It is often up to a teacher and a particular class to decide what equipment to use to introduce electric circuits. There are two general types of equipment used in schools for experimenting with electric circuits:

• Circuit boards (such as the Worcester Circuit Board) are designed with simple components so that the shape of the circuit which is constructed looks like a circuit diagram. This helps students to work from a circuit diagram or draw one themselves as a record of the work they have done. Some teachers find circuit boards can confuse less able students - they don’t realize that parts of the board without anything connected are not part of the circuit. Circuit boards have an advantage in that the connection of the cells in parallel is discouraged.
• Separate components connected by wires. This can be a cheaper solution, but it can also produce a tangle of wires so that the circuit becomes confusing.

Give students simple instructions on how to use the kit. As work progresses, make simple testing devices available, to test whether a cell is flat, a lamp is broken, or a lead not providing a good connection. These are easy to assemble with the item to be tested being the missing component in a simple series circuit consisting of lamp, cell and connecting wires. Learning how to trouble-shoot a circuit probably teaches more than circuits which give the predicted result the first time.

Good maintenance is essential

Time spent in checking the equipment before a lesson will pay dividends in the students’ understanding.

Some agreement must be established within the class so that the brightness of one lamp used with one cell is ‘normal’ brightness. In more complex circuits the brightness of the lamps can then be compared to this standard.

For this to be clear, students need to be given cells which have the same voltage (checked when they are driving a current through a lamp and not on open circuit), and all the lamps in a student’s collection need to produce the same brightness with the same cell. This is quick to do if three cells are connected in series to three rows, each consisting of three lamps, so that all lamps glow with normal brightness. If possible, new cells should be used at the beginning of each year and the old cells used up doing other jobs. The quality control, during production, on simple lamps is not good and even new lamps from the same packet can vary widely.

The difference in brightness of the lamps might be difficult to see in bright sunlight or with laboratory lighting and so the laboratory should be dimmed a little.

What type of cell is best?

The cost of cells has led some teachers to try rechargeable cells, which have their own problems. They have low internal resistance, so, if shorted, allow a large current. And they need to be completely flat before they are recharged. Cheap zinc-chloride cells are best for elementary work. Alkaline-manganese cells may be used where shorted cells are unlikely.

Some teachers even use power supplies. However, power supplies suffer from their internal resistance, just like cells. They may give unexpected, but entirely correct, results when the simple story about electric circuits is being told and internal resistance is being neglected. In order to avoid running down some of the cells and not others during experimenting, students should be issued with switches, or asked to disconnect the circuit when they are doing other things.

Terminology

The language may vary in different teaching programmes with an insistence on cell for the simple 1.5 volt (approximately) simple cell and battery being reserved for several cells in series. Bulb may also be used instead of lamp.

Once your students understand how circuits can be set up, it is time to introduce them to the idea of the lamp as an informal ammeter. A fully-lit lamp connected to one cell can be said to indicate ‘one lamp’s worth of current’ (whatever current really is). Two lamps lit by one cell will each have less than ‘one lamp’s worth’ of current through them. One lamp connected to two cells will have more than ‘one lamp’s worth’ of current through it.

Some students may wish to know more about the electric current. At an introductory level, discussion along the following lines might be suitable.

You cannot see an electric current, or hear it, or know about it, by anything except by what it does.

How do you know that your Uncle George has a bad temper? Because he talks very crossly when you annoy him. You only know he has a bad temper by its effects. You cannot see a warning light on his head labelled ‘bad temper’ or a tribe of little demons dancing in his stomach to keep him irritable.

Some of you may have heard that when there is an electric current there are little electrons running along in the wire but you cannot see them any more than you can see the demons in Uncle George’s stomach. If we behave as good scientists and stick to the evidence, we can say that we see a lamp that's lit and a wire that’s hot. From this we infer there is an electric current.

Electrical phenomena result from a fundamental property of matter: electric charge. The atoms that constitute most matter we encounter contain charged particles. Protons and electrons each have one unit charge, but of opposite sign. Atoms are generally neutral because the number of electrons and protons are the same.

Electric charges at rest have been known much longer than electric currents.

