# Electricity; The Basics

## What is Electricity?

Electric charges are very important in all of nature and beyond. Charged particles produce a force-field called an electric field. Charged objects use this force field to attract other charged objects, or repel other charged objects.

Charges are responsible for a whole range of things that happen in physics, from the forces that hold you up in your chair as you read this, to the circuits in the computer that you are reading this from. Light from the Sun occurs because of charged particles called electrons.

There are two main charged particles to consider:

• The electron
• The proton

All matter is made up of protons, neutrons, and electrons. The neutron has zero charge and is found in the nucleus of an atom. The proton has a positive charge and is found in the nucleus.

The electron has a negative charge and is found orbiting the atom. If the numbers of protons and the numbers of electrons are the same, the object has zero charge.

That doesn’t mean that there is no charge; it means that the charges add up to zero. An object that has zero charge is called neutral. If there are different numbers of protons and electrons, the object is charged, which means it can make an electric force field to attract or repel other charged objects.

Protons are in the nucleus and NEVER move. Only electrons can move. Therefore:

• An object is positively charged if there is a deficiency (too few) of electrons;
• An object is negatively charged if there is an excess (too many) of electrons.

## Static Electricity

If we separate positive and negative charge from each other, we have to do a job of work. This is because they are pulling against us to get back together again.

In physics, we say that we have used energy to do that job of work. But that’s not the end of it. The two separated charges can come back together, and we can get them to do a job of work as they come back together. We refer to this energy as a potential difference or voltage.

We use these ideas in static electricity which arises from separation of charge in an insulating material. The material has to be insulating, because if we used a conductor like a metal, the negative charges and positive charges would come back together immediately.

Let’s suppose we rub a polythene rod with a cloth:

Electrons from the cloth are rubbed onto the polythene rod. This gives the polythene rod a negative charge.

Now suppose we charge an acetate rod with the cloth:

This time we rub electrons off the rod onto the cloth. The rod becomes positively charged, and the cloth becomes negatively charged.

If we hang the rods so that they can swing freely, we observe the following:

• A charged polythene rod brought close to another charged polythene rod repels;
• A charged acetate rod brought close to another charged acetate rod repels;
• A charged polythene rod brought close to another acetate polythene rod attracts;

We can conclude from this simple experiment that:

• like charges repel; unlike charges attract.

Voltages in static electricity tend to be high. You can easily get voltages of 5000 V on your jumper on a dry day, or 30 000 V from a nylon carpet. These can give sparks and a small shock, but the currents are so tiny that they cannot harm you.

There are many demonstrations in Physics that can be used to show static electricity, for example the Van der Graaff generator

Static electricity has uses, for example, in the photocopier. It can also be a source of hazards, for example sparks that can occur when an aeroplane is being refuelled.

This could be very dangerous. Beyond being a physics curiosity for the electrical engineer, static electricity is of limited concern beyond the fact that static electricity can do a lot of damage to delicate electronic components.

## Current Electricity

When we get charges to flow in metal wires, we can do rather more than show physics curiosities; we can do something useful with it. We will look at current electricity, the electricity that runs through wires made of conducting materials. For current electricity to flow, we need:

• a complete circuit;
• conducting materials;
• a source of voltage (e.g. a battery).

All metals are conducting materials, as is the non-metal carbon. Silicon and germanium are called semi-conductors which means that they can conduct electricity under certain circumstances. Some compounds can be made to conduct electricity under certain circumstances as well.

Insulating materials keep parts of the circuit separate, for example the positive and negative terminals of a battery. If the two are not kept separate, there will be a short circuit. This can cause an electrical explosion or a fire. The picture shows damage due to a short circuit.

## Circuit Diagrams

We don’t have to be good artists to draw good circuit diagrams. They are useful because:

• they show how the components are laid out;
• they show how the components are connected to each other;
• they show what is NOT connected together, which is just as important as what is;
• anyone can understand how the circuit works.

This is a simple circuit for a torch.

To make sense of circuit diagrams you must learn the following symbols:

It is also important that you know not just how parts of the circuit are connected, but also how parts are NOT connected:

The connection between wires is shown by the black circle, which can be thought of as representing a blob of solder. Connections are called junctions.

