I know this question has been posted before but there are a few questions I have that I couldn't find anywhere else, which I guess stem from the fact that I don't understand the concept of voltage.

1) From what I've figured out voltage is the potential energy between two points in a circuit. What is it meant then when you hear things like a "9 volt battery". If it has to be between two points then what are the reference points when people talk about an x-volt battery?

2) In a table of a series circuit like this (with only a battery and 3 resistors):

By the time you get to the third resistor, all of the voltage has been dropped. So how does the circuit even manage to finish? If only 9 volts are supplied and by the third resistor all 9 volts have been dropped, how can it complete the circle? I guess I also don't understand the concept of a voltage drop.

3) How is it that in a parallel circuit each branch has equal amounts of voltage? To me it seems like the voltage should be divided by the amount of branches because with each additional branch the potential amount of electrons to flow through would get smaller, which obviously isn't right.

 

I see your position, and I sympathize.
I would like you to try a very primitive approach I wrote up some years ago. It's dead awful basic, but it makes a connection for some people.

http://forum.allaboutcircuits.com/threads/ohms-law-for-noobies-or-the-amp-hour-fallacy.69757/

 

Here is your circuit:




It has four elements and four electrical nodes. I arbitrarily named three of the nodes B, C and D, but I could have called them Tom, Dick, and Harry.

Be default and convention, the fourth node is Gnd (triangle symbol), which is always considered to be at 0V.

When we discuss voltages in this circuit, we think about the potential difference between Gnd and B, for example. This would be written as V(B), which is just the battery voltage of 9V.

If we specifically want to talk about the voltage drop across resistor R1, then we would use this notation: V(B)-V(C).

If we want to talk about the currents in the four elements, then because this is a series-circuit, by Kirchoff's law, the current in all elements is the same. Source V1 is a special case...

Shown are the voltages and currents in this circuit.

Exercise left for you: What is the voltage across R2?

What is the voltage at the bottom of R3?

 

1) From what I've figured out voltage is the potential energy between two points in a circuit. What is it meant then when you hear things like a "9 volt battery". If it has to be between two points then what are the reference points when people talk about an x-volt battery?

The two points of reference are the opposing poles of the battery. Batteries are amazing devices that convert stored chemical energy into electricity, in a way that maintains a nearly constant voltage between those poles.

By the time you get to the third resistor, all of the voltage has been dropped.

Well, only after the last resistor has the voltage fully dropped. There is a voltage drop across that last resistor, in proportion to the current that is flowing and its ohms. As you have shown, the current is the same all around the circuit.

I guess I also don't understand the concept of a voltage drop.

I find the water analogy useful. Voltage is the height of a water tower, the head. Current is ... current, the flow rate of the water from top to bottom. Voltage times current is power - the rate you can extract energy from the waterfall. The gravitational potential energy stored in the water is released as it falls. The chemical energy in a battery is released as current "falls" from one pole to the other. Resistance is like a restriction in the piping coming down from the water tower.

The water analogy is pretty good for Ohm's law, energy conversion stuff but falls apart in many other electrical problems, and so is not taught much anymore because of this.

3) How is it that in a parallel circuit each branch has equal amounts of voltage? To me it seems like the voltage should be divided by the amount of branches because with each additional branch the potential amount of electrons to flow through would get smaller, which obviously isn't right.

It may help to consider the outlets in your house. They're all in parallel, and you DON'T expect them to change voltage as you plug in more or less items. They are essentially constant voltage no matter how many lamps you plug in. In the water analogy, it's like adding another pipe for water to fall from the tower. The two pipes see the same head of water in the tower and give the same flow for their resistances.

 

1) When you look at a battery, there is a positive and a negative post. The negative post has an excess of electrons and the positive post has a deficit of electrons which creates a potential difference in charge. If you look at the negative terminal as a zero volt reference, then anything above or below that will give you a potential difference whether it be 9V or -9V. This voltage represents pressure and is measured using your voltmeter.
2) In perfect circuits such as the one you posted, all of the voltage is used up and leaves one to question how the electrons get back to the source. The truth of the matter is that there is some resistance in all parts of the circuit including conductors and connections, no matter how minute it is. Therefore there is always a little pressure left after all the work is done, to push the electrons back to the source. Remember, electrons go from point A to point B and do "work" along the way. Voltage just moves them along. The electron flow is your current.
3) If you can imagine a car battery and say you lay out five feet of cable and attach one end of each cable to the positive and negative post respectively, at the opposite end of those cables you would still measure battery voltage, correct. If you were to take and join some lights "across" the positive and negative wires (in parallel), each light would receive battery voltage. What will change as you add each branch is the amount of current that will be asked to flow from the battery. If each light required 1 amp, then 6 lights would require 6 amps in total but one amp will travel through each branch. The pressure across each lamp never changed because you are feeding each one off those two cables.
To understand parallel a little better, think of a toll booth with one hundred cars waiting to go through single file, been there, done that, took an awful long time.
Now open up five more lanes. Resistance decreases and flow increases.

 

The thing they don't usually tell you when you start is that the word 'voltage' is often a misused shortening.

Length is measured in metres.
My car is about 3 metres long
My lorry may be 20 metres long
A car parking space is 3.5 metres long
A lorry parking space is 21 metres long

But Length is not the only quantitity of significance, measured in metres.

If I want to park my car or lorry I need to know the length difference between the vehicle and the car parking space.

For a car this is +0.5 metres
For a lorry this is - 13.5 metres

So knowledge of length difference will tell me that I can't get the lorry into the car parking space and that I can get 7 cars into the lorry parking space.

So much for length.

There are two quantities measured in volts

Electric potential and electric potential difference.

In practical circuits we rarely work in electric potential, but use potential difference and abbreviate it to 'voltage'.

So when you see a reference to 'voltage' at AAC etc think of potential difference (PD).

Potential drop, by the way is further more restricted abbreviation for a particular method of circuit analysis. It can be confusing to think of potential drop until you know more.