The amber effect

The property now called static electricity was known to the philosophers of ancient Greece. In fact the word electricity comes from ‘elektron’, the Greek name for amber. Amber is a resinous mineral used to make jewellery. It is probable that small fibres of clothing clung to amber jewels and were quite difficult to remove. Trying to rub the fibres off made the situation worse, causing early philosophers to wonder why.

William Gilbert mentioned the amber effect in his ground-breaking book On Magnetism, published in 1600. He noticed that the attraction between electrics was much weaker than magnetism and wrongly said that electrics never repelled.

Benjamin Franklin

A giant leap of understanding was required to explain observations like these in terms of positive and negative electrical charge. In the 18th century, Benjamin Franklin in America tried experiments with charges. It was Franklin who named the two kinds of electricity ‘positive’ and ‘negative’. He even collected electric charges from thunderstorm clouds through wet string from a kite.

Franklin was an advocate of a ‘single fluid’ model of electric charge. An object with an excess of fluid would have one charge; an object with a deficit of fluid would have the opposite charge. Other scientists had advocated a ‘two fluid’ theory, with separate positive and negative fluids moving around. It took over a century for the debate to come down on Franklin’s side.

It is interesting to note that Franklin coined several electrical terms which we still use today: battery, charge, conductor, plus, minus, positively, negatively, condenser (= capacitor), among others.

Electric currents

Electric currents were not fully investigated until batteries were invented in about 1800. Passing currents through salt solutions provides evidence that there are two kinds of charge carriers, positive and negative. The charge carriers that boil out of white hot metals are negative electrons, and movements of electrons produce current in a cool, metal wire.

For a time electric currents seemed so different from electric charges at rest that the two were studied separately. It seemed as if there were four kinds of electricity: positive and negative electrostatic charges, and positive and negative moving charges in currents. Now scientists know better. There are just two kinds, positive and negative, exerting the same kind of forces whether they were ‘electrostatic charges from friction’ or ‘moving charges from power supplies’.

A modern view

Electric forces are what hold together atoms and molecules, solids and liquids. In collisions between objects, electric forces push things apart.

Today we understand that electrons may be transferred when two different materials contact each other and then separate. You can list materials in order, from those “most likely to lose electrons” (gaining positive charge) to "those most likely to gain electrons” (gaining negative charge). This is called the triboelectric series.

At some point during the early teaching of electric circuits, students will want to know what an electric current is. Indeed students may already have their own ideas about what it is and how it behaves. There has been much research into the ideas students bring to their lessons, and the misunderstandings they develop during the teaching/learning process.

Electric current is known only by its heating, magnetic or chemical effects. Beyond this there are only models which explain such effects and make possible reliable predictions.

Misconceptions common among students

• the ‘clashing currents model’ in which electric current is thought to leave both ends of the cell and meet at a component, for example a lamp, and make it operate;
• the ‘single lead model’ in which students see the need for only one connecting wire leading from the cell to the lamp (this is often exacerbated if all the connections are not clearly visible on the circuit itself);
• the ‘current is used up around the circuit model’ in which the current is thought to leave one terminal of the cell and is used up in the components; nothing returns to the other terminal. In fact, why have a return wire?

Teachers' models

There are many models which teachers use to describe electric circuits. Different ones are useful in different situations. Three of these are listed here:

• the water circuit in which the flow of water is likened to the electric current;
• a grid of wide and narrow streets, complete with car parks and one way systems, on which cars pass at speeds determined by the density of traffic;
• the pupil circuit in which sweets are given up by the ‘cell pupil’ (energy) and ‘pupil charges’ transfer them to ‘component pupils’.

When discussing the water circuit as a model for an electric circuit, you could say to students:

There is something the same all the way round the circuit, the same reading with a simple ammeter, or the same brightness of a series of lamps. One of the lamps could even be placed in series between the two cells and will be just as bright as the others.

That is why scientists say, “There is a current; there is something running round the circuit which stays the same all along, just like a current of water in a river.” If a river is carrying 1,000 litres per minute past one place, it must be carrying 1,000 litres a minute past any other place farther down the river unless there is some side stream or a mysterious hole in the ground. Some scientists like to think of this electric current story as rather like water being pumped round a closed ring of piping.