## Quantities in Electricity

Electricity has two important measurements from which other measurements can be worked out:

• Potential Difference or voltage
• Current

### Current

Current is a flow of charge. We measure charge not in the total number of electrons, but in packets called coulombs (C). (You buy a kilo of sugar, not 1 000 000 crystals of sugar.)

• 1 C = 6 × 1018 electrons

You can see why we don’t count the number of electrons flowing.

Current is measured in ampères or amps (A). If 1 coulomb of charge flows every second, a current is 1 amp.

• 1 A = 1 C/s

From this we can write an equation that links current and charge.

• charge (C) = current (A) × time (s)

In Physics Code:

• Q = It

In triangle form:

Make sure that time (t) is in seconds. You know how many seconds there are in a minute, and how many there are in one hour, don’t you?

A Model for Voltage

Voltage is the “electrical pressure” in a circuit. (The correct definition is energy per unit charge, but you may find that a difficult concept at this stage.) Look at this picture of a water circuit:

The pump pumps water at a certain pressure. The work that can be got out of the load depends on two things:

• The number of litres of water passing every second;
• The pressure the water is under.

This model can apply to an electric circuit:

• The pump is the battery;
• The load is the load (e.g. bulb, motor, etc);
• The water flow is the current;
• The pressure is the voltage.

There are all sorts of other models to explain voltage.

## Potential Difference

Potential difference is the more “formal” term for voltage. I tend to use voltage in these notes as well.

Potential difference is defined as:

• the energy per unit charge turned from electrical energy into other forms of energy

In other words, potential energy is defined in terms of joules per coulomb.

We can write this as an equation:

• potential difference (V) = energy (J) ÷ charge (C)

In Physics Code we write:

• V = E ÷ Q

In triangle form:

## Sources of Voltage

Three obvious sources of voltage are:

• Cells (batteries);
• Generator;
• Power pack, which you use in your physics practicals.

Strictly speaking a battery consists of two or more cells, although to describe a single cell as a battery is perfectly OK.

The positive terminal of a cell is represented by the long line on the symbol; the negative is shown by the short line.

Conventional current flows from positive to negative. Although we know that positives don’t move and electrons (negatives) do, the early physicists got it wrong. To get round it physicists have brought out the idea of conventional current. In these notes and all text books, we will regard all currents as conventional.

Each cell gives out a voltage of 1.5 volts. So two batteries wired in series as below will give out a voltage of 3.0 V.

## Measurements from Simple Circuits

In the above we saw that there were two main electrical measurements we could make easily:

• Voltage – this is done with a voltmeter;
• Current – this is done with an ammeter.

We use voltmeters and ammeters in circuits, in that the ammeter is wired in series with the component, while the voltmeter is wired in parallel.

We usually treat ammeters and voltmeters as perfect:

• A perfect voltmeter has an infinite resistance so takes no current.
• A perfect ammeter has zero resistance. Therefore there is no voltage drop across it.

However, real voltmeters and ammeters are not perfect.

## Voltmeters

Real voltmeters have a high (but not infinite) resistance and are connected across the component. The meter on the left is an analogue instrument.

It has a needle and a scale. It also has quite a low resistance, which means that it will not measure the voltage across high value resistors accurately.

A digital voltmeter is shown in the picture on the right. Digital voltmeters have a very high resistance, about 107 W (10 000 000 W or 10 Megohms), which makes them almost perfect. The picture shows a commercial digital voltmeter, with a home-made instrument built by students of the Technical University of Berlin.

Whatever the type of instrument, it is vital that the range selected is appropriate to the voltage measured. The picture below shows the mess that can be made when a 30 volt instrument was connected to a 230 V supply. One of the multiplier resistors has completely blown apart.

## Ammeters

Ammeters have a very low value of, but quite definite, resistance. The meter has a very low value resistor called a shunt wired in parallel.

Many schools and colleges buy analogue meters that can be turned into voltmeters, ammeters, or ac meters by plugging appropriate multipliers and shunts onto the instrument.

