Describing circuits

When a battery is connected to a bulb to make a complete circuit, the bulb lights up. If you are interested in understanding how electric circuits work, this familiar event raises a number of questions.

While the bulb is lit energy is shifted or transferred (see the SPT: Energy topic), to the surroundings as the filament of the bulb glows and light is emitted (see the SPT: Energy topic).

• Where does this energy come from in the first place?
• How is the energy shifted to the surroundings by the bulb?
• How does the bulb come on so quickly?

You probably have some pretty good ideas about answers to these questions. What is needed is a way of thinking about electric circuits that allows us to picture what's going on inside them (inside the battery, wires and bulb). You can see the effect of what's going on (the bulb lighting up); what is needed is a model for the electric circuit to help you understand why that happens.

So what actually happens?

What happens when a battery is connected to a bulb to make a circuit? The bulb lights up very quickly as the circuit is completed. The situation switches from equilibrium, where there is very little happening, to a steady state, where the bulb is glowing, very quickly. We're going to suggest that you concentrate on the steady state, where the bulb is glowing steadily.

The energy must come initially from the battery which acts as an energy store (see the SPT: Energy topic). This being the case, what happens in the circuit to enable the energy which originates in the battery to be shifted to the surroundings via the bulb? The energy story gives us an one level of description of what happens but provides no details about the mechanism.

A helpful way to think about this follows.

Electric current is a flow of charge

When the battery is connected up to the bulb to make a complete circuit, there is an electric current everywhere in the circuit. Something flows steadily. That thing is charge, and there can be many different objects that carry the charge.

The current is the same at each point in the single circuit loop – there are no leaks! And no charge accumulates at different points.

The charge originates in the circuit itself. It's already there. That is what it is to be a conductor – to have charged particles that can move when the conductor is connected into a complete circuit.

These charged particles may have other movements as well as drifting steadily, but it is the steady drifting that we'll concentrate on as this movement is the electric current. The charged particles drift steadily in one direction as well as any other movements. The other movements were there before the circuit loop was completed and remain afterwards. The drifting velocity is added to the other velocities.

In metal wires we now know that the charged particles that drift are negative (but it's not at all easy to show this until post-16 study.). That's what's shown in the top pair of diagrams here. But in many other cases, the charged particles that drift are positive (e.g. conduction in nerve cells, electrolysis). We think it's best to be agnostic about the charged particles, but not about the current in the loop: something flows, and the flow is the same at every point in the loop. But we'd suggest representing the direction of conventional charge flow, as in the bottom diagram (where the charge carriers are positive) if you do choose to show charge flows.

The charged particles originate in the circuit itself – when they flow there is a current

In metallic wires the electrons are the moving charged particles and originate in the wires of the circuit. They are simply part of the atoms that make up the battery, wires and bulb. When these components are not connected into a circuit, you might imagine a sea of free electrons buzzing around the fixed array of positive ions (rather like the particles in a gas).

In nerves and electrolysis the current is not carried by electrons. We'll refer to electric currents in terms of a flow of charge, as this covers all cases.

In metallic wires

The moving charged particles are simply part of the atoms that make up the battery, wires and bulb. When metal atoms combine to form a wire, the result is a lattice of fixed positive ions and and electrons that are free to wander.

The atoms were neutral, therefore the wire will be neutral as well, as charge is conserved. These electrons do wander, at high speed, randomly whizzing about in very short hops, changing direction often, with different thermal motions (100–1000 kilometre / second).

When these components are connected into a circuit, a steady very small drift velocity (a few millimetres in each second) is added to the large thermal velocities (the movement of the electrons is rather like the movement of molecules in a cloud of gas drifting sedately along). The charged particles that were already in the wires now move consistently, in addition to their random short hops.

The electric current in wires is made up from millions of minute, negatively charged particles called electrons, which drift along the wires. As a result the charge flows around the circuit.

Here are two representations of this movement. Current is always represented by an arrow which points along the wire or other circuit element, so that it is pointing away from the positive terminal of the battery and towards the negative. The current arrows point in the opposite direction to the charge flow because electrons are negative.

