Birmingham July 2012

Friday 6th July

The third lecture was given by Jim Woodfin of Queen Mary, University of London. The lecture was called Electrical conduction (the full story).

clip_image002

Whatever school year you are in you will learn something about electricity and your teacher will use models to help you learn. The problem is that none of the models are perfect and it is only through mathematics that the best understanding can be gained.

At key stage 3 we tell you that electricity is a flow of charges in the wire (like water flowing in pipes) and that two things are needed for a current to flow: a power supply and a complete path. This is called an electric circuit. If you want to do things like produce light you need to add a component like a bulb. A switch is usually added to switch the current on and off quickly. You learn the symbols for these different components and the behaviour of series and parallel circuits. You learn that to measure the current an ammeter must be placed in series with the component being investigated and that to measure the voltage a voltmeter must be placed parallel to the component being investigated. You learn that voltage is a measure of electrical energy between two points in the circuit. The model you learn is that the power supply gives the charges energy to move but the problem with this model is that it doesn’t explain why switching on the power supply immediately gives you light or heat etc. You would expect there be to a time interval whilst the charges pick up energy in the power supply. This is not the case. You learn about the similarities and differences between series and parallel circuits. You learn that by adding more cells in the battery pack or by increasing the power supply voltage increases the current. In a simple series circuit all the voltages across the components add up to the power supply voltage. In a simple parallel circuit the voltage across each component equals the power supply voltage. In a series circuit the higher the voltage the more power is delivered by the circuit and the current is the same in all parts of the circuit. In a parallel circuit current splits up or rejoins at a junction and the current drawn from the power supply increases as more branches are added. If the voltage is kept the same but the current increases there is greater activity.

You also learn that a current can have a heating effect and a magnetic effect (a compass needle is affected).

At key stage 4 you learn about more electrical components and you revise series and parallel circuits. You also meet some formulae: I = Q/t which is current is equal to charge flowing divided by the time taken to flow. You learn that voltage should be called potential difference and = W/Q = work done/charge flowing. You also learn about resistance = V/I = pd/current. You learn about how resistance is different in thick and thin wires and different components. The model we use is that in metals the current is made up of electrons that are freed from the metal atoms and can flow when placed in a complete circuit. You learn to identify different electrical components by their current potential difference graphs. You learn about household electricity, that earthing any part of a circuit does not interfere with the circuit and about ac and dc current. You learn how to calculate electrical power (P = VI = E/t) and the relationship between energy and charge, E = QV. The model of electrical conduction is still quite poor.

At AS level, key stage 4 work is revised as it is easily forgotten. You learn that resistance of a wire is not just affected by the pd across but is also affected by its length, thickness (cross-sectional area) and the material it is made of (resistivity ρ), R = ρl/A. You learn that the temperature can also affect resistance and that if the temperature is low enough the material can become a superconductor. You learn how to calculate resistance in series and parallel circuits and you are expected to use algebra to find alternative ways of calculating values e.g. P = IV but it can also be I^2R. You learn about the potential divider and how it can be used to produce different pd values. You learn that the voltage value given for power supplies is actually the Emf (electromotive force) and that the pd available to a component is less due to the presence of internal resistance in the power supply if current is drawn. The greater the current drawn the less pd available: V = E –Ir where V is the pd, E is the emf, I is the current drawn and r is the internal resistance. However our model of what is going on hasn’t changed very much. We know the current is dependent on the number of charge carriers per unit volume (copper has 1E20 “free” electrons per cubic cm), the drift velocity of the charge carriers, the cross sectional area of the material and the charge of the charge carrier. The drift velocity is actually very small. It is the “signal” to get the charges moving that is very fast. Charge carriers, usually the electrons carry electrical potential energy by their spacing to the components.

We will now start to look at electricity in greater depth that is not required at school level.

clip_image004

The diagram above is showing that the charge carriers do not move uniformly (electrons moving from the negative terminal get bunched up as they are being repelled by that terminal). This goes against the idea that the current is the same in all parts of the circuit. It so happens that our ammeters are not sensitive to know that this is happening. When like charges are brought together it is like compressing a spring. Absolute potential is due to charge separation V = kQ/r and the relative predominance of a positive or negative charge. Pd is a difference in potential (i.e. a difference in spacing). So electron spacing has to vary round the circuit.

Flow of charge is the current made up of “free” electrons. There is about 1xE20 per cubic cm in copper. They are already present in the wires and components. When the circuit is complete a “signal” passes round very quickly (much faster than the charges themselves. The voltage is like a pressure difference. The battery is considered to be a source of chemical energy. The electrons “carry” energy as electrical potential energy to the components due their spacing. Resistance can be thought of as a constriction in the circuit like standing on a hosepipe when water is trying to run through it.

To get a better idea of what is happening in a circuit we need to go down the quantum mechanics route meaning that it is only through mathematics that we can get a true picture of what is happening.

The slide below links thermodynamics to electron flow. Something that isn’t done at A level.

clip_image006

In the slide below SUVAT refers to the equations of motion that AS students learn.

clip_image008

clip_image010

clip_image012

j = current per unit area, n = number of charges per unit volume, e = charge value, v = drift velocity, E = uniform electric field, τ = time between collisions, Vrms is the root mean square speed, m = mass of the charge carriers, k is the Boltzmann’s constant, T is the absolute temperature in Kelvin, σ = conductivity, L is the distance travelled between collisions and ρ is the resistivity. The slide below tells us that resistivity is proportional to the square root of absolute temperature.

clip_image014

clip_image016

Pd is the electrical potential energy per unit charge. Potential energy for a point charge +q near a point.

clip_image018

clip_image020

clip_image022

R is the universal gas constant

clip_image024

clip_image026

clip_image028

clip_image030

clip_image032

clip_image034

clip_image036

clip_image038

clip_image040

Whatever year you are in, electricity is taught using models and we think of electrons as being free in a metal to form the current. With quantum mechanics this isn’t the case.

References: http://en.wikipedia.org/wiki/Electrical_conductivity

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s