When you use a meter like this, you need to know what voltages or currents you are using. It would be no good measuring a current of 50 mA (milliamps) using the 10 A shunt.

If you were measuring a voltage of 30 V, you would use the 50 V range on the multiplier. You also need to read the correct scale. If you are using the 50 V range on the multiplier, you need to use the bottom scale. A needle deflection to 1 would be 10 V.

If you use the 10 A range on the shunt, 6 on the top scale will be 6 A. However, if you were using the 2 A range, you need to have to multiply the top scale by 0.2 – if you have a reading of 6 on the top scale, the current is 6 × 0.2 = 1.2 A.

## Multimeters

The Multimeter is a combined instrument that can:

• Measure voltage
• Measure current
• Measure resistance
• Measure frequency in some instruments.
• Test diodes and transistors in some instruments.
1. Function/Range Switch: selects the function (voltmeter, ammeter, or ohmmeter) and the range for the measurement.
2. COM Input Terminal: Common ground, used in ALL measurements.
3. V Input Terminal: for voltage or resistance measurements.
4. 200 mA Input Terminal: for small current measurements.
5. 10 A Input Terminal: for large current measurements.
6. Low Battery LCD: appears when the battery needs replacement.

There may be an internal fuse or a cut out to prevent excessive currents in ammeter mode, which otherwise might damage the instrument.

The digital multimeter is very close to being a perfect voltmeter, with a very high input resistance, with a very low input current.

Digital multimeters have functions with which they can test capacitors, diodes, and transistors. They can also display frequency.

## Further Electrical Quantities

Having measured the voltage and the current, we can work out other quantities that are of interest to the electrical and electronic engineer:

• Power: Power is the rate at which electrical energy is turned to other kinds of energy. Power is the voltage multiplied by the current.
• Resistance: Resistance is the amount by which a conductor opposes the flow of current. Resistance is the voltage divided by the current.
• Conductance: Conductance is the amount by which a conductor allows current to flow. Conductance is the current divided by the voltage.

There is another quantity that is of more interest to the physicist, charge. Charge is the current multiplied by the time.

### Power in a Circuit

Power in a circuit can be worked out using the simple relationship:

• Power (W) = Voltage (V) × Current (A)

In physics code, this is written:

• P = IV

The physics code for current is I which stands for “intensité du courant”, the French phrase meaning “intensity of the current”.

Power is measured in watts (W). Remember:

• 1 mW = 1 × 10-3 W
• 1 kW = 1000W
• 1MW = 1 × 106 W

In electronic circuits, the power may be low, say ½ watt. However, if the resistors are rated at ¼ watt, they will start to get hot.

Worked example:

• A current of 2.0 mA is flowing at a voltage of 12 volts. What is the power that is transferred?

Answer

• P = VI = 2.0 × 10-3 A × 12 V = 24 × 10-3 W = 0.024 W

This power is well within the capacity of a ¼ watt resistor.

### Resistance

Resistance is the opposition to the flow of an electric current. In physics, it is defined as the ratio of the voltage to the current.

• Resistance (W) =Potential difference (V) Current (A)

In Physics code:

• R = V/I

The formula is often referred to the Ohm’s Law Equation. Ohm’s Law states that:

“the potential difference across the ends of a conductor is directly proportional to the current flowing through the conductor, provided that temperature and other physical conditions remain the same”

The unit for resistance is ohm (W). (The curious symbol ‘W’ is Omega, a Greek capital letter long Ō.) There are some very important multipliers:

• kilohms (kW): 1 kW = 1000 W
• megohms (MW): 1 MW = 1 × 106 W

In some schematics, you will see the letter R for ohms, and k for kilohms. 22 R stands for 22 W; 22 M = 22 × 106 W

Worked example:

• A current of 2.0 mA is flowing at a voltage of 12 volts. What is the resistance of the component?

Answer

• R = V/I = 12 V ÷ 2.0 × 10-3 A = 6000 W = 6 kW

You must be able to recognise and use the multipliers for resistance.

