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Level 1
Level 1 does not require any previous knowledge. Suitable for absolute beginners.

Voltage explained simply

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.

Positive and negative electric charge

Elektrisch positive / negative Ladung - Anziehung und Abstoßung Hover me!Get this illustration
Charges of the same sign repel each other. Charges of different sign attract each other.

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 \(\text{C}\):\[ [q] ~=~ \text{C} \]

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: \[ [q] ~=~ 0.000\,000\,000\,000\,000\,000\,1 \, \text{C} \] 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 \(Q\).

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 \(U\).

Voltage \(U\) is generated between two oppositely charged boxes.

  • 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 electrical voltage always refers to two different points. So always keep the question in mind: Voltage between which two points?

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 put the test charge directly on the positive pole. The test charge is attracted to the negative pole, so it experiences an electric force. This force causes the charge to accelerate. Just before it hits the negative box, the test charge reaches some velocity. But if a test charge has a velocity, then it also has kinetic energy. So the test charge has gained energy by moving from the positive pole 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 \(\text{J} \):\[ [W] ~=~ \text{J} \]

Relationship between voltage and kinetic energy Hover me!Get this illustration
A small test charge gets kinetic energy when it moves from the positive pole to the negative pole.

Let\s hold on to an important insight:Charge separation results in charged particles gaining energy as they travel the distance between the positive and negative poles.

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 \(U\):1\[ U ~=~ \frac{W}{q} \]

Formula 1 translated into words means:

Electrical voltage \(U\) is a measure of how much energy \(W\) a charged particle would gain if it traveled from the positive to the negative pole.
ExampleA test particle with \(q = 1 \, \text{C}\) travels from the positive pole to the negative pole and gains \(W = 10 \, \text{J}\) energy. So the voltage is according to the formula 1:\[ U ~= \frac{ 10 \, \text{J} }{ 1 \, \text{C} } ~=~ 10 \, \frac{ \text{J} }{ \text{C} } ~=~ 10 \, \text{V} \]Here we have called \(\frac{ \text{J} }{ \text{C} }\) (Joule per Coulomb) for short as \(\text{V}\) (Volt). In this case we say: There is a voltage of \(10 \, \text{V}\) between the positive and negative pole.

Voltage can generate 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.

Voltage drop between negative and positive poles Hover me!Get this illustration
Both poles are conductively connected to each other. The voltage and current drop over time if charges are not supplied.

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.

There is such a voltage source even in your room. It is a socket. The two holes of the socket form the two poles, so to speak, and if you connect them with a plug, then you have \(230 \, \text{V}\) available without interruption. You can use this voltage to power a lamp or to charge your cell phone. This constant \(230 \, \text{V}\) is provided by a power plant somewhere.

Is 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. Especially when the connection is your own body...

In the next video, we will look at the Ohm's Law, which describes exactly how current and voltage are related.

Ist Strom oder Spannung gefährlich?

Spannung an sich ist nicht gefährlich, egal ob \(10 \, \text{V}\) oder \(10\,000 \, \text{V}\). SOLANGE die Ladungen getrennt sind, passiert nichts Besonderes! Die positiven Ladungen ruhen in der einen Schachtel vor sich hin. Und die negativen Ladungen in der anderen Schachtel. Obwohl die Spannung zwischen den Polen \(10\,000 \, \text{V}\) sein kein. Erst, wenn wir die beiden Pole leitfähig verbinden, fließt ein elektrischer Strom und der kann wiederum gefährlich werden. Der Strom wird umso gefährlicher,
  • je größer die Spannung \(U\) ist
  • und je besser die Verbindung die Ladungen durchlässt.

Natürlich sollte die Verbindung zwischen den Polen nicht dein Körper sein! Auch, wenn dein Körper nicht so eine gute Verbindung darstellt, wie beispielsweise ein Kupferkabel, kann eine ausreichend große Spannung die Ladungen auch durch deinen Körper 'durchdrücken'. Die Folgen sind zum Beispiel: Verbrennungen an den Stellen, wo der Strom durchgegangen ist.

In der nächsten Lektion schauen wir uns das Ohm-Gesetz an, mit dem wir genau beschreiben können, wie Strom und Spannung miteinander zusammenhängen.

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