We refer to the electrons drifting for a very good reason. The additional motion towards the positive terminal causes them to move only about 1 centimetre in each minute. This is very slow: take a minute out from reading this to move something one centimetre across the desk in front of you. This speed is millions of times slower than their random (thermal) buzzing around, so we have simplified the diagrams, by not showing the buzzing around. We don't suggest you take another minute out to mark out the 600–6000 kilometre they will have travelled, as it is very far from a straight line.

In a metallic conductor there are lots of electrons but they move around the circuit very slowly.

In other cases we can perfectly well get a current made up of the movement of charge carriers that are not electrons. But electrical current is always a movement of charge.

There are, however, other situations in which the current is not carried by electrons. For example, a salt solution will conduct an electric current, and here the moving charged particles which constitute the current are provided by the ions in the solution. Currents in nerve cells are the movement of ions.

In the following nuggets we'll refer to electric currents in terms of a flow of charged particles, as this covers all of the situations. In your own teaching we'd suggest that you don't insist on flows of electrons until you can reasonably demonstrate that this is what is happening in a wire.

Find out when the charged particles start to move

It would appear that when we turn on a switch the electric charge moves immediately in all parts of the circuit and instantly lights a bulb. Even if we connect all the wires available in the laboratory, to make a big circuit, the light bulb still appears to react immediately.

Actually it does take a very short time for the electrons to start moving. The electric field that sets the electrons in motion takes a finite time to pass through the wires. The field propagates (moves) at approximately the speed of light: 300,000 kilometre / second, that is 300 millimetre in a thousand-millionth of a second.

Does this delay matter? An electrical signal would take a mere hundredth of a second to pass from the UK to the USA through cables under the Atlantic Ocean. However, a modern computer will time itself on a signal changing many millions of times a second. With signals that are fractions of a millionth of a second long, even small delays in signals travelling along wires must be taken into account when designing circuit boards.

The bulb in our circuit does not turn on immediately, but the delay is so short that it is only significant in the most extreme applications.

The battery has two linked jobs in the circuit

The battery provides a push that keeps the charged particles in motion:

The battery is a store of energy that is emptied more or less rapidly as other stores are filled (by the action of other components in the circuit).

In a complete loop, the battery does both jobs: in a broken loop, neither.

Strictly speaking, the term battery refers to a number of individual cells connected in series, and so we might talk about a 1.5 volt cell and a 9 volt battery (which consists of six 1.5 volt cells).

In practice this distinction between battery and cell adds nothing essential to the understandings of the workings of electric circuits. Since the word battery tends to be more commonly used, we'll refer to batteries throughout this topic.

Note that here we've only said what the battery does, not how these two things happen, or how they are linked. As we do that, then we'll be developing a model of an electric circuit.

Current is rate of flow of charge

Electric current consists of moving charged particles. So the charged particles are moving around a circuit.

To make sense of electric circuits you'll have to model the behaviour of currents in circuit loops. Now we'll consider how electric currents can be measured and how we can make sense of these measurements.

The electric current in one part of a circuit is measured with an ammeter, which gives a reading in ampere.

To take the measurement, a gap is made in the circuit and the ammeter is connected into that gap, so that the charged particles moving around the circuit must pass through the meter.

Since the ammeter is connected directly into the circuit, it must have a low resistance so that it does not reduce the flow of charge, which it is being used to measure.

Increasing the current

What does the ammeter actually measure when it is connected in a circuit? You might visualise the working of an ammeter as counting charges as they move through the instrument, to see how many pass each second. The amount of charge passing per second is a measure of the electric current:

Lots of charged particles passing per second: a large current

Few charged particles passing per second: a small current

We can refine this to electric current = amount of charge passing per second.

This is equivalent to electric current = rate of flow of charge.

More formally, perhaps:

current = chargeduration

You can write this out in symbols:

I = Qt

Where I is current; Q is charge; t is time for which charge flows (the duration).

You could also write the whole relationship out with units:

current measured in ampere = charge measured in coulombtime measured in second

To increase the size of the electric current,

• Either more charged particles must be set in motion (change the material or the thickness of the wire),
• Or the charged particles must be made to travel more quickly around the circuit.

Both of these actions result in more charge passing any point in a circuit each second and this is a bigger electric current. In episode 02, you will see how the electric current can be increased.