### Conductance

The reciprocal of resistance is called conductance, which is used by some electrical engineers in the power industry. When wires have very low resistance, it is reasonable to say that they have a high conductance. Conductance is given the physics code G.

The units for conductance are Siemens (S), although in some books and magazine articles, you may see it written as mho (Ohm written backwards. Get it?).

### The Heating Effect of a Current

We can combine the equations for resistance and power to give these two equations for power:

• P = I2R or P = V2/R

Power is in Watts (W) or kilowatts (kW) or milliwatts (mW)

Worked example:

A current of 2.0 mA is flowing through a 50kW resistor. What is the power?

Answer:

• P = I2R = (2.0 × 10-3 A)2 × 50 000 W = 0.2 W = 200 mW

## Series and Parallel Circuits

### Series Circuits

In a series circuit, the electrons in the current have to pass through all the components, which are arranged in a line. Consider a typical series circuit in which there are three resistors of value R1, R2, and R3. The values may be the same, or different.

There are two key points about a series circuit:

• The current throughout the circuit is the same
• The voltages add up to the battery voltage.

Therefore:

• VT = V1 + V2 + V3

From Ohm’s Law we know:

• VT = IRT;
• V1 = IR1;
• V2 = IR2;
• V3 = IR3
• Ž IRT = IR1 + IR2 + IR3

Therefore:

• RT = R1 + R2 + R3

This is true for any number of resistors in series.

### Parallel Resistors

Parallel circuits have their components in parallel branches so that an individual electron can go through one of the branches, but not the others. The current splits into the number of branches there are.

The current will split into three. For a parallel circuit we know two things:

• The voltage across each branch is the same
• The currents in each branch add up to the total current.

From this we can write:

• Itot = I1 + I2 + I3

From Ohm’s Law, I = V/R, we can write:

I T = V ; I1 = V; I2 = V; I3 = V

RT R1 R2 R3

Ž V = V + V + V

RT R1 R2 R3

Ž

This is true for any number of parallel resistors.

We can combine resistors in both series and parallel.

## Kirchhoff’s Laws

These two simple laws were drawn up in the Nineteenth Century by Gustav Robert Kirchhoff. They explain all observations we see in electric circuits.

We can explain everything we have looked at in series and parallel circuits in terms of the two laws. They can also be used to explain more difficult circuits which cannot be explained in terms of simple series and parallel circuits.

### Kirchhoff I

This states that the total current flowing into a point is equal to the current flowing out of that point. In other words, the charge does not leak out or accumulate at that point. Charge that flows away must be replaced. It is conserved.

For Example; If we use I3 = I1 + I2.

Mathematically we can write this as:

• I1 + I2 + -I3 = 0

Notice that I3 has a minus sign. This means that the current going out is regarded as negative while current coming in is positive. At no point is there any reference to charge pooling at the junction, for the simple reason that it does not.

In some text books you will see written SI = 0. The strange looking symbol S is Sigma, a Greek capital letter S, which means “sum of”. So the sum of currents is zero, as we have seen above.

Suppose we had a high voltage junction where was a fault. A spark was jumping as well as current flowing away (i.e. not all the current was in the spark.)

### Kirchhoff II

Kirchhoff’s Second Law is not quite so easy to grasp.

The potential differences around a circuit add up to zero.

Provided the charge returns to the same place as it started, the gains and losses are equal, no matter what route is taken by the charge.

The battery in this circuit has an emf (electromotive force or open terminal voltage) of E. The curly E (E) is the battery voltage. We will look at emf later.

Let us do a journey around the circuit from A to B to C, and back to A.

• From A to B the p.d change is IR1 volts
• From B to C the p.d. change is IR2 volts
• From C to A the pd. change is E volts.

If we add up all the voltages, we can write IR1 + IR2 = E or IR1 + IR2 + -E = 0 or S(p.d.) = 0

This is another way of saying that the voltages add up to the battery voltage.

## Characteristics of Components

We can easily measure voltage and current, using the data to plot voltage current graphs.

The variable resistor is there to change the voltage and the current. A variable power supply (like a lab-pack) will also do the job, and a variable resistor is not needed.