Bring out the analogy between:

• the pump and the cell
• the tubing and connecting wires
• the wide and narrow tubes and resistances
• the flow meter and an ammeter, and
• the pressure gauge and a voltmeter

Once students have used other components then the model can be extended in imagination to the idea of one-way valves representing diodes, and reservoirs representing capacitors. Stress that the flow of water is the same all round the circuit, unless of course you have a leak!

Once the model has been described then discussion can return to the electric circuit.

Is there really something that moves round through the copper wires and through the lamp and makes the lamp light or pulls the magnet? As far as you or I can tell, this electric circuit behaviour is rather like the behaviour of a current of water flowing that makes the same thing happen all the way round. We do not know, yet, whether anything is really flowing and certainly not what it is. If it flows it might be some kind of juice flowing this way round the circuit (positive juice) or it might be some opposite juice (negative juice) running the other way round the circuit. Or it might be both of those each running its own way.

Instead of some smooth juice flowing like water in a pipe the current might be a movement of little particles, moving along like a line of rabbits in a burrow or an army on a road. Again this might be a row of positive bits travelling this way or negative bits travelling that way or both kinds each travelling its own way.

Which of all these things do you think is right? Nothing travelling at all, or a juice travelling one way or another, or little bits of electricity travelling one way or another?

Whatever the answers at this stage students need to wait for further evidence. Nowadays scientists know that there are things which move when an ‘electric current’ happens, in some cases several kinds of things. In fact, contrary to wishful hopes, nothing in elementary physics teaching, even cathode ray tubes, requires a view that electric charges come in small particles. Continuous (negative) juice would do just as well. Only when students meet Millikan’s experiment do they require particles of electric charge to explain the data.

For the moment stick to the standard agreement, used by all electrical engineers, which is the idea of bits of positive electricity coming out of the red knob of the cell and going round the circuit in one direction to the negative end of the cell. That was settled long before anyone knew about electrons and is used to put arrows on the electric circuit drawings. Later on you will be able to decide for yourselves what is really going on and you might find it even more complicated than you think.

Introductory level ideas

At introductory level, the descriptions of what happens in electric circuits are simply qualitative. It is not appropriate to discuss concepts quantitatively.

Intermediate level ideas

Defining current

Current can be described as a flow of charge measured in coulombs. You then describe and define the coulomb in terms of copper plating. You can even state that unit current, one ampere (or amp), means one coulomb per second in terms of copper plating (0.000 000 329 kg of copper carried across every second in a copper plating bath). Although that does not agree with the present fashion of defining currents by forces, it gives students a much easier way of picturing currents. They already have, from common knowledge, a strong feeling for currents as streams of little electrons, and if you bunch those electrons into large coulombs of charge you can easily persuade them to think of currents being measured in coulombs per second.

Defining Potential difference

Once students understand energy transfers, potential difference can be discussed clearly, and the volt defined as a joule per coulomb. Discussing power supplies as sources of energy, and electric charges as carriers of energy helps the beginner to understand why a current in a series circuit does not diminish as it flows through energy transfer components such as lamps. You can treat potential difference as a fundamental measurable quantity, described as energy transfer for each coulomb that passes through the region in question; e.g. the energy transferred from the battery to the lamp and hence into the environment.

It is of course unscientific fantasy to picture coulombs carrying loads of energy on their backs and disgorging some of the load in each part of the circuit, then gathering a fresh load each time they pass through the battery. Yet if you warn students from time to time that this is an artificial picture, with unrealistic details, they can use the model to develop a useful insight into potential difference.

Then resistance, which may well be more convenient in developing a professional scheme of electrical units, takes a secondary place as [potential difference]/[current] with one ohm merely defined as a name for one volt/amp. That is just dictionary work.

With these descriptions and definitions of potential difference and current, it is obvious that potential difference x current gives us the power, the rate at which energy is transferred. In slang terms ‘volts x amps = watts ’.

And when you generate an e.m.f. you can give a clear description of that concept too.

Advanced level ideas

In more formal treatments of electricity, unit current is chosen as the fundamental quantity (defined in terms of the force between parallel currents). Resistance is a useful derived quantity, a secondary standard that can be preserved and copied easily. Then the unit of potential difference is derived from the units of charge and energy (or current and power).