The ampere: a measure of electrical current, which is the rate of flow of charge

When an ammeter is used to measure the size of an electric current, the reading from the meter is in units of ampere. Connect the ammeter into the circuit in series so that there is no branching: the current in the wires will be the same as that in the ammeter.

A steady electric current of 1.0 ampere means that one coulomb of charge is passing per second.

What does this mean? How many electrons make up one coulomb's worth of charge? Since the charge on one electron is 1.6 × 10^-19 coulomb, then there must be about 6 × 10¹⁸  electrons (6 million, million, million!) in one coulomb of charge.

When thinking about electric currents in wires, a good mental picture is one of huge numbers of electrons drifting around the circuit at a rather sedate pace!

The unit of electric current is the ampere.

The symbol for the ampere is: A

Whatever the conductor, whatever the charge, the connection between current and the accumulated quantity of charge that has passed is universal.

Electric currents do not get used up

Electric currents do not get used up. In a simple circuit with one battery and one bulb, the size of the electric current is the same wherever you measure it.

There are no side-paths down which the charges can pass and the charges themselves cannot just disappear.

Please note that we're showing conventional charge flow in the diagrams.

Current as flow of charge

You can picture a steady and continuous flow of charge around the whole circuit. The rate of flow of charge (the current) for the whole of the circuit is fixed by what's in the circuit: the battery and the other elements, such as bulbs. Things other than batteries reduce the flow: the flow of charge everywhere in the whole circuit decreases: the current in each element of the circuit also decreases.

Later, we'll build on these ideas by considering what happens when changes are made to our simple circuit, and how we can use the electric circuit model to both predict and explain what happens.

Consequences of a slow drift

In a complete circuit charges drift round at a speed of about 1 centimetre per minute. This is important, and very slow (try moving at 1 centimetre per minute). Think about a very big circuit – so the connections between the battery and bulb are made with very long wires. When the big circuit is completed, the bulb appears to light immediately. Think about this for a while. The effect of the current in the bulb is immediate, yet the charges that started in the battery have scarcely left the terminals. So any model in which charges carry energy or take energy from battery to the bulb in order to light the bulb will clash badly with this experience. If the big circuit runs from the front of the classroom to the back, such a model predicts that the bulb might then take 10 hours to light up! What happens, of course, is that as the circuit is completed, all of the charges in the circuit (including those in the filament of the bulb) start moving together and the filament warms up instantly. That's why it's not a good idea to say energy is carried from battery to bulb.

The rope loop teaching model offers a convincing account of this experience, that does help you picture what's really happening.

A convention for direction

Scientists agree to use a convention which shows the direction of the electric charge flow (the current) in a circuit as being from the positive terminal of the battery towards the negative terminal. This is in the opposite direction to the actual flow of electrons – the most common moving charges in metal wires, so in most classroom circuits, and in many situations in the home as well.

This somewhat unhelpful state of affairs came about because the convention was established before it was known that electrons move through the wires of a circuit.

The current direction convention is not important for understanding electric circuits and we'd suggest not making a big fuss about it in the discussions you have with children. You can think about something flowing and not worry to much about exactly what is flowing.

How charged particles move, and the consequences of historical decisions

Read more about which way the charged particles actually move – and find out whether it is important at this level.

In the metal conducting materials that we use to make electric circuits, it is the negative charged particles (the electrons) that are physically able to move around:

By convention, however, the electric current is taken as flowing in the opposite direction towards the negative terminal.

Why should it be that the conventional electric current is taken as being in the opposite direction to the motion of the electrons? The answer is that the convention arose historically.

Early experiments by William Gilbert (1544–1603), physician to Queen Elizabeth I, investigated electrical charging by friction of many substances. By comparing, for example, glass rubbed with silk and ebony rubbed with wool, Gilbert concluded that there were only two types of charge and that charged particles of the same kind repelled, whereas opposites attracted. He called those produced by the action of friction on fur as positive and those by friction on rubber as negative.

It was noted in later experiments that when charged objects were brought into contact with the Earth through a conductor, a small charge flowed for a short time. When cells were invented, it was observed that a cell's carbon electrode behaved in a similar way to fur, and a silver electrode in a similar way to rubber. Thus, an excess of electric fluid (positive charge) appeared to be transferred from the positive carbon electrode (anode) to the negative silver electrode (cathode).