Remember that the voltmeter is connected in parallel across the component; the ammeter is connected in series.

The investigation of voltage-current characteristics lends itself well to data-logging techniques. The voltmeter and ammeter sensors are wired in exactly the same way as ordinary meters. They are then connected to the computer.

From this circuit, we take readings of voltage and current plotting them as a graph called a VI characteristic.

We normally put the voltage on the y-axis and current on the x-axis. This allows us to determine the resistance from the gradient. This is a voltage current graph for an ohmic conductor:

The straight line shows a constant ratio between voltage and current, for both positive and negative values. We say that the voltage is directly proportional to the current.

This means that the graph is a straight line of positive gradient going through the origin. So when the voltage is negative, the current is negative, i.e. flowing in the opposite direction. Ohm’s Law is obeyed.

The resistance rises as the filament gets hotter, which is shown by the gradient getting steeper.

## Resistive Transducers

A resistive transducer is a device that senses a change to cause a change in resistance. Transducers do NOT generate electricity. Examples include:

Light Dependent Resistor ⇒ Resistance falls with increasing light level ⇒ Light operated switches

Thermistor ⇒ Resistance falls with increased temperature ⇒ Electronic thermometers

Strain gauge ⇒ Resistance changes with force ⇒ Sensor in an electronic balance

Moisture detector ⇒ Resistance falls when wet ⇒ Damp meter

These are called passive devices. (Active transducers do generate electricity from other energy sources, or have a power supply.)

A thermistor (a heat sensitive resistor) has a resistance that goes down as it gets hotter. This is because the material releases more electrons to be able to conduct.

The gradient is decreasing, indicating a lower resistance. There is, however, a health warning. As the current goes up, the thermistor gets hotter. As it gets hotter, it allows more current to flow; Therefore it gets hotter and so on.

This is called thermal runaway, and is a feature of many semi-conductor components. At the extreme the component will glow red-hot, then split apart.

The thermistor is used wherever any electronic circuit detects temperature.

## Light Dependent Resistors

The light dependent resistor consists of a length of material (cadmium sulphide) whose resistance changes according to the light level. Therefore the brighter the light, the lower the resistance. We can show the way the resistance varies with light level as a graph.

A graph will show us the variation using a linear scale. The graph to the right shows the plot as a logarithmic plot, which comes up as a straight line. Logarithmic plots are useful for compressing scales. The picture on the right shows how an experiment can be carried out

A logarithmic scale is based on powers of 10. In a logarithmic graph, the scale does not go 0, 1, 2, 3, etc. It goes 100, 101, 102, 103, 104… (1, 10, 100, 1000, 10000…) We say that the scale goes up in decades. By using a logarithmic scale, we can put a very large range of values in a small space, i.e. a side of A4 graph paper instead of several hundred metres.

LDRs are used for:

• Smoke detection
• Automatic lighting
• Counting
• Alarm systems

Resistive components can get hot when excessive current is flowing through them, and this can impair their function, or damage them. This can be prevented by connecting a current limiting resistor in series.

At a certain light level, a light dependent resistor has a resistance of 100 ohms. It can only handle a current of 10 milliamps before it risks heating up. If the LDR is connected to a 20 V supply, what value resistor should we place in series?

We know two things about a series circuit:

• The current is the same all the way round;
• The voltages add up.

So we can say that the current through the series resistor will be 10 mA.

Therefore we can work out the voltage across the LDR:

Remember that 10 milliamps = 0.01 amp.

V = IR = 0.01 A × 100 ohms = 1 volt.

Therefore we can say that the voltage across the series resistor is 20 – 1 = 19 volt. So we now work out the resistance with R = V/I = 19 volts ÷ 0.01 = 1900 ohms.

## Diodes

Diodes are semi-conductor devices that allow electric current to flow one way only. The circuit to measure the characteristic of a diode is like this, based on a potentiometer.

The potentiometer allows a range of values from 0 volts to the battery voltage. We will look at the potentiometer in more detail in a later tutorial.