However convenient that scheme may be, it leaves the nature of potential difference itself without a clear description. Certainly at introductory level, students find ‘voltage’ a mysterious concept, often vaguely described as an electrical pressure, and frequently described as multiplying current by resistance. When the use of potential difference is extended to cases where there is no current, or cases where there is no Ohm’s law resistance, it remains very puzzling.

Developing electrical knowledge – from introductory to advanced level

There is a danger here of confusion between several different purposes in building electrical knowledge. There is the matter of careful definition of fundamental units and the deriving of secondary units; that is a matter for advanced level courses. There is the matter of describing and defining physical quantities to be measured in those units. There you need to know the physical relationship, extracted from experiments, such as thermal transfer varies as the current², or rate of copper plating varies as the current. There are ‘operational’ definitions, in the technical sense of that word, which describe the scheme of measurement in terms of actual apparatus that could be used.

In earlier days, scientists sometimes used concepts that could not be given an operational definition. Nowadays they are more careful and try to define, or at least describe, concepts of physical quantities in terms of possible, or at least conceivable, methods of measuring them. Such definitions should yield a clear knowledge of the concept; but they do not always lead to the most convenient unit in which to measure the physical quantity. The unit chosen may be defined quite separately – you often find it was chosen earlier in the history of the subject.

There is no logical objection to defining the unit of current in terms of the mass of copper deposited per second in electrolysis, although current is formally measured in terms of force between wires or coils carrying currents.

You can define one coulomb as one ampere-second but that is of little value in giving students a picture of it. Talk of coulombs as things that go round the circuit, the things that you might count flowing past any point you might choose in the circuit, much as a policeman might count ‘cars per minute’ for traffic flow or a hydraulic engineer ‘gallons of water every minute’. In electric circuits scientists and engineers count coulombs per second and call them amps.

Introductory level ideas

At introductory level, students need only have the idea that something flows around a complete circuit, transferring energy from the power supply to devices such as lamps.

Worries about absolute standards and units belong in advanced level teaching and not in an introductory scheme of activities. Students accept the kilogram as a well understood unit when it is no more than a copy of some chosen standard.

If students ask how anyone knows the size of a coulomb, the best reply at introductory level is that you simply read the ammeter which tells the rate at which coulombs are passing and multiply by the time in seconds. That puts the blame for the definition on the ampere, and the ampere you could say is defined by the reading of a standard ammeter kept at some standardizing laboratory in each country in the world. You may need to point out to students how one ammeter can be compared with another and that in turn with a standard ammeter.

Intermediate level ideas

At intermediate level, instead of saying what things are travelling in a circuit, electrons or electric charges, emphasize a cruder view. Say that something travels that you measure in chunks called coulombs. Coulombs travel along a wire in a circuit and you can count them as they go by with an ammeter and a clock.

Students need to be equally confident in expressing some energy transfers in joules per coulomb. You can price oranges in pence per dozen, or milk in pence per litre, knowing quite well what kind of things a dozen and litre are. So, make a coulomb too almost real, by tracing it round the circuit pushed by coulombs behind it and pushing the coulomb in front (by means of electrostatic fields), slipping smoothly through low resistance, banging its way through high resistance, shoving against the edges of the armature-wires in a motor, carrying the material of chemical ions across with it in electrolysis; always paying out joules as it goes.

Say a current of 2 amps means that 2 coulombs of electric charge pass each point in a circuit every second. Then whenever you give pupils data, ask them to interpret it: the current is 2 amps; that means 2 coulombs per second. If the current is 5 amps, how much charge passes a given point in 10 minutes?

Advanced level ideas

In advanced courses, 1 amp is defined as the current which when flowing in each of two infinitely long parallel wires one metre apart produces a force of 2 x 10^-7 newtons on each metre of either wire. That definition has two virtues: it reduces the number of arbitrary standard units and it makes it possible to carry out some very important calculations; e.g. the force on a current-carrying coil placed in a region near another current-carrying coil. This should not worry beginners to the subject.

