# Why is Kirchhoff's law true?

1. Dec 29, 2013

### Entanglement

I mean why does the potential have to reach zero on reaching + terminal I know that should be intuitive, but what makes me confused that the path of gaining the potential which is inside inside the battery ( from + to - ) is different from the path of consuming the potential which will be any way outside the battery from negative to positive, it is intuitive if we are talking about potential gained by gravity for An example when we throw a ball upwards gaining potential it will take the same path on consuming it so all the potential must change to kinetic but this is unlike electric potential where it gains potential in a path and consumes it in stotally different one !

2. Dec 29, 2013

### Staff: Mentor

The analogy to gravity is fine. The battery (more general: a power supply) is something that lifts up charge against a potential difference - like moving stairs can move people upwards.
Just by writing down potentials you have to imply Kirchhoff's law, otherwise there would be no (meaningful) potentials.

3. Dec 29, 2013

### Crazymechanic

until the circit is closed outside the battery , no charges are interacting inside the battery , if they would the battery would die out long before you would have the chance to use it's stored potential.
the circuit outside the battery , whatever that circuit is , when closed acts as the path or the way through which the battery inner charge can interact and " get together" if you like to say it like that.

remember that the potential stored in charge is useful as long as one type of charge is seperated from the other , like + from -, then they have potential because they want to go together and equal out and while they are on their natural mission in doing so they can do work and we use that work.

In other words if there is no closed circuit attached to both of the battery's terminals then the seperated charges inside the battery cannot interact, but they do so when the circuit or path is formed outside the battery.

4. Dec 29, 2013

### Staff: Mentor

Think of potential like height, and potential difference as the difference in height between two points. If you walk from point A at one height above sea level to point B at another height above sea level your total elevation change will be the same no matter which path you take. You can take a steep path, or a not-so-steep one, or descend into a deep valley and then go up and down a few nearby hills... But if you start at A and end at B the elevation change will be the same, and therefore the total change in your energy.

The two terminals of a battery are at different potentials; chemical processes inside the battery are pushing the electrons "uphill" and then energy is released when they're allowed to roll "downhill" through the circuit. No matter how complex the path, the total "height difference" is the same.

5. Dec 29, 2013

### vela

Staff Emeritus
Slight correction... Electrons are weird and like to roll up potential hills because they're negatively charged. The battery actually pushes electrons down the hill, and they give up this energy as their electric potential (not electric potential energy) increases.

6. Dec 29, 2013

### Naty1

well, no it is no so intuitive for most people. it takes some getting used to.

If you are interested in how potential may be created, check electrochemical reactions, for exampel, as in batteries.

If you are roughly familiar with gravity, the description Nugatory gives might be a useful analogy for you. A weight, or particle, higher off the earth's surface has more potential energy than one closer to the surface.

In an electric circuit, electrons are the typical charge carriers with varying potential energy. [Voltage is energy potential per unit [electron] charge.] You can provide that potential, for example, by solar cells, electrochemcial reactions in batteries, or mechanically, via a generator or alternator. Each electron has had work performed on it, enough to break it free from it's attractive nucleus. In a battery, electrons may flow due to the electrochemical reaction of certain substances in an electrolyte; in an exterior circuit, typically electrons flow and must displace in place electrons.

If the electron flows through a resistor it loses a lot of energy [because each electron there is tightly bound] and as it flows through a conductor less [because electrons there are much more loosely bound]. Resistance in electrical circuits is analogous to friction in mechanical systems....they both dissipate energy in the form of heat.

7. Dec 29, 2013

### Staff: Mentor

Yeah, yeah, yeah....

The "positive" and "negative" labels were assigned backwards, long ago when it was known that there were two flavors of charge but not which one was carried by the more mobile charge carrier. Ever since, we've been explaining backwards sign conventions.... I have a lot of sympathy for SophieCentaur's position of not talking about electron flow at at all.

