Electron flow across a wire depending on the Resistance across it [duplicate]

Question

In my grade 10 Physics book, its written that the electrons collide with the positively charged particles in the resistor and-

These collisions tend to slow down the speed of electrons and hence oppose the flow of electric current.

Suppose an electric current is flowing through a conductor with the arrows showing the direction of ELECTRON flow through the circuit, with a current I.

It has already been stated that the current I is the same across the conductor and on both sides of the resistor. I came to know about the popular "Water-Pipe Analogy" from a video by Indian Physics Professor H.C. Verma, which said that similar to how water flow will act across a pipe if the volume of a portion of the pipe is constricted then the volume of water entering the constriction will be equal to the volume of water leaving the constriction at an instant.

He also explained that if a water speed difference exists between the two ends of the constriction(or resistor for electrons), there will be an accumulation of water(or electrons) in which will probably explode the pipe(or resistor).

My questions are:

• So does this mean that the electrons already determine their speed across a conducting wire when a resistor is being attached to it? Suppose the wire has a minimum resistance of R1 and the resistor has resistance of R2; so are their resistances being added as R=R1+R2 to get the total resistance of the conductor(as is done in resistances attached in series)? So does this mean that the electrons "decide" what speed they have to acquire when coming out from the battery depending on the net resistance of the conductor?

P.S: We have not been taught about the internal functioning of a battery yet, so I might be missing out something on not knowing that.

Answer 1

So does this mean that the electrons "decide" what speed they have to acquire when coming out from the battery depending on the net resistance of the conductor?

No.

Example case 1: Resistance of the circuit is one ohm and electrons come out of a 1.5 V battery into a sharp needle pressed on to the terminal of the battery: Electrons flow out of the battery at quite high speed like 0.001 m/s. (Current is 1.5 A at every point of the circuit and the "pipe" is narrow where the electrons come out of the battery)

Example case 2: Resistance of the circuit is still one ohm and electrons come out of the same battery into a flat piece of metal pressed onto the terminal of the battery: Electrons flow out of the battery at slow speed, like 0.00001 m/s. (Current is 1.5 A at every point of the circuit and the "pipe" is wide where the electrons come out of the battery)

Answer 2

So does this mean that the electrons "decide" what speed they have to acquire when coming out from the battery depending on the net resistance of the conductor?

Yes. The charges “decide” based on the local E field and the electrical conductivity of the material. This is described by the microscopic version of Ohm’s law: $\vec J = \sigma \vec E$.

The E field at any location is determined by the entire circuit, so changing the circuit will change the E field, which will set the current density, which will determine the velocity.