The idea of positively charged flow remained in favour until the work of Joseph John Thomson (1856–1940). In a study of the flow of electricity through gases, (technology used today in neon signs), Thomson isolated a beam of negatively charged particles of much smaller mass than atoms. These originated at the negative terminal (cathode) in his gas tube and Thomson realised his cathode rays were composed of negatively charged electrons. This fundamental particle, the electron, was soon associated with all atoms and shown to be responsible for both static charging and electrical currents in metals.

By this time, however, the convention had been established that electric current ran from the positive terminal (e.g. carbon electrode) to the negative terminal (e.g. silver electrode) of a cell. This flow of charge is a conventional current. In most wires, negative electrons flow in the opposite direction to this conventional current.

The history of cells

In 1791, Luigi Galvani, an Italian physiologist, laid out a frog on a metal table prior to dissecting it. As he sliced through it with a metal knife, he observed the twitching of muscles, which he attributed to animal electricity. Later, when preparing further specimens by hanging them out of doors to dry, he observed muscle contractions if the copper hooks upon which they hung came into contact with iron fence wire. Galvani concluded that electricity resided in the frog's nerve juices, and that the metals in contact allowed the animal electricity to flow.

A second Italian scientist, Alessandro Volta, disputed this, claiming that the electricity originated within the metal parts of the circuit. The controversy was resolved when, in 1800, Volta produced the first Voltaic pile; an electric cell. After touching connected pairs of different metals on his tongue to sense the small voltages, Volta constructed the first cell from alternate discs of zinc and silver, separated by absorbent disks soaked in water. He communicated his findings in a letter entitled On the electricity excited by the mere contact of conducting substances of different kinds.

In their simplest form, modern cells consist of two electrodes of differing materials separated by an ionic solution. When the terminals are connected by a conductor, electrons flow from one side to the other enabling chemical reactions to take place. As these reactions proceed, the chemical store of energy associated with the battery is depleted. Once all the available chemicals have reacted, the cell can no longer shift energy from its store, it is dead.

The amount of energy shifted by the cell as each unit of charge is pushed through the cell (all as a result of the chemical reactions) depends upon the materials used in the cells. The materials most commonly used typically produce a 1.5 volt cell (1.2 volt for certain rechargeable types). A battery (a number of individual cells connected one after the other in a single line – in series) provides a greater voltage. The packaging of a standard 9 volt battery hides six 1.5 volt cells connected in series (more information about voltage follows in episode 03).

Making a cell

A simple electrical cell can be made with fruit and two metals:

Take 1 citrus fruit (lemons or limes work best). Gently squash the fruit to break the flesh structure without damaging the outer skin.

Insert one clean piece of copper and one clean piece of zinc (each about 5 millimetre by 40 millimetre) into the fruit, close together but not touching.

You now have a cell. Unfortunately the energy available from this cell is rather limited. It's only a small chemical store.

Making a battery

Connect several (five or six) separate fruit cells together, use normal lab wires with crocodile clips to connect the fruits, copper to zinc each time.

Connect a light emitting diode (LED) between the terminals of the first and last fruit. It may light. If not, switch it around as the direction of the electric current in the LED is important.

A steady flow

One the circuit is up and running then there is a steady flow of charge, but the battery is needed to maintain that flow. As the flow is steady the average resultant force on a moving charge must be zero. That is the retarding forces and the driving forces must be equal.

Because the conductors making up the circuits are electrically neutral, and there are charged particles drifting along in one direction, there must be fixed charged particles of opposite sign in the wires.

As the moving charged particles move through this array of fixed charged particles, there will be interactions. There are electrical forces between two charged particles (see the SPT: Forces topic). These will vary over time as the charged particles drift closer to or further away from the fixed charged particles, but we'll take an average value to make a simple model. But if the wire is the same everywhere around the circuit, then the magnitude and direction of the force on the moving charged particles must be the same – always opposing the steady drifting motion of the charged particles. What else could it be?