The diode starts to conduct at a voltage of about +0.6 V. We call this forward bias. Then the current rises rapidly for a small rise in voltage. If the current is reversed (reverse bias) almost no current flows until the breakdown voltage is reached. This usually results in destruction of the diode.

### The E24 Series of Resistors

Electronic engineers use standard values of resistor which are given by the E24 series of resistors. If we work out that we need a resistor of 460 ohms, it is usually OK to use a 470 ohms resistor.

If it’s critical to have 460 ohms, we can always use a 430 ohm resistor in series with a 30 ohm resistor. Often a resistor is wired in series with a small variable resistor, called a trim pot, to adjust the voltage across it if a critical value is needed. The trim pot is adjusted with a screwdriver until the desired value is achieved.

This set of values is marketed in decades, or powers of 10:

So we can have values such as:

### Identification of Resistors with the Colour Code and BS 1852 Code

Resistors can make a circuit rather colourful, but that’s not really the intention. The colours have significance.

The values of the bands are shown in the table below:

• The first and second band give the number of significant figures. (In five band coding, it is the first, second, and third bands.)
• The third band gives the multiplier
• The fourth band gives the tolerance.

For example, a resistor marked red orange yellow gold would give:

A tolerance of ± 5 % means that the resistor would have a value between 220 kW and 240 kW.

Some resistors have their values marked not in colours but in numbers and letters. They use the BS1852 resistance code.

Instead of the W the resistors are marked with the letters R, K or M. The R, K or M denotes the decimal point:

There are other suffix letters that denote the tolerance:

Be careful not to confuse the letter K with the K for kilohms. 68KK = 68 kW ± 10%

## Potential Divider

The potential divider circuit (or voltage divider) is a voltage balance, that is used to switch on an electronic circuit when the balance of voltage reaches a certain tipping point.

Although it is simple, the potential divider is a very useful circuit. In its simplest form it is two resistors in series with an input voltage Vs across the ends.

An output voltage Vout is obtained from a junction between the two resistors.

If you imagine the voltage balance tipping, the resistance of the transducer changes. As the resistance changes, the voltage changes.

As the voltage changes past the tipping point, the balance tips from OFF to ON. This result can be thought of as the output voltage being the same fraction of the input voltage as R2 is the fraction of the total resistance.

## Need for a current limiting resistor

The current flowing through the thermistor or LDR will cause a heating effect which will alter the resistance as well as the temperature change. This is known as self-heating. The thermistor gets hot due to the increasing current through it. This can lead to a false reading of the resistance at a given temperature and in extreme circumstances cause thermal runaway.

This happens when the resistance falls, so a bigger current flows, therefore there is a bigger heating effect. The resistance falls further, so there is an even bigger current… The component will glow red-hot and burn out. To prevent thermal runaway, we place a current limiting resistor in series with the resistive transducer. If there is a problem like this in a potential divider, we can use a bridge circuit to take into account any self-heating effect.

## Potentiometers

Potentiometers are a kind of voltage divider. Instead of having two resistors, they have a slider that moves from one end of a resistor to the other. You buy potentiometers that can be used either as a variable resistor, or a potentiometer.

The variable resistor is wired in series with a component. It takes no current from the power supply. However, it can only alter the voltage a small amount into the component. If the component has a comparatively high resistance, the range of voltages is very limited.

With the potentiometer, we can have a full range of voltages from +Vs to 0, giving a wide range of voltage control. A model train controller works in this way. However it always takes a current from the supply, which will lead to a heating effect, and will run a battery down.

## Electrical Properties

### What are models?

Models in physics are ways of explaining difficult concepts in easier terms. Often models may not describe a system completely accurately, but most people who use the model have an idea of what is happening, even though the reality is more complicated. Mathematical modelling is often done in physics.

The simplest way to do this is to put a formula into a spreadsheet. The computer does lots of number-crunching, and draws graphs of the results. You can change the different parameters (values) that the formula uses to see what happens.

### How is electricity conducted?

Electricity moves due to the movement of charge carriers. If we think about an ionic solution, the positive ions are attracted to the negative terminal (the cathode), while the negative ion are attracted to the positive terminal (the anode).

