Without prefix:What is the explanation for Kirchhoff's Voltage Rule?

[sophiecentaur]

From this discussion, I am getting the impression that the battery, in some way, provides the an electron (or current) with enough energy to make it around the circuit. It's as if the battery knows that there are resistors, and compensates for this by providing more energy than the current (or electron) would need if there were no resistors. Is this correct?

All the battery needs to "know" is how much current is needed to maintain its voltage across its terminals. It hasn't a brain with which to 'know anything' but charges are produced (internally) at its terminals until the current it releases is limited by the PD that exists (externally) at its terminals. How long it takes for that voltage to appear will be determined by the step response of the circuit. This could be a few ns or ten days. This is where the idea of trying to explain the process in 'mechanical' terms becomes pointless.
Kirchoff does not claim to apply at switch-on so why try to reconcile what it says with the switch on situation or to prove him 'wrong', in some way?

There are always resistors in a circuit that Kirchoff II describes. Read it.

 

[Crazymechanic]

I think the battery nor the circuit doesn't know anything , the electricity just flows from the highest potential to the lowest , because she always does that.Just like a river runs downhill not uphill.

Also the battery doesn't try to compensate for anything she just does her chemical reactions and current flows until the reactions are over and so is current.

 

[DrZoidberg]

There are many models one can use to analyze a situation. e.g. kirchhoffs rules, the charge model, electron model, etc. In engineering you should always use the model that can solve a given problem with the least effort. Otherwise things just become more complicated than necessary.
Sure the charge carrier/electron model is the more fundamental one. i.e. You can derive kirchhoffs laws from the charge carrier model but not the other way around, but it's not a good choice for designing electric circuits.

However there is no reason not to discuss what's happening on the level of electrons if you are interested in that.
To understand why electrons behave the way they do you need to look at the electric fields. Let's say you have a battery and a wire with a high resistance connecting it's two terminals. The wire's diameter is equal everywhere.
Now the current will be equal everywhere in the wire and the electrons will move at an equal speed everywhere. Electrons in a wire do not behave like water molecules in a pipe. They do not simply bump into each other and thereby pushing each other along. They are always moved by an electric field. The current density in metal is ALWAYS equal to the electric field strength inside the metal times the conductivity.
That means the electric field inside the wire must be equal everywhere.

But that seems strange since the electric field of a battery should look like the magnetic field of a magnet. i.e. it should be stronger close to the battery and weaker further away. So how can it be equal over the entire length of the wire? There is only one possible solution. There is "static charge" on the surface of the wire that is distributed such that the superposition of the field of the battery and the field of the charges produce a field that is equal everywhere in the wire.
If you have a network of resistors those "static charges" will distribute themselves such that an equilibrium is reached i.e. all the currents are such that the "static charges" do not change anymore. That equilibrium is reached when kirchhoffs laws are fulfilled.

It's as if the battery knows that there are resistors, and compensates for this by providing more energy than the current (or electron) would need if there were no resistors. Is this correct?

The battery always provides the same amount of energy independantly of the resistance. Some of that energy may be released in the internal resistance of the battery though.
If we replace the wire in my example with one made from a metal with higher resistivity, the electrons will move through it at a slower speed but will experience more "friction". But in total the energy they receive from the battery and the energy they release into the wire will stay the same.

 

[sophiecentaur]

But that seems strange since the electric field of a battery should look like the magnetic field of a magnet. i.e. it should be stronger close to the battery and weaker further away. So how can it be equal over the entire length of the wire? There is only one possible solution. There is "static charge" on the surface of the wire that is distributed such that the superposition of the field of the battery and the field of the charges produce a field that is equal everywhere in the wire.
If you have a network of resistors those "static charges" will distribute themselves such that an equilibrium is reached i.e. all the currents are such that the "static charges" do not change anymore. That equilibrium is reached when kirchhoffs laws are fulfilled.

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That's a good way to look at it.
It's like a string of capacitors, connected between the wires, in parallel. The Electric field between the wires (in V/m) will depend upon the spacing (can vary wildly, over the circuit) and will be far greater than the fields within the wire. It's only when you get to the Resistor that the 'series' field becomes significant.