The battery therefore needs to exert a constant average force on each charge, equal and opposite to the retarding force, wherever the charge is in the circuit. This driving force must be along the axis of the conductor, aligned with the current. As the battery has a positive and negative end, (it's a chemical charge pump), the driving force acting on the charge is again electrical. And as the drifting speed of the moving charged particles is constant everywhere in the circuit, so the average driving force must be the same everywhere in the circuit.

The action of the battery

So the concentrations of charged particles on the battery drive the charged particles around the circuit. But just how do they do this?

It cannot be simply that there is a great concentration of charge on the positive terminal and this exerts the force. There are two good reasons why the current cannot be explained by just referring to a concentration of charged particles on the terminal.

The force acting on the moving charge would get smaller, the further the charge gets from the battery – and we have just found that it needs to be constant everywhere so that the resultant force on the moving charged particles is zero everywhere.

The force provided by the battery needs to be aligned with the conductor – however many bends we put in the conductor.

Nor can it be the case that it is just the like (moving) charged particles repelling, as the body of the conductor is, and remains, electrically neutral. Therefore, on average, any moving charge in the body of the conductor will be surrounded by opposite charged particles closer to it than its nearest similar charge. These opposite charged particles, being closer, will exert much larger forces on the moving charge than its nearest moving charged particles.

So here is what does happen.

The battery sets up a distribution of charged particles on the outside of the conductor, and these charged particles exert the driving forces on the moving charged particles.

It does take a very short time for the distribution of charged particles to be set up, with all kinds of feedback loops operating over very short timescales (the electromagnetic signals carrying the information about how to set up this charge distribution travels at the speed of light).

The distribution of charged particles then exerts forces on the flowing charged particles, so causing the varying drift velocities in the different parts of the loop. The velocities will not be constant because:

• There must be changes of direction to make a loop.
• The charged particles move at different speeds in different parts of the loop (although the current is the same in each part of the loop).

Varying the elements in the circuit

Now the model needs refining, to explain why some parts of the circuit glow and others do not. Here we'll focus on wires, but the same arguments are true for any conductor.

As you will have noticed, filaments in bulbs are simply very thin wires, so let's build a very simple circuit, where one section of the wire is thinner – that's the only change.

Firstly let's focus on what happens to the charged particles, comparing their motion in the thick wire to the motion in the thin wire. For simplicity we'll make the two wires of similar material – so everything is the same, apart from the thickness of the wire, and so the cross sectional area.

It does not take much thinking to see that the charged particles must move faster in the thinner wire, to avoid a steady buildup of charge at one end, and a steady loss of charge at the other. This is a simple consequence of the charge not getting lost or used up on the way round the circuit loop. Charge is conserved.

(An aside – this is really just a transport problem – we're modelling the charged particles as a kind of incompressible fluid. Very similar models are used for traffic and pedestrian flow, not to mention rivers and glaciers.)

What is the effect of this faster movement in the thinner wire on the forces acting on the moving charged particles? You can figure this out for both the retarding forces and the driving forces (remember that these must be equal). Again it's not hard to reach the conclusion that the forces in the thinner wire must be larger. The moving charged particles maintain a steady higher speed, and so interact with more fixed charged particles each second. More interactions lead to a larger average retarding force, and so a larger average driving force.

Why some parts glow

The filament glows and the connecting wires in the circuit do not. Why?

You have found that the forces acting on the moving charged particles by the battery and by the fixed charged particles in the filament are larger.

A larger force acting for a similar distance shifts more energy (See the SPT: Energy topic). So, for each metre or centimetre or millimetre of filament wire that the charged particles travel along, the large forces acting on them shift lots of energy: for each metre or centimetre or millimetre of connecting wire that the charged particles travel along, the very small forces acting on them shift a tiny quantity of energy.

The retarding force shifts energy to the thermal stores of the surroundings.

The driving force shifts energy from the chemical store of the battery.

The quantities of energy shifted are identical, because the driving and retarding forces are identical.

To increase the energy shifted, increase the speed of the charged particles by decreasing the thickness of the wire.

Shifting energy in a circuit

Read more about the mechanisms by which energy is shifted in a circuit.

