# Electric current

**Electric current**\(I\) - is the amount of charge that crosses a cross-sectional area within a certain period of time.

## Level 1

You have surely seen the indication of an electric current on your charger cable: For example an input current of 0.5 Ampere. Let's try to understand what this value physically means.

## Electric charges

In our universe there are electrically charged particles that interact with each other. Some are positive (+), others are negatively (-) electrically charged. Electrons and protons, of which atoms are made up, are for example such electrically charged particles. Electrons are negatively charged. Protons are positively charged. When you bring two positively charged particles closely together, they repel each other. Two negatively charged particles also repel each other. When you bring a positive and a negative particle together, they *attract each other*.

Charges (+ and +) or (- and -) of the same polarity repel each other. Charges (+ and -) of different polarity attract each other.

Through such repulsion and attraction, charged particles interact with each other. Experiments have also shown that these charged particles do not all attract or repel each other equally strongly! There are charged particles that attract each other more than others. To quantify this difference in attraction and repulsion, we say that charged particles carry different charges \(q\). The charge is measured in the unit *Coulomb* and is abbreviated with the letter \(\text{C}\). The greater the charge \(q\) of a charged particle (e.g. \(q = 1\,\text{C}, 2\,\text{C}, 3\,\text{C}\)), the more it is repelled or attracted by other electrically charged particles.

In order to distinguish positive and negative particles, we assign a negative sign to negatively charged particles. For example: \(q = -1\,\text{C}\), \(-2\,\text{C}\), \(-3\,\text{C}\). And positively charged particles we assign a positive sign. For example: \(q = +1\,\text{C}\), \(+2\,\text{C}\), \(+3\,\text{C}\), whereby we can of course leave out the plus.

## When charges move...

But what do electric charges have to do with electric current? Let's do a little thought experiment with what we know so far. We'll take two boxes, with a hole that can be opened and closed. First, we close both holes. In one box, we put many *positive* particles. Each of them carries the same charge \(q\) and for fun it is one Coulomb: \(q = 1 \, \text{C}\).

In the other box we place many negative particles, each with a *negative* charge: \(q = -1 \, \text{C}\). The two boxes now form a large electric charge. We can also say that the negative box forms a **negative pole** and the positive box a **positive pole**. The two charged boxes will now of course attract each other. To prevent this, we fix the two boxes so that they cannot move towards each other.

Next, we connect the two boxes with a conductive wire, for example with a copper wire. By "conductive" we mean that charges can move through this wire.

What happens to the positive charges in the positive box when we open it? The positive charges can now move to the negative box along the wire. Why are they doing this? Well, because they are attracted by the negative charges. This movement of the charges is an **electric current** and it is in the direction of the negative pole.

Qualitatively speaking, the current becomes larger when more charges pass through the wire. But how do we quantify the current now? Let's abbreviate the electric current through the wire with the letter \(I\). If we cut the wire, we would get a round circular area. This circular area is called theem>cross-sectional area of the wire. Then we concentrate on a cross-sectional area of the wire. The positive particles will of course pass through this area.

To quantify the current, we simply count how many charges \(q\), pass through a cross-sectional area of the wire within a given period of time \(t\).

If we have counted \(N\) positive particles each with the charge \(q\) within a certain time period that have crossed the cross-sectional area of the wire, then the total charge that has crossed the cross-sectional area is \(Q\): `\[ Q ~=~ N\,q \]`

Since the electric current \(I\) is the amount of charge \(Q\) that passes through a cross-sectional area of the wire per time \(t\), we must divide \(Q\) by \(t\) to obtain the electric current:

**Electric current**

`\[ I ~=~ \frac{Q}{t} \]`

**Unit of electric current**:

The charge \(Q\) has the unit \(\text{C}\) (Coulomb). The time \(t\) has the unit \(\text{s}\) (second). So the electric current \(I\) has the unit \( \text{C}/\text{s}\) (Coulomb per second) or short: \(\text{A}\) (Ampere).

The current \(I\) is greater the more charge \(Q\) passes through the cross-sectional area of the wire within a certain time \(t\).

**Example**

A charge of 0.5 Coulomb passes through the cross-sectional area of a wire within 10 seconds. So here is the time: \(t = 10 \, \text{s}\). And the charge \(Q\) that has crossed the wire in that time: \(Q=0.5 \, \text{C}\). If you divide the charge by time, you get the charge per time, that is, the electric current:`\[ I ~=~ \frac{ 0.5 \, \text{C} }{ 10 \, \text{s} } ~=~ 0.05 \, \frac{ \text{C} }{ \text{s} } ~=~ 0.05 \, \text{A} \]`

**Is one ampere a large current?**

In our thought experiment, we assigned a random value of one Coulomb to the positive particles. But in reality the particles carry a much charge. Usually the negative electrons are responsible for the electric current in conducting wires. They carry a tiny negative charge, namely \(q = -0.000 \, 000\, 000\, 000\, 000\, 000\ 16 \, \text{C}\). For the electrons to generate a current of \(I = 1 \, \text{A}\), 6250 QUADRILLION of electrons per second must pass through the cross-sectional area of the wire! This number is unimaginably large!

So, to sum up: The current \(I\) describes how much charge per second is transported through a cross-sectional area. In order for the current to be generated at all, charged particles must be set into directional motion. This directional motion occurs when positively and negatively charged particles are separated and then attract each other. The separation of charges is characterized by the so-called *electric voltage*. But this is a topic for another lesson.