Voltage Explained

concept
Voltage is probably the most important of the three big circuit values we'll learn about in this course (the other two being current and resistance). Voltage is a measure of how much energy the electrons in a certain part of a circuit have. If we say that some point on a circuit has x voltage we're saying something about how energetic each of the electrons at that point is. In this course the voltage at a particular point is usually the same for the entire lifetime of the circuit however in future courses this won't be the case. In real world circuits voltage is most often the way we communicate information. Voltage is how we represent signals and how we perform operations on them like filtering and turning them into coloured pixels on your screen.
fact
Voltage is a measure of the potential energy of the electrons between two parts of a circuit.
fact
Voltage is measured in a unit called Volts (V).
Voltages are often written straight onto a circuit digram if it is known what the voltage at that point is ahead of time. A voltage is measured like a distance, you always need two points to measure between. There is no absolute measure of voltage, you can't ask "what is the voltage of my finger?", you always need to ask "what is the voltage of my finger relative to that table?".
fact
Voltage is always measured between two points. The voltage $$V_{AB}$$ is the voltage of point A relative to the voltage at point B.
example

Find the voltage $$V_{AB}$$ across the resistor in the diagram below

$$V_{AB}$$ means the voltage at A minus the voltage at B or, in other words, how many volts we need to add to electrons at B so that they're at the same energy level as the electrons at A. From the diagram we can see that $$V_A = 5$$V and $$V_B = 2$$V so the voltage across the resistor $$V_{AB}$$ must be given by: $$V_{AB} = V_A - V_B = 5 - 2 = 3$$V
We usually pick a point on a circuit and call it "ground", this means that if we don't mention a second point for a voltage we assume that the second point is ground (and we define the voltage at "ground" to be 0 since it is measured relative to itself).
fact
Every circuit has a universal reference point called "ground". When we say "the voltage at point A" we mean relative to the ground point. Ground's voltage is assumed to be 0.
This ground point is not the same between two separate circuits. Confusingly if we have two circuits that are not connected their grounds could have a non-zero voltage between them. Always remember that there is no absolute measure of the voltage at a point and choosing a "ground node" is just a trick to make talking about voltages simpler. You can pick absolutely any point on your circuit to be the ground node. By convention we pick the negative side of a battery, but this is just a common convention and not required.
fact
The ground on a circuit is denoted by the symbol:
example

Find the voltage across the resistor in the diagram below:

One side of the resistor is connected to point A which is listed as being 5V, the other end of the resistor is connected to our ground point (everything touching the same wire is the same point on a circuit). Since the voltage at ground is 0V by definition we have: $$V_{AB} = V_A - V_B = 5 - 0 = 5$$V And there is 5V across our resistor.
example

Find the voltage at point A in the diagram:

In this case we can see that there is 10V across our resistor. The + and - signs show which end has more voltage relative to the other. The other end is connected to ground, so that end is 0V. Now that must mean that our point A is at 10V since $$V_A - V_B = 10$$V. So point A = 10V
It may be confusing that we started this topic claiming that you can't talk about the voltage at a point and then we just did some examples about the voltage at a point. And you're right, that is confusing. Whenever we say "the voltage at point A" we really mean "the voltage at A relative to ground", but that's a mouthful and engineers are lazy. It's important to remember that a single point never has a voltage, but if we talk about the voltage at a point we mean relative to ground.

Batteries

Batteries are the main source of voltage in many of the circuits we'll be looking at. A battery has a positive terminal and a negative terminal.
fact
A battery is a device which adds voltage to an electron as it passes from the negative side through to the top. Most components will lower an electron's voltage as the electron passes through. You can think of batteries as the motors running an electrical circuit.
fact
In a battery electrons flow from the positive side, around the circuit the battery is connected to and then into the negative side where they are given more voltage (equal to the battery voltage) and pushed out the positive side again.
fact
A battery is written into a circuit diagram in a few ways as shown below. In each image the negative side and positive sides have been marked.
fact
If the circuit contains just one battery and no point on the circuit is marked ground then the negative side of the battery will be ground. This is just a common convention.
fact
Voltages add as an electron moves around a circuit. For example if two 5V batteries are placed back-to-back then an electron will gain a total of 10V as it passes from the negative side of the first through to the positive side of the second
practice problems