When we say that it is the charged particles moving round the circuit, that enables the shifting of energy from battery to surroundings, what exactly do we mean? The answer to this question is not straightforward! It may be of interest to you, but is certainly not appropriate for pupils in the 11–16 age range.

The essence is that when the simple circuit is complete all of the charged particles in the circuit are set into motion as they are pushed away from the battery terminal of the same charge and attracted towards the battery terminal of the opposite charge by the distributions of charge set up by the battery. (In metallic wires negatively charged electrons throughout the circuit are pushed away from the negative terminal and attracted towards the positive).

An alternative way of thinking about this is to say that the battery creates an electric field around the circuit between its positive and negative terminals, and the charged particles both start, and are kept, moving due to the effect of this field (just as a mass has a force exerted upon it in a gravitational field). All of the charged particles in the circuit experience the force or push of the battery, even if they are not in direct contact with either of its terminals (just as objects with mass experience the pull of the Earth without being in direct contact with it). This is the phenomenon of action-at-a-distance, which is discussed in detail in the SPT: Forces topic. Almost as soon as the electric circuit is completed, an electric field is created throughout the circuit.

These electrical fields are not equally great everywhere in the circuit. Where the fields are greater the charged particles shift most energy in moving a small distance. (See the SPT: Energy topic for more detail).

Remember that the comparative thickness of the wires affects how much the charged particles are impeded (thin wires have greater resistance). The charged particles are moving faster in this thinner wire. To keep the charged particles moving at a greater steady speed, there is a larger field where the wires are thinnest. That is where most energy gets shifted.

As a charge (along with the countless other charged particles) moves round the circuit under the influence of the electric field, it is impeded by the fixed ions, that make up the connecting wires and bulb filament. As both the moving charged particles (often electrons) and the ions are charged, there is a retarding force between the moving charged particles and the fixed ions, leading to a series of interactions between the moving charged particles and the fixed ions.

As a result of each interaction, the mobile charged particles are slowed down and the ions vibrate more. The charge is then accelerated by the battery's electric field and moves off once again before undergoing another interaction with a different ion. In the thin, highly resistive wire of the bulb filament, there are many such interactions, so the ions here vibrate a lot. In the connecting wires, there are fewer interactions and so the ions vibrate rather less.

The difference in the rate of interactions leads to far less electrical working in the connecting wires and far more in the filament. The thermal store of the filament is therefore filled and the filament warms up and glows. The connecting wire does not glow, as its thermal store is much emptier.

So most energy is shifted by the interactions of the ions and mobile charged particles in the filament wire, not the connecting wires.

What happens in the battery?

When the charged particles reach the positive terminal of the battery, energy is shifted as they move across onto the negative terminal. Again, a large force (and so a strong electric field) is necessary in this section of the circuit loop, as a large quantity of energy is shifted as each charge moves across this short section of the circuit. All this happens within the battery, but only at the cost of emptying the chemical store of the battery. When this store cannot do its job any more, we say it has gone flat.

There is no mystery here – you simply engineer the parts of the circuit so that the forces on the charged particles vary as they drift around the circuit at more or less constant speed. A greater retarding force caused by the material that the charged particles are moving through is balanced by a greater driving force from the electric field set up by the battery.

This description underpins the two jobs for the battery outlined earlier in this episode.

It is not the case that charged particles must actually pass through the battery to shift energy. All of the charged particles in the circuit can shift energy due to the electric field created by the battery.

What gets used up?

When a battery is first connected to a bulb, the bulb warms up and lights up the surroundings. It is clear that something must be getting used up somewhere. According to the electric circuit model introduced, it should also be clear that it is the energy provided by the battery, which is gradually dissipated, as a result of the lighting and heating.

When all of the chemicals in the battery have reacted and the battery cannot supply any more energy, we say that the battery has gone flat. The charged particles stop moving and the bulb goes out. On first coming across these ideas, it is quite common for people to think that the electric current gets used up. However the current is simply the flow of charge that shifts energy. The charge is neither lost nor used up, so the current is the same everywhere in the electrical loop. What happens is that the store of energy in the battery empties as energy is dissipated through heating and lighting in the bulb.

Resistance

How is the drop in energy in the chemical store linked to the rise in energy in other stores (for a glowing bulb the energy of the thermal store of surroundings increases)?

