Have you ever wondered what the \( 1.5 \, \text{V} \) on an AA battery means? Or, what it means that an outlet provides \( 230 \, \text{V} \)? Or, what it means that a USB port needs \( 5 \, \text{V} \) to function? These are all questions that have to do with voltage. Let's try to understand what these numbers mean physically.

With this basic knowledge it will be easier for you later on

to analyze simple electrical circuits,

to carry out calculations with electrical quantities,

or simply get a feeling for voltage numbers on your everyday devices.

Necessary for the voltage: Positive and negative charges

Particles can carry negative or positive electric charge. Let us denote this charge with the letter small \(q\). Charge is measured in the unit Coulomb and abbreviated with the letter \(\text{C}\):

Charge unit

Formula anchor$$ \begin{align} [q] ~=~ \text{C} \end{align} $$

Particles, like the protons that make up our universe, carry a very small positive charge of \( q = 10^{-19} \, \text{C} \). That is 18 zeros with a 1 behind the decimal point:

This is a quite tiny amount of charge for our standards. Only if we take a lot of particles, they will carry a noticeable amount of charge in sum. So let's take a lot of charges.

In order that different particles don't get mixed up, we put the positive particle cluster in one box. And the negative particles into another box. We add up the individual charges small \(q\) together and get a total charge, that we denote with a large \(Q\).

In the positively charged box, the total charge \(\class{red}{Q}\) is positive because positively charged particles carry a charge with a positive sign. And in the negatively charged box, \(\class{blue}{Q}\) is negative because negatively charged particles carry a charge with a negative sign.

Our oppositely charged boxes will attract each other and move towards each other. Because eventually, opposite charges will attract each other. Our boxes are just like two big charges. We say: they exert an electric force on each other. The more charges in the boxes, the greater the attracting electric force.

Charge separation generates voltage

Let's do a thought experiment. We fix the two boxes so that they cannot move towards each other. In this way, the opposite charges will remain separate from each other.

The accumulation of negative charges in the one box is called minus pole and the accumulation of positive charges in the other box is called plus pole.

The charges from both poles attract each other, they want to move towards each other. But they can't do that because we have fixed them each in two places. The separation of the positive and negative poles creates a voltage between the poles. We denote the voltage with the symbol \(U\).

The voltage \(U\) is smaller when less positive and negative charges are separated. In this case, the total charge \(Q\) in the boxes is small.

The voltage \(U\) is large when many positive and negative charges are separated. In this case, the total charge \(Q\) in the boxes is large.

The voltage arises only when positive and negative charges are separated. In our case, there are two charged boxes separated from each other. The voltage always refers to two different points. So always keep the question in mind: Voltage between which two points?

So always keep the question in mind: Voltage between which two points? Between the points where the two boxes are located.

So when you read or hear something about voltage, always remember that somewhere positive and negative charges are separated from each other and there is in principle the possibility to release them to generate an electric current. But more about that a little later.

Voltage is energy per charge

So far, you have only learned that charge separation is the cause of voltage. Now let's try to understand what voltage means physically. With this you can understand what a number like \(5 \, \text{V} \) means.

For this purpose we take a small positively charged particle with the charge \(q\). Let's call this particle a test charge. With this we can test how big the charge separation is and therefore how big the voltage between the poles is.

Let's place the test charge directly at the positive pole. Then the test charge is attracted to the negative pole. It therefore experiences an electric force. This force causes the test charge to accelerate. Just before it hits the negative box, the test charge reaches a certain speed because it has been accelerating the whole time.

But if a test charge has a velocity, then it also has motion energy (kinetic energy). The test charge has thus gained kinetic energy by moving from the positive pole to the negative pole. The test charge had no kinetic energy at the beginning, but has received kinetic energy by the acceleration to the negative pole!

Let us call this gained energy \(W\). The energy is measured in Joule and the unit is abbreviated with the letter \(\text{J} \):

Energy unit

Formula anchor$$ \begin{align} [W] ~=~ \mathrm{J} \end{align} $$

Let's hold on to an important insight:

If we now divide this gained energy \(W\) by the charge \(q\) of the test particle, we get a quantity that gives gained energy per charge: \( \frac{W}{q}\). And this quantity \( \frac{W}{q}\) corresponds to the voltage \(U\):

Formula: Voltage is energy per charge

Formula anchor$$ \begin{align} U ~=~ \frac{W}{\class{red}{q}} \end{align} $$

Voltage generates current

If we conductively connect the two poles, the positive charges can move to the negative pole. We assume here that the negative charges are firmly anchored in the negative box and cannot move. Otherwise, they would also move along the junction to the positive pole. That would be okay, but it would make our thought experiment unnecessarily complicated. Therefore, we only consider the current of positive charges.

The electric current \(I\) is the amount of charge per second that travels through this connection. It is clear that the charges only travel through this connection if there is any charge separation at all. Without charge separation, there is neither a voltage nor a current here.

We can exploit this current to make a small lamp light up. The charges move and move... But with time, the number of positive charges in the box decreases. The charge separation decreases. The current decreases. The light shines dimmer and dimmer. As fewer charges are separated, the voltage naturally decreases as well, until there are no more charges in the positive box. Then the voltage is zero. The current stops flowing. The light stops shining.

The charges are no longer separated from each other, but are all in one box. The opposite charges have neutralized each other. The total charge in the box is now zero: \( Q = 0\).

How can we make it so that the light continues to shine constantly? We must keep the charge in the box constant, so that the voltage and the current remain constant. Then the lamp will keep the same brightness all the time. If we supply charges, by whatever means, to the boxes, then we have thereby created what is called a voltage source with which we can then generate a non-decaying current which in turn causes the little light to glow steadily.

Is current or voltage dangerous?

Voltage in itself is not dangerous, whether it be \(10 \, \text{V}\) or \(10\,000 \, \text{V}\). AS LONG as the charges are separated, nothing special happens. The positive charges are resting in one box. And the negative charges in the other box. Although the voltage between the poles is not zero.

Only when we conductively connect the two poles an electric current starts to flow, and that current in turn can become dangerous. The current becomes more dangerous...

the greater the voltage \(U\)

and the better the connection betweeen the poles.

Of course, the connection between the poles should not be your body! Even if your body is not such a good connection, such as a copper cable, a sufficiently large voltage can also 'push' the charges through your body. The consequences are for example: burns in the areas where the current has passed through.

In the next lesson, we will look at the Ohm's Law, which allows us to describe exactly how current and voltage are related.

+ Perfect for high school and undergraduate physics students + Contains over 500 illustrated formulas on just 140 pages + Contains tables with examples and measured constants + Easy for everyone because without vectors and integrals