Voltage is similar to height. It plays the same role for electric charge as height*gravity does for a ball on a hill. So high voltage means high potential energy the same way a ball being high up on a hill means high potential energy.
Voltage is not potential energy, the same way height is not energy. However, if you have a certain amount of charge $q$, you can multiply it to the voltage to get the potential energy, which his $Vq$. This is similar to the way you can multiply height to mass*gravity to get $mgh$ for the potential energy of a ball on the hill. So voltage is potential energy per unit charge the same way height*gravity is potential energy per unit mass.
Voltage must be measured between two points for the same reason height must be. When someone says "the height here is 1000 feet", they are actually comparing it to a point at sea level. In electronics, "sea level" often gets replaced with "ground". So if someone says, "this fence is electrified at 10,000 Volts", they mean there is a 10,000 Volt difference between the fence and the ground, the same way they mean that there is a 1,000 foot drop between the current elevation and the ocean. However, you can use any two points to measure height differences. If you drop a ball, it makes more sense to talk about height above the floor of the room you're in than to talk about sea level. Similarly, if you want to look at a single resistor, it makes the most sense just to talk about the voltage change across that resistor.
The work done on a charge as it moves from point to point is the quantity of charge times the voltage difference. This is just like the work done on a ball as it slides down a hill is the mass of the ball times the height of the hill times gravity.
A single battery cell can only produce a couple of volts. That's how much the potential changes for a single electron in the chemical reaction in the cell. This is a bit like the way a pump that works via suction can only lift water about 30 feet into the air, since that's the potential energy from buoyancy from the entire atmosphere. You can stack multiply batteries on top each other to get a higher total voltage drop (as is done in 9V or 12V batteries) the same way that you could use multiple pumps to suck water higher than 30 feet.
If you increase the voltage across a circuit element, in general the behavior might be quite complicated. This is like saying that if you tilt a ramp to a steeper angle, you will change the way that objects slide down the ramp. In many materials, we find that the behavior simple: current = voltage/resistance. So if you double the voltage, you double the current. This is called Ohm's Law. An accurate description of why it is true is probably a bit too advanced for right now. You will do okay for intuition if you start thinking of electrical current as being like water flowing through a tube. Then Ohm's Law says that if you're powering the flow by having the water flow downhill, if you make the downhill flow twice as steep, the water flows twice as fast. Yes, you can think of it as saying that the electrons are going faster.
Adding resistors in series is like adding several pipes to go through. If you try to push the water through more pipes, it will become more difficult. If you were letting water flow down a hill through a series of pipes, the more pipes you have, the less each pipe can be pointed downhill. That means that adding more pipes makes the water flow more slowly everywhere. Similarly, adding more resistors in series reduces the current everywhere.
The quantity you actually measure when it comes to current is the total flow - number of electrons per second passing through. If you have a 1-ohm, 5-ohm, 1-ohm resistor series, they will all have the same current going through them. This is because if they did not the current would start building up somewhere, and that would change the flow. (This actually happens, just very quickly because the wires have very low capacitance.) The way they all get the same current is they have different voltages. Most of the voltage drop for the entire circuit will be across the 5-Ohm resistor. This is like setting up pipes so that a skinny pipe goes down a steep portion of a hill while two fat pipes go down shallow portions of the hill. The total water going through each pipe per second would be the same. In this case, the water would move faster through the skinny pipe (the high-resistance portion). This is just because the total flow is the same, so if the cross-sectional area is less, the velocity is higher to compensate. This sort of picture roughly works with electrons as well. It is called the Drude model. It is the easiest to visualize, but it is not true to the quantum picture of modern physics.
Batteries do die slowly, yes. That is why flashlights, for example, grow dimmer and dimmer before turning off entirely.
To say a circuit component has a voltage is just saying that there is a certain voltage drop across that element. It is like saying that each pipe in a series of pipes running down a hill has a certain height difference, and that the height difference for the entire system of pipes is the sum of all the height differences of the individual pipes.
If two resistors are in parallel, they have the same voltage drop. This is like saying that two pipes side by side have the same height difference. The one with 1-Ohm resistance will have five times as much current going through as the one with 5-Ohm resistance.
