaneous. There is no first and no next.
• In Maxwells equations (2) there is a wave that propagates in space and time, but there is no such thing as "a resistor" We have 3D space filled with materials of differing conductivity, and where the dimensions of those materials is important (i.e. the size and shape of the resistive stuff).
I am urging all of us PF regulars, to resist the urge to mix the metaphors on PF and to never mention a physical phenomenon (no matter how real) except in the context of 1, 2 or 3. Would you agree?

7. Mar 21, 2017

### Blissed

Thanks for the explanation, it seems like my confusion mainly came from observing the transfer of energy in terms of KE. So my follow up question is, how exactly then is the energy transferred to a resistor?

8. Mar 21, 2017

### sophiecentaur

I couldn't agree more but the OP seemed to be needing some reason to accept that in the idealised context. My 'explanation' is a fair enough way to connect the stark, axiomatic approach to circuit analysis with 'real behaviour'. We do tend to take for granted that using the steady state condition as a start in solving problems makes sense to the uninitiated. It's the same with problems about forces on frameworks; how does the bolt in the wall know what its share of the load on the shelf is? With EE it's even worse because we are actually dealing with something moving.
That's a good principle to aim at. But it would involve cutting short an awful lot of threads.

9. Mar 21, 2017

### Staff: Mentor

Power, rate of delivery of energy, is voltage times current. V*I You need both. That is the point that many students miss.

Sorry, I disagree. Your explanation is not 'real behavior' as I explained in #6. That's why I object. And yes, cutting short those mixed metaphors in very many PF threads is what I advocate.

We might avoid this debate if students were taught Maxwells Equations first, and circuits second. Then they would appreciate and welcome the simplifying assumptions of circuits analysis. But alas, teaching almost always goes from simplest first to less simple later, leaving many students with some (3) but zero learning about (2).

10. Mar 21, 2017

### Blissed

So in the microscopic level, what exactly is happening to the charges as they move through the resistor, what causes them to transfer energy to the resistor? I know power is the rate at which energy is transferred, but I would like a conceptual understanding as to how this occurs, hence I thought it was the collisions due to the KE that caused the energy transfer. Now I know that the KE of the electrons are irrelevant, what causes the energy to be transferred?

11. Mar 21, 2017

### cnh1995

12. Mar 21, 2017

### cnh1995

The electric and magnetic fields carry the energy, and not the wires. If you want to dig deeper, look up 'surface charge feedback' and 'Poynting Vector'.
https://www.physicsforums.com/posts/5521826/
https://www.physicsforums.com/posts/5667921/
https://www.physicsforums.com/posts/5507882/.

13. Mar 21, 2017

### sophiecentaur

That would exclude the majority of School Students from any work on electric circuits. The Maths involved in Maxwell's equations is not all taught, even at A level.

14. Mar 21, 2017

### sophiecentaur

I just read this again. It is quite justifiable for someone to challenge the notion of a step change of an uninterrupted steady state condition when we all know that we turn on the current at some point and it takes time for the steady state to be reached. Simply saying that it takes time for the situation to settle down is not an arm waving low level analogy. The question from Blissed (?) was about 'how the resistor knows' what to do. If you take time out of the problem then this is not a problem because the question is not allowable. But the approach to Physics that insists on the steady state can be very confusing. What alternative justification would you suggest? Or would you just tell Blissed that he has to accept that that's the way we do it? I think that would be playing right into the hands of those who say that we want Physics taught by rote. I know you don't want that(?),

15. Mar 21, 2017

### .Scott

Sorry. I was trying to avoid the term "potential".

16. Mar 21, 2017

### lychette

1 volt means 1 joule per coulomb, you cannot avoid energy when referring to voltage.

17. Mar 21, 2017

### Staff: Mentor

18. Apr 1, 2017

### Joseph M. Zias

I suggest reading "Matter and Interactions" by Chabay and Sherwood, Vol. II. Also, going back a bit in time I always liked "Electrical Science" by Norman Balabanian for a good treatment of the basic circuit laws. As mentioned before there are a LOT of references on surface charges, power flow, and the Poynting vector.

19. Apr 1, 2017

### dreens

It's possible to understand this without delving into the subtleties of electromagnetic fields, especially since your question focuses on resistors and not inductors.

It helps to think of a fluid analogy. Consider water flowing in a river. Even though at the microscopic level the fluid flow is composed of water molecules with kinetic energy jostling each other, the way to understand the system is in terms of its macroscopic properties, it's pressure and it's velocity. You wouldn't solve for the speed of water flowing into the atlantic ocean from the Mississippi river by taking the average initial gravitational potential energy of the rain water when it landed on the continent and converting to kinetic energy, would you? No, because fluid flow is an inherently frictional process. The speed of the water as it flows is related to the resistive friction the fluid experiences with it's channel and the height decrease along it's flow path. The energy transfer is all frictional at the microscopic level, but it doesn't mean the fluid doesn't have a well-defined mass-flow rate everywhere along it's course.

The situation is nearly identical in a circuit. In fact, you could just think of it as a fluid flow of electrons. The electrons constantly jostle each other and their micromotion is random and frictional, but they can be well described by the bulk properties voltage and current. The electron flow is most impeded during it's travel through the resistor- often because the flow is forced through a narrow and long channel (a wire-wound resistor), maximizing collisions between electrons and the material. Because of this, the voltage drop is largest there. But since it is a fluid flow, this doesn't mean the fluid somehow runs out of kinetic energy and stops flowing at the other side of the resistor. It just means that the fluid pressure (voltage) has dropped back to its initial value.

20. Apr 1, 2017

### rumborak

Ha, I almost suspected my earlier thread on the topic was going to get mentioned :D

I too am still left unsatisfied. On the one hand I know that it is the electrons that *facilitate* all that is happening in a circuit, and at the same we also know that it is the Poynting vector that shows the flow of energy, and for the most part that vector is flowing *outside* the wire, and only enters into the resistor.

Take for example the fact that the Poynting has the magnetic field as a key factor in its definition. But, how is the magnetic field even relevant to the electrons?

The Khan video was *very* unsatisfying for the topic at hand, because he already started with the fact there's a voltage drop over a resistor. After that it was algebraic shuffling, but the question remains, why is there a drop? What happens inside the resistor that causes this?