8. Dec 30, 2013

### CWatters

What do you mean by "reach zero"? To be clear..KVL says the sum around a loop equals zero not that the voltage at any point is zero.

Think of the battery as a fixed ideal voltage source....it will force enough current to flow around the other path so that the voltage drop is the same.

9. Dec 30, 2013

### Entanglement

Yes, I know the point that the sum of potential around any loop equals zero but that also means that on reaching the positive terminal the potential will be zero

10. Dec 30, 2013

### Staff: Mentor

No, the difference to the positive terminal is zero at the positive terminal (should not be surprising, as we are at the positive terminal). The potential itself has no meaning, only potential differences are relevant.

11. Dec 30, 2013

### Entanglement

I don't get it so electrons may still have potential at the positive terminal although the potential difference is zero
For an example if the source gave an electron a potential of 15 voltage at the potential difference between - and + will be 15+(-15)=0 and the potential should be zero from where could it get an extra potential

12. Dec 30, 2013

### Staff: Mentor

Yes, as the absolute value of the potential is arbitrary and without a physical meaning.
Consider the analogy to gravity on earth: A common convention is to choose the floor as zero. Then an object with a mass of 1kg, lying on the floor, has zero potential energy, and lifting it by 1m needs roughly 10J, afterwards it has 10J of potential energy.

Another common convention is to set the potential of "infinite distance to earth" to zero, so here on the surface of earth the object has a gravitational potential energy of -62MJ. That is a large number, and it has absolutely no relevance if you want to lift the object by 1m. Then you change this number from -62MJ to -61.99999MJ. The difference - the same 10J as before - is the relevant quantity, as you need those 10J to lift the object.
You could also choose the center of earth to be zero, then the same object would have a potential energy of something like 45MJ (guessed, the precise value does not matter). Again, that value is not relevant if you want to lift the object by 1m.

The absolute value of the potential has no physical meaning, it is just a tool to calculate things - you can choose it as you like (for one point, then everything else is determined by the meaningful potential differences).

13. Dec 30, 2013

### Entanglement

Do you mean that potential is a site or location dependent value,and that site can be differently chosen according what is most suitable ?

14. Dec 30, 2013

### Staff: Mentor

For gravity, yes. For electric potential, I would not say "site"/"location", but the concept is the same. You are free to choose where "zero" is.

15. Dec 30, 2013

### Entanglement

I understand it when talking about potential due to gravity, but I don't get it when it comes to electric potential can you make it clearer ?

16. Dec 30, 2013

### Staff: Mentor

It is the same concept. "Zero potential" (or any other value) is a completely arbitrary choice. You can define the positive terminal of a power supply as zero, or the negative, or define the positive terminal as +100V. It does not matter.
A convenient method is to connect one side to ground, and to define that as zero, but it is not necessary.

17. Dec 30, 2013

### Entanglement

Is that because the electron always has a potential that is unknown ?

18. Dec 30, 2013

### Staff: Mentor

It is not unknown, it is arbitrary.
A potential is a mathematical tool to describe things, it is nothing with a physical meaning.

19. Dec 30, 2013

### Entanglement

Cool I got it

20. Dec 30, 2013

### CWatters

As others have said you can't talk about potential difference without specifying a reference.

To use the mountain climbing example...If you start at the top of a mountain (the +ve terminal) and go down to say sea level (the -ve terminal) by one route and then climb back to the top (the +ve terminal) by another route then the net change in Potential Energy is zero.

Intuitively.. The potential difference between the +ve terminal and the +ve terminal must be zero as it's the same place. You can see this for yourself by connecting both leads of a voltmeter to the +ve of a battery.

That doesn't mean the potential at the top of the mountain (or the +ve terminal) is zero with respect to other places. In the case of a battery powered circuit the potential difference between the +ve and -ve is what gives the electrons the energy to flow around the circuit. In effect the battery acts like a ski lift raising the PE back up again.