Atoms are really distinguished from each other due to their nuclear properties . It is the number of protons in the nucleus that defines the electric potential which will trap electrons and create a neutral atom. Thus metals have a specific type of nucleus that generates the potential which gives rise to loosely bound electrons in the outer shells. It is a complicated interplay between the potentials of electrons and protons that generates the electron shells described by the quantum numbers.
So it is a many body interaction that will keep electrons mobile in metals, and the positive "holes" immobile at the location of each atom.
In a conductor, electric current can flow freely, in an insulator it cannot. Metals such as copper typify conductors, while most non-metallic solids are said to be good insulators, having extremely high resistance to the flow of charge through them. "Conductor" implies that the outer electrons of the atoms are loosely bound and free to move through the material. Most atoms hold on to their electrons tightly and are insulators. In copper, the valence electrons are essentially free and strongly repel each other. Any external influence which moves one of them will cause a repulsion of other electrons which propagates, "domino fashion" through the conductor.
In semiconducting materials there is small mobility of both electrons and the holes left behind, again because of the potential solutions of the many body problem:
A silicon crystal is different from an insulator because at any temperature above absolute zero temperature, there is a finite probability that an electron in the lattice will be knocked loose from its position, leaving behind an electron deficiency called a "hole".
If a voltage is applied, then both the electron and the hole can contribute to a small current flow.
The conductivity of a semiconductor can be modeled in terms of the band theory of solids.
You cannot explain the behavior of matter below the nano scale , classically. Atoms and electrons are already quantum mechanical entities. It is the reason why quantum mechanics was invented and believed to be the underlying level of nature. Quantum numbers make a huge difference in the behavior of "particles" in the microcosm of atoms and molecules.
Edit looking at your figure: It is not talking of motion of physical positive charges, holes, but of hypothetical ones. In a semiconductor, the holes move, i.e.a neutral atoms become positively charged sequentially. In metals , the positive charge is attached to the individual atom, generating the potential that gives the energy levels. For holes to move, atoms at the atomic level have to exchange electrons. In metals the electrons are shared by all atoms and the mobility of holes is zero
The word "hole" is used in semiconductors as the subtraction of an electron from a neutral atom. The word "hole" that you use classically is the "space left from the motion of an electrin in a band" Electrons in bands are associated with the whole crystal, not with individual atoms.
Best Answer
here is why you can kill yourself with the knife-and-toaster trick.
the AC power line into which the toaster is plugged consists of a hot line (black wire) that has 120VAC on it and a ground return line (white wire) which is at zero VAC or very close to it.
The toaster has a switch inside which feeds power to the bare resistance wire inside the slots when the lever is pressed down and turns it off when the toast is done. this looks like:
black wire (120VAC)------switch-----resistance wire-----white wire (0VAC)
On older toasters and older outlets, the power plug can be inserted into the power outlet in one of two ways: one where the hot wire leads to the switch (as shown above) and one where the hot wire is connected to the resistance wire. In this configuration, the resistance wire is at 120VAC even when the toaster is off.
In this case, if you touch the resistance wire with your knife your hand is connected to 120VAC which wants very badly to flow to ground potential. If the floor is concrete and just a tiny bit damp, your body completes the circuit and you get shocked badly. If the floor is dry linoleum, you may get a surprising tingle.
Note that this can happen EVEN WITH THE TOASTER OFF.
On modern toasters and modern electrical outlets, the plug and outlet are designed so you cannot stick the plug in "backwards": the hot side will always be connected to the switch, so that if the switch is off, the bare wire inside the toaster is at 0VAC and touching it with a knife will not shock you.
Now we treat the case where the toaster is ON and you jam a knife down the slot WHILE IT IS TOASTING, and touch the resistance wire inside. The end of the resistance wire that is closest to the switch is at 120VAC and the end that is closest to the white return wire is at ~0VAC. In the middle of the resistance wire length, the voltage is at ~60VAC.
If your knife touches the wire at a point along its length where the voltage present there just happens to be sufficient to establish current flow through your body, you will get shocked (see above).
If you are lucky enough to have a toaster with a 3-prong plug, then all the metal parts inside the toaster that are NOT touching the resistance wire are tied to a good electrical ground. this includes the thin wire guides that prevent the toast from touching the hot wires. in this case, if you jam a knife down the slot the chances are your knife will touch a guide wire BEFORE it makes contact with the hot wire and if the knife then touches the hot wire, the current will be shorted to ground via a better path than that provided by your body, and you will not get shocked.