What exactly is potential difference? What are the factors that effect it? I am asking this question because at first I thought that this concept was pretty clear to me, but it is not. So, my first question:


*

*Is potential difference only a property of an electric field? If not,
what is it? 

*Does the physical nature of any conductor(like shape or size)
effect the potential difference between 2 points in the conductor?

*When current flows through a circuit and when charges are traversing through the circuit, why do we say there is a potential drop? Isn't it constant?


Now, I move on to asking some more things about potential difference, but this time including resistors. I completely understand that when resistors are placed in series, the total resistances is the sum of all individual resistances. But, I am not able to understand this:


*

*Why is the sum of potential difference between the end points of the
resistors equal to the total potential difference? Can someone
explain this to me in a more intuitive way? (I request the readers to
throw some more light on this)

*Why do we say that current flowing through each resistance is the
same? Is it not logical enough that in the conductor, the parts with
lower resistance will have a higher current flow? Because if this is true, by Ohm's law we can get each resistor's resistance value to be same, even though I used different resistors!


I request the readers to provide the answers to all my 5 questions, I really need these answers. And, please explain each question individually.
 A: Electric potential and electric field are two ways at looking at the same thing.
Electric field is a vector and is defined a the force on unit positive charge and potential as a scalar and is defined as the work done by an external force in taking unit positive charge from a position of zero potential to the point.
They are linked in that the electric field is equal to minus the potential gradient.
So electric filed is to do with forces and potential is to do with energy.
A key concept is that the electric field is a conservative field which means that the work done in taking a charge between two points is independent of the path taken.
This idea is used when there are resistors in parallel and you say that the potential difference across the resistors is the same.  What that means is that taking a charge along one branch requires the same amount of work as taking the same charge along the other branch.
For resistors in series going through one resistor (A to B) requires some work to be done and then some more work needs to be done in going through the next resistor B to C.  Adding this work together gives you the amount of work which needs to be done in going from A to C.
So the pd(A to B) + pd(B to C) = pd (A to C).
The current passing through resistors in series is the same is a consequence of the law of conservation of charge which means that the amount of charge per second (the current) which enters must be the same as the amount which leaves.  Charge cannot be spontaneously destroyed or created.
A: *

*Potential difference is really a property of any field. It exists in gravitational fields as well for example.

*The conductor through which charges propagate does not change the
potential difference across the circuit. Dependent on the source of
the electric field, current will adapt to resistive properties to
ensure the voltage drop equals the potential difference across the
circuit.

*The potential drop part means that the electrons loose electric
potential as they move through the wire. This can also be compared
to a gravitational field. Imagine you started at a height of 50 m
above the ground. As soon as you moved downwards you move along a
potential gradient and you lose potential.  Potential in a circuit
is inversely proportional to the distance from the source of the
field which again goes to show that the potential must decrease as
the electron moves to the positive part of the battery.

*Looking at the second part of your question, the measuring across
the resistors is just an approximation. In reality, the wire after
and before the resistors has some resistance as well but it is
usually negligible (a property that is desirable in a wire).
