Our first step into the world of electricity.

• Electric Charge
  • Charge carriers
  • Quantisation & Elementary charge
• Current
• Formula describing current in a conductor: I = nAvq

Let’s go!

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What is electric charge?
A property of matter which interacts with the electric field. It takes 2 values, positive & negative. Usually, it is represented by the letter “Q”.

Basically, we have no idea. It’s a property of matter which we gave a name, and can take 2 opposing values. We could just as easily call them Blue & Red or Cheryl & Daryl. However, naming them + & – makes calculations quite easy.

What is a charge carrier?
Particles which carry charge. Usually, charge carriers are allowed to FLOW or MOVE freely in space. Examples include:

• Electrons
• Protons
• Ions

One thing to note about electric charge is that it is QUANTISED.

What is quantisation?
A quantised value can only take certain values, & not others.

Electric charge can only exist as an integer multiple of 1.6×10^-19 Coulombs.

Why are charges quantised?
Because the smallest* carrier (the ELECTRON) is quantised.
This means that there a minimum amount of charge: the charge of 1 electron.

There is another unit we can use to measure charge: e.
1e = 1.66×10^-19

*Later we will deal with QUARKS which have smaller charge values: 1/3 e or 2/3 e. However, quarks cannot exist alone, so they will always join to make particles with integer multiples of e.

What is the conventional unit we measure charge in?
Coulombs (C).
1 Coulomb is defined as the charge passing a point when there is a current of 1 Ampere for 1 second.*

Q = It

*Why this arbitrary definition, why not define it in terms of e?
Because electrons were discovered long after current was described, so scientists stuck to the older definition – ALL units are arbitrary, we tend to follow history!

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What is a current?
The rate of flow of electric charge across a point.
Current = amount of electric charge passing through a point per unit time:

I = Q/t

Rearranging this, you get the formula which defines the Coulomb above!

What is the direction of conventional current?
Conventional current describes the flow of POSITIVE charges from POSITIVE terminals to NEGATIVE terminals.

More generally, we take it to flow AWAY from high positive potentials to lower potentials (or negative potentials).

In real life, current is usually carried by NEGATIVELY-charged electrons which flow the OPPOSITE way, which can be a little confusing for us. The reasoning is history, which you can learn through this video by TED-Ed: https://www.youtube.com/watch?v=MBRTR2dlwvA

Current technically describes the flow of charge carriers anywhere, but we will focus on current flowing through ELECTRICAL CONDUCTORS.

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What is a current-carrying conductor?
A conductor which has current in it (duh).
Specifically: a conductor which contains charge carriers moving in an average direction with an average drift speed.

One current-carrying conductor we use in everyday life is the WIRE – approximated as a cylinder. Here’s a section of some:

There’s another formula we can use to describe current in a current-carrying conductor:

I = nAvq

n = number density = number of charges per unit volume
A = cross-sectional area
v = drift speed
q = individual charge

Here’s a proof of this formula:
We know from before that current is number of charges flowing over time:
I = Q/t

The total charge Q is the sum of individual elementary charges. Therefore, the total charge Q is the number of charge carriers (N) multiplied by the individual charge q:
I = Nq/t

Another value (n) can be described for the amount of charge carriers per unit volume.

We call this NUMBER DENSITY:
n = N/V

In a cylindrical current-carrying conductor, the volume is described as the cross-sectional area (A) multiplied by the length (x):
n = N/Ax

Therefore,
I = nAxq/t

Drift speed is the AVERAGE speed of all the charge carriers within a conductor.
Since speed is the distance it travels per unit time. In this case, it travels along the length of the wire (x):
v = x/t

Therefore,
I = nAvq