Students may ask if a coulomb is the same kind of thing as an electron. Say that you can think of the electron as a very tiny particle which has a mass like any other piece of matter but also carries a charge. A coulomb is the charge of a vast number of electrons. In fact the size of an electron’s charge can be measured in coulombs; that means experimentally comparing two sizes, one electron charge and one coulomb of charge, i.e. Millikan’s experiment.

One electron charge = 1.6 x 10^-19coulomb

One coulomb is 6 x 10¹⁸electron charges

A coulomb is always 6 x 10¹⁸ electron charges but in many cases of currents (e.g. in conducting solutions, in gases and in some semiconductors) some of those charges are negative and moving one way and the rest are effectively positive and are moving the opposite way.

If we were beginning the development of the science of electricity all over again in the twenty-first century, we might well take the electron charge as our basic unit instead of the coulomb. But electricity is too well established for us to make that change comfortably. Also the electron charge would prove far too small for convenient use in many practical applications.

Scientists often speak of a coulomb ‘falling through so many volts' and 'transferring so much energy;. That is rather like a 1 kilogram rock falling through so many metres. More energy stored gravitationally is then kinetically if the rock falls down the side of a 100 metre cliff than if it falls only 10 metres.

In a similar way a 1 coulomb charge transfers more energy if it falls through an electrical potential difference of 100 volts than if it falls through 10 volts.

The rock falls through a gravitational potential difference and the charge falls through an electrical potential difference.

You can draw a hill diagram showing how the battery 'pushes a coulomb of charge up' so that it can then run down the various hills to the bottom on its way round the circuit. The coulomb does not really have joules like bottles in a rucksack. The coulomb is pushed by electric forces generated by the battery. Those forces grip it wherever it is in the circuit and drive it on round. Energy stored chemically is transferred to the components.

You might picture a 6 volt battery giving 6 joules to every coulomb with instructions ‘remember to spend all this energy on your way round the circuit and then you will get another load of 6 joules for the next round’.

In a way the battery is like a moving ramp such as the machine used to raise gravel to the top of the tower for sorting it, or like an escalator for people. It raises electric charge, measured in coulombs, uphill to a higher level of electrical potential. Then as the electric charge travels round the rest of the circuit it is running downhill, warming up the filament of the lamp as it makes collisions of some kind in the filament. The connecting wires are assumed to have almost no resistance and so the coulomb just rolls along without transferring any energy.

Conductance and resistance

In some circumstances it is useful to consider the conductance of a component rather than its resistance. An increase in conductance suggests an increase in charge carriers – which is often the case when the ‘resistance’ is said to decrease. Using both terms can help students get a feel for the microscopic changes that are altering measurable quantities.

Why use a variable resistor?

Students are occasionally confused when the independent variable does not change in a regular manner. Including the variable resistor allows this to happen, but confident students can simply leave it out and use the power supply to produce their own figures for the voltage values.

Voltage or potential difference?

Voltage is an everyday term which may suit students at an introductory level, but they should later be encouraged to use the correct, descriptive term ‘potential difference’.

Using a potential divider

More able or experienced students can be encouraged to construct a potential divider circuit as shown in these experiments. This will allow them to gain a full range of readings.

It would be easy to leave AC as a slightly mysterious version of the direct currents that you deal with in simple DC experiments, and to suggest that detailed studies belong to later work in engineering. But AC is our standard form of supply. It is far more economical in distribution than DC because of the efficiency and simplicity of transformers.

Students are likely to be interested in the characteristics of AC. There are obvious ones (such as giving the same heating effect as direct current yet failing to move a DC ammeter visibly), and surprising ones involving phase differences. It is important to point out the differences between peak values, average values, and root mean square averages.

For elementary purposes, alternating current can be thought of as a current which is, at any instant, flowing in one direction or the other. As the alternating voltage changes direction, so does the current it pushes through a resistive circuit.

There are many ways of explaining root mean square (rms) voltage and current at different levels of complexity, to advanced level students.

• For the simplest level, say that you sample the current (or potential difference) at tiny intervals of time. Square each value, add up the squares (which are all positive) and divide by the number of samples to find the average square or mean square. Then take the square root of that. This is the root mean square (rms) average value.