In a metallic conductor (wire), the simplest model of conduction is to consider the metal as a lattice of metal ions in a sea of free electrons. The electrons move about randomly.

When a voltage is applied across the ends of the wire, the electrons continue to move randomly, but there is an overall drift to the positive end of the wire. So you will (rightly) think that electrons go from negative to positive.

The protons don’t move. So this idea is opposite to what you have been told. The explanation is that the earliest physicists got it wrong. They didn’t know about electrons in the Eighteenth Century. So instead of rewriting all the rules of electricity, people talked about conventional current going from positive to negative.

We can write an equation for the conduction of a current in a wire. The current depends on:

• The speed of the charge carriers (v (m/s));
• The area of the wire (A (m2));
• The charge on the electrons (e = 1.6 × 10-19 C);
• The number of charge carriers per unit volume (n (m-3)).

The symbols in italics are the physics codes for the various quantities, and the units are given as well.

The formula is:

• I = nAve

The number of charge carriers per unit volume is probably the hardest quantity to get your head round. It means the number of electrons in a cubic metre of the material. For example, copper has 8 × 1028 electrons in each cubic metre of material. You can look up the number of electrons per cubic metre in a data book.

The result from this calculation shows that the speed of electron drift is slow, 1 mm every 5 seconds. The propagation of the message “that the current is flowing” is very fast, not far off the speed of light.

But the drift speed of electrons is not at all fast. We can show this by putting a small crystal of potassium permanganate (a dark purple ionic compound) onto a filter paper which has been soaked in sodium chloride solution. When a current flows, the purple permanganate ions move towards the positive terminal, but it takes some time.

The tungsten filament has a higher resistance than the copper wire. For the same current to pass through, the electrons have to go faster, because:

• The number of charge carriers per cubic metre is smaller;
• The area is smaller.

This is opposite to the generally perceived idea that electrons are slowed down by high resistances.

### Resistivity

The resistance of a wire depends on three factors:

• the length; double the length, the resistance doubles.
• the area; double the area, the resistance halves.
• the material that the wire is made of.

Resistivity is a property of the material. It is defined as the resistance of a wire of the material of unit area and unit length.

The formula for resistivity is:

In physics code we write this as

• r = AR/l
• The unit for resistivity is ohm metre (Ωm), NOT ohms per metre.
• Notice too that the physics code r (rho, a Greek letter ‘r’) is the same as that for density. Resistivity has NOTHING to do with density.
• The area is in square metres. Real wires have areas in square millimetres; 1 mm2 = 1 × 10-6 m2

The reciprocal or inverse of resistivity is conductivity. It has the physics code s, (“sigma”, a Greek letter ‘s’), and units Siemens per metre (S m-1).

Conductivity is given by the relationship:

### Super-conduction

A super-conductor is a material that has zero resistance. A current flows when there is no potential difference. The piece of metal floating above the magnet shows that there must be a current flowing.

For all metals the resistivity (hence resistance) decreases as they get colder.

For some metals like copper and silver, there is still a tiny bit of resistance left at very low temperatures.

Very low temperatures have to be maintained, which is expensive. Room temperature superconductivity has not been seen.

Super-conductivity is seen in:

• Aluminium
• Tin;
• Some alloys;
• Some heavily-doped semi-conductors.

All superconductors have a critical temperature above which the phenomenon stops. The graph below shows the idea:

Above the boiling point of liquid nitrogen, 77 K (-196 oC), superconductivity can be observed in a few materials. These are called high temperature superconductors.

Very large magnets such as those found in the large hadron collider have coils made of superconducting materials. It is believed that the superconductivity will last 100 000 years, as long as the coils don’t go above their critical temperature.

The mechanism for super-conduction is complex, and cannot be explained in terms of electrons colliding with ions.

## Semiconductors

Semiconductors have a resistivity (or conductivity) that is intermediate between a conductor (like a metal) and a insulator (like glass). They are usually based on silicon, which is in the same group as carbon. Group IV elements have 4 valence electrons and form a lattice like this:

The valence electrons form covalent bonds. There are very few free electrons so pure silicon is a very poor conductor.

