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I had asked this question:No matter the arrangement of resistors in a circuit, a battery will still produce a current as if it were connected to an imaginary combination of the individual resistors within the circuit? Can anyone explain why this is so, can the charged particles know there is a resistance before they leave the power supply? when I was learning electric circuit basics. I now believe I have an answer for it, but I do not know if it is wholly correct.

So, when a battery is connected to a circuit with a resistance of let's say $R$. The potential difference is established within the circuit almost at the speed of light. For a negligibly short amount of time, the current is not homogenous within the circuit, since there are also particles within the wires or resistance. The particles which initially leave the battery with a specific speed are faster than the particles which are already found in the wires, since they were not charged in the battery. The charges leave the battery in a certain amount of time, however, they lose some time over the resistance and this causes charge to accumulate. However, after this almost instantaneous moment, the charges which left the battery enter it in a certain time, lets say tx and the battery also produces charge q over time tx. Is this a correct understanding of this question?

If you could not understand what I have stated above, here is a much simpler version. Which explains why current does not pass through a resistance if there is another path w/out resistance.Let's suppose that a single battery is connected with a wire, which does not have resistance. Electrons will start to flow , in reality, with a wire with resistance, a potential difference would be generated across it. The current would build up until the potential difference is equal to the voltage of the battery. In the case in which potential difference is not created by the wire because there is no resistivity, the potential difference across will immediately become equal to that of the battery.

ten1o
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Velocity of particles carrying electric current in an average conductor is about 1 cm/s, so it is very slow. But nevertheless, when difference of electric potential is established throughout the wire all of them start moving practicaly at the same time. Of course, there is inhomogenius current in the begining but that is all brought to a steady state very fast because of course all of the particles effect other particles in a circuit. So battery is not a source of particles, it is primarily a source of electric force id est, potential difference. Electrons that are already in the wire are the ones that make up the current. So as the current starts to build up, yes, slower regions and faster regions do exist, but because this is a circuit after all, they effect each other like cars moving in circles, when one slows down, all the others must do the same..

Žarko Tomičić
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As an example take 2 resistors in parallel, 1 ohm and 2 ohm and V is is 10 volts. Let's turn on the switch for a short time so 100 electrons flow (this is a very small current). At one battery pole 100e leave the battery and enter the wire and 100 electrons leave the the other wire at the other pole and enter the battery, not the same electrons. About 67 electrons pass through the 1 ohm and 33 through the 2 ohm. Yes the potentials were set up at very rapidly but the e move slower.

The above is based on an ideal circuit, in reality there is something called parasitic capacitance and inductance which initially slow the 100e down and also slow down the potential build up. In advanced electrical engineering and physics one takes this onto account (ex radio equipment or any circuit with an inductor and or capacitor) but for learning DC circuits with resistors this effect is ignored. Parasitic capacitance is due to the electrons in the wire setting up an E field in space and parasitic inductance is created by electrons moving causing a magnetic field, this creation of a magnetic field opposes the motion of the electrons until the field is established.

PhysicsDave
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