Let's think about a complete circuit that has been running for a while – apparently in a steady state. Charged particles in all parts of the circuit are kept in motion by the action of the battery. Remove the battery and the charge flow stops – everywhere. As the charged particles pass through the bulb, energy is shifting to the thermal stores of the surroundings. The bulb itself consists of a very thin wire, or filament, inside a glass globe. So long as there is a current in this thin filament, some energy is shifting from the chemical store of the battery and to the thermal store of the surroundings.

How does this happen? As the charged particles (or electrons) move around the circuit, they are constantly being impeded by the fixed array of ions through which they pass. That is why the battery is needed to keep the charged particles moving. However, in the bulb the geometry (very small cross-sectional area) and internal structure (the layout of the ions) of the filament wire combine to make it particularly difficult for the charged particles to pass through (larger forces on the moving charged particles), and energy is therefore shifting here rather than in other lengths of wire making up the circuit.

The filament wire is said to provide a high resistance to the passage of the charged particles. As the charged particles are first set in motion, the ions of the filament are made to vibrate more and the filament warms up.

Where energy is being shifted, and where it is not

Once there is a steady current, the filament remains at the same temperature, and energy is shifting to the thermal store of the surroundings. We'd recommend starting by restricting discussions to the steady current, and adding the complexity of the transient process later, and then only if the conversation turns in that direction.

By way of contrast, the connecting wires for the circuit are usually made from relatively thick (i.e. large cross-sectional area) lengths of copper wire, which have a minimal resistance. The circuit components are designed so that most of the energy is shifted by the intended component (i.e. by the bulb and not by the connecting wires).

Remember: wherever there is an electric current in something which has resistance, energy is shifted.

An easier route

We can also describe the action of a simple circuit in terms of pathways (see the SPT: Energy topic). Electrical appliances are sold on the basis of how much energy they are shifting each second: you buy bulbs on the basis of their power rating – they are marked in watts, not in joules. So, although electric circuits are so prevalent because they shift energy, this effect is through accumulated electrical working, not the steady shifting that is what we detect with our eyes. Describing what is happening now in a circuit is best done in terms of power. If you settle on a duration and so consider the circuit running for a fixed length of time – what has happened – then you can sensibly discuss energy. Indeed that accumulation over time is what your domestic bills record.

What is happening in a simple lamp and battery circuit is happening continuously: only when you consider the accumulated effect of this activity can you ask and answer questions about joules. When the bulb is connected to the chosen battery, the brightness is set by choice of bulb and the current in the bulb. This brightness is a result of power being dissipated.

Starting with what we know: where the charge is in charged conductors

Simlarly charged objects repel. Put two in a vacuum and you can predict the forces (one on each charged object). There's a discussion of this in the SPT: Forces topic and more in the SPT: Force and motion topic on how those forces varies with separation (the charged objects don't need to be very close to each other). Here your needs are simple: the charged objects move apart, accelerated by the electrical forces acting on each charged object. In our simple universe, they'll move apart for ever. In a conductor, the charged objects are also free to move, but eventually get to an edge where they're not free to move, assuming the conductor is surrounded by an insulator.

In true physics style we'll start with the simplest conductor we can think of – a sphere. This is symmetric, so the charged particles will end up spread evenly over the surface as there's no reason for any other distribution of the surface charge. The sphere will be either positively or negatively charged (more on how to achieve this in the SPT: Forces topic), but all of those charged particles will be at the surface of the sphere.

Now we'd suggest moving to another simple shape – more like the wires which circuits are made of. To keep things simple it'll be a very very long wire, and you'll concentrate on parts far from the ends. In this way you'll be able to reason using cylindrical symmetry to predict the distributions of charged particles. Can you? We'd hope that you managed to see the connection and predict that the charged particles will be, once again, evenly spread across the surface.

Taking shorter cylinders makes the charged particle distributions harder to figure out, but the principles are the same: the charged particles are all at the surface. (The sharp corners destroy the symmetry, so you'd have to do some hard sums to predict the distributions of the charged particles, or have access to a very sensitive charge-meter to measure them – and you will not find one of those in schools.)