However, if we dope the pure silicon crystal by adding an impurity, for example, phosphorus, we can change things.

We have a spare electron left over, because phosphorus is a Group V element, which has 5 valence electrons. 4 are used to make covalent bonds, while the one left over is free. The free electron acts as a negative charge carrier. We call this kind of material a n-type semiconductor.

If we use aluminium, or other Group III element as a dopant, we only have 3 valence electrons. Therefore there is one of the silicon electrons that is unpaired.

This missing electron is called a hole and it acts as a positive charge carrier. Since the silicon atoms can borrow electrons from their neighbours, the hole can move about, and move away from the original aluminium atom. The hole will move towards the negative terminal of the semiconductor.

In the picture above, we see holes being attracted towards the negative, and electrons being attracted towards the positive.

If we place an n-type semiconductor next to a p-type, we find that some of the holes will diffuse into the n-type material at the interface, or junction, between the materials. We also find that some of the electrons will diffuse into the p-type material.

The electrons and the holes combine and act as neutral. So the n-material there has been depleted of electrons, and the p-material has been depleted of holes. We call this region the depletion layer and it acts as an insulator.

If we apply a positive voltage to the n-type material (and a negative voltage to the p-type), the depletion layer gets wider. This is because more holes are attracted from the p-material towards the negative (and electrons to the positive). The increased combination of electrons and holes increases the width of the depletion layer.

If we swop the polarity about, so that the n-type material is negative, the holes get attracted to the negative and the electrons get attracted to the positive. The depletion layer is lost, and conduction starts.

This could be thought of merely as an interesting physics curiosity, but is actually an important concept at the heart of all solid state electronic devices.

### Conduction bands

The models that have been explained above are not perfect. They do not cover every aspect of electrical conduction. In the early part of the Twentieth Century, quantum physics grew to allow physicists to explain a lot of observations that cannot be explained by normal (or classical) physics. Quantum physics is not at all easy to understand, but there are two things that we can use:

• Electrons perch on the rungs of an energy ladder;
• Electrons exist in probability clouds.

The key point is that electrons are quantum beings. If you try to catch an electron, you will never do so. The closer you are to getting hold of the little brute, the less likely it is that you will catch it.

Let’s try to illustrate these ideas with another model:

Fingers” is a criminal. He is in prison, but he doesn’t think he should be inside. He wants to be outside to commit more crimes.

In the real world, Fingers can jump, but not that high. He could not jump from the Inside to the Outside. So he remains in the nick. But in the quantum world, Fingers is in a probability cloud.

Fingers’ probability cloud extends to just over the prison wall. So there is a tiny, but real, probability that he could happen to be just on top the prison wall, so he could make good his escape. Also, in the quantum world, the closer the coppers are to nicking him, the more likely he is to get away.

Now electrons perch on different rungs of the energy ladder. They have to be on a particular rung; they cannot perch between rungs. Because they live in probability clouds, there is a chance that they can fly up to the next rung of the energy ladder, as long as another electron comes down from a higher perch (which it will). For most of their time, electrons are in the valence band, perching on the normal rungs of their ladder.

Above the normal rungs (the valence band) there is a forbidden gap, a space where there are no rungs for them to perch. Above forbidden gap is the conduction band in which the electrons are free to move about.

It’s a bit like aeroplanes flying about an aerodrome. They can be on the ground, but once in the air, they must not fly below 500 m in the region of the aerodrome. They can fly at any height above 500 m, but if they fall below, the pilots could be in trouble.

The electrons can get sufficient energy to jump the forbidden gap to go into the conduction band. This is because of the probability cloud. If the forbidden gap is small, as in metals, the probability that the electrons will make it to the conduction band is high. In a pure semiconductor, the forbidden gap is bigger, so the probability of electrons jumping to the gap is smaller, but not impossible.

If we put impurities into the crystal lattice of the semi-conductor, we put extra levels in the forbidden gap, a bit like wires for the electrons to perch on. This allows for a greater probability of the electrons reaching the conduction band.