For example, suppose there are 8 time intervals as shown in the diagram above:

Values	7	10	7	0	-7	-10	-7	0
Squares	49	100	49	0	49	100	49	0

Sum of squares = 396 Average of squares = 396/8 = almost 50 Square root ~ 7 With more intervals the rms average turns out to be (peak value)√ 2  = peak value1.41 = 0.707 peak value
• For those who are familiar with the graphs of sine and cosine functions, then the following algebraic method can be attempted.
• I = I₀sinωt and I² = I₀²sin²ωt
• The heating effect depends on I²R, and so an average of I² is needed and not an average of I.
• To find the rms value, you need the average value of sin² as time runs on and on.
• The graph of sinωt and the graph of cosωt look the same, except for a shift of origin. Because they are the same pattern, sin²ωt and cos²ωt have the same average as time goes on.
• But sin²ωt + cos²ωt = 1. Therefore the average values of either of them must be 1/2.
• Therefore the rms value of I₀sinωt must be I₀√ 2 
• The rms value is 0.707 times the peak value, and the peak value is 1.41 times the value the voltmeter shows. The peak value for 230 V mains is 325 V.
• Alternatively: Plot a graph of sin²θ. Cut the graph in half and turn one half upside down, or copy onto a transparency and fit together. The two halves fit together exactly, showing that the mean value is 1/2.

• Note that, when using unsmoothed rectified AC from a simple power supply, the estimate of the power obtained by multiplying the readings of a moving coil DC voltmeter and a moving coil ammeter is likely to be nearly 20% too low. This is because each moving coil meter measures the simple time-average of the half-cycle humps, not the rms average.
The rms values of current and voltage multiplied together give the actual power. This is a vital fraction when trying to do quantitative power and energy experiments such as specific thermal capacity. The values are only 80 % of the value at best

You need to avoid planning an electrostatics lesson and then finding that the atmosphere and the equipment are so damp that they get no effect at all, or else the results you do get appear to give the ‘wrong’ result so are confusing. There are precautions that can be taken which will usually ensure success.

All dusters used to charge objects should be freshly laundered and fluffy, and kept in a clean bag. When laundering, do not put fabric conditioner in the water as it's an anti-static agent. Students should have clean hands. Polystyrene balls, balloons, acetate and polythene rods should all be cleaned regularly. It is helpful to store all electrostatic equipment, including the Van de Graaff generator, in a cupboard which is kept warm and dry with a low wattage lamp burning. However even on a wet day, putting all the equipment near to an electric heater for some time before the lesson ensures that it is dry enough.

Today’s synthetic materials are well-known for becoming charged very easily, so that cars and carpets can give quite a nasty shock. Try separating bed-clothes in the dark of night and you will really see sheet lightning!

In modern laboratories with water fed through plastic pipes, it may be very difficult to find any point electrically bonded to earth. In such cases, an earth for electrostatics experiments can be provided by burying a substantial metal rod in the ground with a wire running through the wall to a terminal in the laboratory.

It helps to be familiar with the electrostatic series:

• Perspex (acrylic) ELECTROPOSITIVE
• Glass
• Silk
• Wood
• Sulphur
• Cotton
• Ebonite
• Indian rubber
• Polythene ELECTRONEGATIVE

If two materials are rubbed together, the material higher in the list will gain a positive charge, while the lower material will gain a negative charge.

Good luck: these lessons can be fun!

Principle of operation

Some insulating materials when separated from the surface of others, leave those surfaces electrically charged, each with the opposite sign of charge and with a high potential difference (p.d.).

A machine to make charges was invented in 1929 by a young American called Van de Graaff. Huge machines, some over 30 m high, based on his ideas have been built to produce extremely high potential differences.

Belts and rollers

A flexible belt made from an insulating material and running continuously over two rollers can, by the same process, produce a supply of charge where the surfaces separate. The two rollers have to have different surfaces (often acrylic and metal) and together with the belt-rubber, are chosen by experiment.

Combs

Charges are “sprayed” on to and removed from the moving belt by “combs” situated adjacent to the rollers. Actual contact between the combs and the belt is not essential because of the high potential differences. Combs can be simply a stretched wire, or a sharp or serrated edge: action depends on very high potential gradients due to their small radii (similar action to lightning conductors).

The lower comb is maintained at or close to earth potential and is a drain for negative charge, leaving the belt with positive charges that are carried up to the top comb.

