Metals consist of small crystals; within each crystal exists the "free electrons" which are shared by all of the atoms in the crystal lattice. The number of free electrons per atom depends upon the details of the atoms, but is most often 1 or 2. The free electrons are visualized as "the electron sea" in the Drude model, devised ~1900, and is semi-classical. Introductory condensed matter texts often start with this model. The situation is slightly more complicated with alloys, but the same ideas hold.
In the electron sea the electrons are electrically shielded from each other by (a) the net positive charges of the ion cores and (b) the uncorrelated motions, essentially random, of the free electrons, which are described using the kinetic theory of gasses.
The crystal boundaries serve to impede the free flow of these electrons from one small crystal to the next, and also serve as scattering sites which continually randomize the motions. The velocities of the free electrons are quite large. When an external electric field is applied, it appears as a net "drift velocity" in the electron sea. This is the current in that piece of metal.
When you bring two clean pieces of metal together all of the above is still true, but there is an additional restriction: each crystal has an effective "crystal voltage" on its interior, and for crystals of the same type it should be the same. But when different metals are joined, the difference in the crystal voltage causes a voltage drop when going in one direction, and an increase in the other. This voltage difference is known as the Seebeck effect, discovered in 1821. Since the internal voltages change slightly with temperature, it is possible to measure temperature change electrically; this is the physical basis for the thermocouple.
So adding additional metal increases the total resistance of the circuit, depending upon the resistivity of the additional metal, its dimensions, and other properties.
The current is the net flow of electrons; each individual electron barely moves, but the effects are passed down the line. With alternating currents for every move forward, there is a corresponding move backward -- hence no net motion from the electron drift at all.
I will assume a constant current in the circuit in my answers.
a) If you compare two circuits with the same properties, up to a different resistor, which have the SAME VOLTAGE applied, then in the circuit with the lower resistor there will be a higher current. Since all the other properties of the circuit didn't change, the overall drift velocity $v_d$ will also be higher.
b) It depends on your resistor wether the drift velocity is bigger in the wire than in the resistor (everything has just to satisfy your formula $ I = v_d n A e$. If you find a Resistor with $n_{Resistor}$ being bigger than $n_{Wire}$, and give it the same area $A$ the wire has, then the drift-velocity will be lower in the resistor. This is also pointed out in the answer you've linked, in the last section. Still, usualy resistors have lower charge densities, so they require a higher drift velocity.
If by "opposite to the electric field" you mean "in direction of the force that acts uppon them" (eletrons have negative charge), then yes. The situation in the resistor is an equilibrium situation, where the electric field accelerates the electrons (converting its potential energy to kinetic energy) while at the same rate collisions of electrons convert the kinetic energy of the electron into heat.
Of course they still move through, they just need a shorter amount of time: Even without resistance of the wire, saying that there is NO potential difference throughout the WHOLE wire is a property of the equilibrium situation, and as long as there is a net flow of charge, this equilibrium situation will not be reached:
Let's say the resistor has infinite resistance, and you connect wire and battery. What will happen? In the beginning, there is a potential difference throughout the wire. Electrons become accellerated. They will flow through the wire until they reach the resistor. With the electrons comes the charge, and with the charge comes potential. Since there now are more electrons in the wire, the potential difference has shrinked. As long as there will be a potential difference, electrons will become accelerated, until somewhen the potential is really constant throughout the entire wire.
This won't happen if your resistor has finite resistance, in that case there will be electrons drained out of the wire all the time, which creates a slightly little potential gradient at that part of the wire, and at the same time there are electrons pushed into the wire out of the battery, which also creates a tiny potential gradient.
The resistance being zero will just make the electron movement faster, and therefore they can balance out the potential difference between the start of the resistor and the battery faster. But as long as there is a current flowing, the potential difference between start of the resistor and the battery will not be zero, but a little bit more.
You are right, forces can only act on the electron when there is a potential gradient, but since there is no resistance throughout the wire, it is sufficient if the electron is accelerated at the start of the wire and slowed down at the end (for example).
- Voltage drop means that electrons have lost potential energy throughout the resistor. This doesn't neccesarrily mean that there are more electrons on one side of the resistor compared to the other side, it just can mean that. The question here is the geometry of the resistor: The charges in the wire before and after, and the ones in the resistor have to create a potential (via 1. Maxwell equation) that has the mentioned potential difference throughout the resistor.
However, I usualy would also think that there is a potential gradient pushing electrons through a wire when there is more of them on the first side than on the second. So in principle the answer is "yes", but I don't know if it always has to be like that.
Best Answer
Let us take a simple example , a battery with two wires soldered so there is no surface between the pole and the wires. If we bring the two wires near each other , at a small distance a spark will happen ,a short, due to the migration of positive and negative charges over the distance between the two wires.
Contacts have been devised so as to be able to close the distance without sparking.The metallic surface of the contact,
allowing the charge transfer without sparking.
After this there are studies on what is called "contact resistance", from the abstract
You ask:
Well , it is quantum dimensions at the level of contact, one could call it jump,
Not really, as there is resistance to overcome.
From the abstract:
If "welded in" then they are bonded.If the contact is movable there will always be resistance