You can now draw the distributions of charged particles on the surfaces of isolated conductors with enough accuracy to develop the argument about where the concentrations of charged particles are in circuits. From these concentrations you'll be able to account for the steady flow of charged particles in electrical loops, however the wires are laid out on the bench.

Batteries are charge pumps

Electric circuits are not electrostatics, and the thing that makes the difference is the battery. Here we suggest that you ignore the complicated internals (leaving that to the chemists) and think of the battery as a charged particle pump.

So a simple, but very useful, model of a battery, not yet placed in a circuit, is an isolated pair of conductors, the terminals, one positively charged, one negatively charged. You can use the representations of isolated charged cylindrical conductors (imagining the terminals as short lengths of wire) to draw a functional representation of an isolated battery. It's just a linked pair of charged cylindrical conductors. The important feature of it being a charged particle pump is that the link between this pair of conductors replenishes this difference if some charged particles are removed from either cylinder. The battery pumps electrical charge because it pumps charged particles.

Adding extra uncharged cylinders to both terminals of the battery is identical in its effect to extruding the terminals. Any electrical charge that flows from the terminals to the newly added wire is replaced by the action of the electrical charge pump. You still don't have a circuit, as the ends of the wires are not joined, but you might like to think about what you expect to happen when they are.

Making connections to build electrical loops

Imagine joining the ends of two charged cylinders together. Now there's some attraction, as well as repulsion. It's not too hard to imagine the end state, and even the average intermediate behaviour, although the detail of the evolving situation is likely to be complex. There will be a steady neutralisation of the charge, from the centre outwards, as the concentrations of charge dilute by neutralisation.

Now imagine connecting two ends of the battery to two cylinders, which are the models for wires. Each cylinder will become electrically charged – it's just like the battery with extruded terminals. Now join the far ends of the cylinders together, to form an electrical loop. As the battery is an electrical charge pump, the inboard end of the cylinders, connected to the terminals, will remain charged, but the ends where the two cylinders are joined will be neutral, as the charged particles from the oppositely charged cylinders neutralise each other's effect. The situation in the cylinders will reach a steady state like one of the intermediate states when two isolated oppositely–charged cylinders were joined.

Now you can see that there is a gradient of surface charge around the circuit, and that any mobile charged particle in the circuit will have forces acting on it by these local concentrations of charge. Let's look at a straight section of such a cylinder and try to figure out the resultant force on the charged particle. On one side there will always be more surface charge than the other. So there will be a resultant force on the mobile charged particle as a consequence, down the concentration gradient. And that seems to be the case whichever way the wire is orientated.

Round the bends in a circuit

Now concentrate on a curved section of such a cylinder: again in order to figure out the resultant force on the charged particle. Start with the straight wire: the surface charge around any circumference is uniformly distributed: it varies only as you move along the wire. Now bend the cylinder to model a bend in the circuit: there is now a greater area on the outside, so more charge, if the surface charge density remains constant. Now the resultant force on the mobile charge, from this ring of charge, is directed towards the centre of the bend, which drives the charge around the bend.

Finally, again thinking about a constant straight cylinder, the surface charge is not the only charge exerting a force on the mobile charged particles – there is also the charge on the ions in the lattice. These necessarily act as retarding forces, since the conductor is neutral, and the ions are opposite in charge to the surface charge. So the average resultant force on the mobile charge is zero: the driving force due to the surface charge is equal and opposite to the retarding force due to the ions. The average speed of the mobile charged particles in this cylinder is constant.

Here is the whole discussion as a summary, from electrically charged conductors to complete circuits.

When charge flows energy is shifting

So, to summarise the main points:

In a circuit that has been complete for some time, charged particles (usually electrons), already everywhere around the circuit, are kept in motion by the battery. In this steady state, the filament of the bulb is shifting energy as the charged particles pass through it. This energy is dissipated in the surroundings.

A partial model

In this way you might imagine the circuit continuously shifting energy, with the battery's store of energy steadily emptying on one one side of the loop as energy is dissipated to the surroundings in many thermal stores in other parts of the same loop. The circuit connects these changes of the energy in the stores.

Note that for the first tiny fractions of a second, when the loop is first completed, the filament will be warming up, so the energy description will be modified.