Collecting sphere

The top comb is connected to a collecting sphere which, having inherent electrical capacity (proportional to its radius) will collect and store the charge on its outer surface until discharged either by breakdown of the surrounding air as a spark, or by conduction to an adjacent earthed object.

Charging current

So long as the belt continues to move, the process continues, the drive (motor or manual) supplying the power to overcome the electrical repulsion between the charges collected on the sphere and those arriving on the belt.

The charging current is usually a few mA and potential difference achieved by “junior generators” will be 100-150 kV and by “senior” generators up to about 300 kV.

The whole apparatus

The mechanical arrangement of the belt/roller system is very simple. The lower roller is driven either manually or by motor. The former usually involves a hand wheel and pulley with belt-drive; this pulley can be mounted directly on the motor spindle. In “junior” models, fixed speed, shaded-pole induction motors are usual; “senior” models often incorporate small H.P. variable-speed (sewing-machine) motors, with carbon brushes, control being by either a simple rotary rheostat or a solid state circuit. The motors, control switches and mains input socket are housed in a metal or plastic enclosure, although some junior models have used a transparent plastic cake-cover.

The support column for the collecting sphere can be a simple PVC plastic rod or acrylic tube or a pair of acrylic strips with separators. In some models the belt is enclosed within a plastic pipe with “windows” along its length. Not all generators have means of adjusting the separation of the upper and lower rollers i.e. the belts have to be tailored for a particular machine.

Since the diameter of the collecting sphere determines the maximum p.d. (voltage) achievable, large spheres are mounted on taller columns to be more remote from the earth motor and control box.

Machines are usually supplied with a “discharger", often another, smaller, sphere mounted on a metal rod that has to be earthed to draw sparks from the collecting sphere.

Demonstrations and accessories

Certainly the Van de Graaff generator can produce striking demonstrations. The usual experiments are:

Faraday’s cylinder to show electric charge resides on the outer surface of a charged hollow conductor.

Bouncing ball. Suspend a conducting ball a non-conducting thread. When the ball touches the charging sphere, it will become charged and be repelled away from the sphere. If the ball is then allowed to discharge (touching an earthed surface, or leaking charge to the air) it will be attracted once more to the sphere, to be recharged ... and so the process continues.

The head of hair is another demonstration of repulsion. Real hair or shredded paper strips bunched at one end are used and provide a sensitive means of detecting charge.

The electric wind is produced by release of ions at the end of a pointed conductor and is enough to deflect a candle’s flame.

Hamilton’s mill utilizes the electric wind at the pointed ends of four arms to cause rotation about a pivot. This is similar to the action of a lightning conductor, which allows charge transfer at sharp points.

Kinetic theory model You can show random motion of metallic balls continuously affected by repulsion and loss of charge within a transparent vessel.

Neon indicator shows luminous discharge from the gaseous excitation by the high electric fields near the generator.

An apparatus note on the Van de Graaff generator gives information about good housekeeping and repairs:

Van de Graaff generator

Van de Graaff generator demonstrations can provide useful insights into electrical phenomena, which are at the same time memorable.

• It is essential the Van de Graaff generators for school science are obtained through reputable school science equipment suppliers. The sphere has a capacitance, and will store energy electrostatically as a result of the separation of charge. The energy stored electrostatically by the sphere should not exceed 0.5 J.
• Do not add devices to the sphere that increase the capacitance.
• Van de Graaff generators with mains powered pulleys must be electrically inspected and tested in the same way as other mains powered equipment.
• When carrying out the hair-standing-on-end demonstration, do it with one person at a time. After the demonstration, to avoid a sudden discharge, the person should take their hand off the sphere and touch the surface of a wood bench top (avoiding metal fittings such as gas taps). Alternatively, hand the charged person a wooden metre rule. After a few moments, they will be discharged.
• It is not advisable for people to participate in practical work with Van de Graaff generators if they have heart conditions, or a pacemaker, or other electronic medical equipment fitted.
• The electrical discharge from a Van de Graaff generator can wreck electronic circuits, so equipment such as computers and instrumentation with electronic circuits should be kept well away.

The Van de Graaff generators designed for schools are usually the triboelectric type; these are the most suitable. The transfer of charge is achieved by a rubber belt driven by a plastic pulley, with an arrangement of metal combs at either end of the belt. Charge is transferred to a metal sphere (a capacitor) and very high voltages are achieved between the sphere and ground, typically in the range 200 kV to 300 kV.

Using a Van de Graaff generator, one is quite likely to receive a short shock by accidental or intentional contact with the charged dome. An enquiry to CLEAPSS has revealed no recorded incident of direct injury caused by shocks from the correct use of school Van de Graaff generators. However, some people are more sensitive than others and can find the shocks very unpleasant and painful. For this reason, only volunteers should take direct part in the practical work.

The shock is a single unidirectional pulse of short duration; a capacitor discharge through the resistance of the body and contacts. Using rough values of sphere capacitance, 10 pF, and body resistance, 1000 ohms, the discharge time through a person will be of the order of nanoseconds and certainly less than a millisecond. The capacitance of the sphere needs to be low enough that at maximum voltage, the energy transferred by the discharge current through the body causes at most no more than an unpleasant or painful sensation. The current flowing and energy transferred to the body should be well below that which could cause any risk of ventricular fibrillation.

For an impulse current I Amps of short duration t seconds ( t < 10 ms) through the body, the principal factor for the initiation of ventricular fibrillation is the value of I  ×  t or I²  ×  t (IEC 2007). At high applied voltages, the resistance of the adult body (left hand to right hand) is at least 575 ohms for 95% of the population (IEC 2005). The total body resistance for children is expected to be higher but of the same order of magnitude. The IEC gives a threshold value of 'Specific Fibrillation Energy', for a 1 ms current impulse, of ValueExponent{2}{-3}A²s. Below this threshold there is no evidence of fibrillation. The Specific Fibrillation 'Energy' can be regarded as the energy dissipated per unit resistance of the body through which the current flows. Note that ‘specific’ here means ‘per unit resistance’ rather than ‘per unit mass’.

At 575 ohms and discharge time not exceeding 1 ms, the energy stored electrostatically by the capacitor would need to be at least 1.1 J to reach the Specific Fibrillation Energy. Although this is a very conservative estimate because the discharge time is likely to be much less than 1 ms, Van de Graaff generators that can store more than 1 J of energy electrostatically by the sphere should be avoided. A discharge of 1 J affects everybody severely (BSI 1991).

An estimate of the energy stored electrostatically by the sphere can be made by calculating the sphere capacitance, C = 4 π ε₀ r (where C is in farads, r is the sphere radius in metres and ε₀ is the permittivity of free space), estimating the voltage, V , using the length of spark gap, and calculating the energy E , in joules, from E = 0.5 CV².

Generally speaking, sphere diameters of Van de Graaff generators should be about 20 cm or less. Using data from one manufacturer’s specification, the sphere diameter is given as 20 cm and the maximum voltage 250 kV, the energy stored electrostatically would be 0.35 J, well below 1 J. If this is compared to a sphere diameter of, say, 25 cm and a maximum voltage of 350 kV, then energy stored electrostatically would be 0.85 J. This would still be below 1 J, but the shocks would be correspondingly more unpleasant and painful, and this may put off some people from using the generator.

If you wish to estimate the voltage across the sphere and ground, you can do this by finding the maximum spark length. Wait until the sphere is fully charged, then bring up a grounded sphere slowly until you obtain a spark discharge. This technique has limitations and you should do it carefully several times to find the maximum spark length. Do the test on a dry day with low relative humidity so the Van de Graaff generator is working at its best.

Note that the rule-of-thumb 3 kV/mm is only a reasonable rule for voltages below 100 kV.

References

IEC 2007. IEC/TS 60479-2:2007. Effects of human beings and livestock – Part 2: Special aspects.

IEC 2005. IEC/TS 60479-1:2005. Effects of human beings and livestock – Part 1: General aspects.

BSI 2002. BS EN 60052:2002. Voltage measurement by means of standard air gaps.

BSI 1991. BS5958-1:1991. Code of practice for control of undesirable static electricity Part 1: General considerations. [Replaced by PD CLC/TR 50404:2003 but remains current.]