Motors switch paths – they're a kind of device

Batteries are just about everywhere. Expensive, portable power is something that we are prepared to pay for. Mobile phones, cameras, music players and torches nearly all rely on batteries. Such chemical stores seem to be essential to the mobile lifestyle. There are a few small devices that rely on a wound-up spring (an elastic store of energy), but these aren't very common.

However, being mobile tends to rely on different chemical stores. People can walk, cycle or catch the train, but many choose to drive. The electric motor is not widely used in cars. Why might that be?

An electric car makes a good example

Getting something moving is, after all, quite simple, at least in principle. Cars are devices for shifting energy from a chemical store to a kinetic store as the vehicle speeds up, and from the chemical store to various thermal stores at cruising speed. Batteries seem to be a suitable chemical store, yet we burn fossil fuels instead – something that few would consider doing to power their mobile phones.

Might it simply be a question of power?

The chemical store associated with a battery is emptied by electrical working. The kinetic store associated with the moving car is filled by mechanical working. One challenge is to switch from electrical working to mechanical working. A device that is carefully engineered to do this is an electric motor. Every time we need to switch pathway, we look for such a designed device, or hire an engineer to design one for us. An electric motor is simply a device that switches from an electrical pathway to a mechanical pathway. This is the first of many such devices that you'll meet. Part of the reason for electric circuits being so pervasive is that there are a wide variety of devices for switching from an electrical pathway.

Designed working power and maximum power revisited

Another feature of such a device is that it has to have a designed working power. There will be a maximum rate at which it can shift energy. There might be a number of reasons for this. One will be to do with efficiency. The motor is designed to operate very efficiently, switching as much power as possible along the desired pathway. However, there will be some misdirection, with energy filling a local thermal store as a consequence. For example, the BMW Mini E (an all-electric car) has an electric motor rated at 150 kilowatt. It can shift energy safely at any rate up to this. This 150 kW sets the maximum acceleration – the kinetic store is being filled at the maximum rate. It also sets the top speed – the thermal stores are being filled at the maximum rate and no more energy is shifted to the kinetic store.

Batteries have one big downside: not much energy can be stored for each kilogram of battery. The Mini E's batteries store about 100,000 kilojoule. If the power in the pathways is at a maximum, 150 kilojoule inverse second (150 kW), then the car doesn't run for long before needing a recharge. More practically, the car has a rather limited range before the energy store associated with the battery needs replenishing. This is quoted as 230 km.

Devices switch pathways – so focus on power-in and power-out

Controlling the rate at which energy is shifting (the power) has been, and remains, a central concern of technology. Directing this power is achieved by selecting well designed devices. Here we promote this idea of device to centre stage, to focus on this engineering aspect, because studies of power are usually concerned with finding out what we cannot do, and then with doing the best job possible within the calculated constraints.

So what does a device do?

A device switches pathway (remember that a pathway is the means of emptying or filling a store). As there are four pathways, different combinations of input and output suggest that there will be many different devices.

Here are the four pathways:

• Electrical working.
• Mechanical working.
• Heating by radiation.
• Heating by particles.

These were first introduced in the SPT: Energy topic.

Some devices are better than others

Just concentrating on electric circuits, so starting or ending with electrical working, there are many possibilities. Lamps, heaters and motors come in many shapes and with different rated powers to suit the tasks for which they have been designed. To make a (qualitative) start in judging how good a device is, consider just the pathways and not the power in each pathway. This greatly reduces the possibilities. A well designed light, for example, is a device that switches most of the electrical working to the heating by radiation pathway, and very little to the heating by particles pathway, and none to the mechanical working pathway. This was discussed rather extensively in the SPT: Energy topic (episode 03). A good electrical motor switches nearly all of the electrical working to mechanical working, with insignificant amounts to heating by particles or heating by radiation. A perfect dynamo switches all of the mechanical working to electrical working. These are just a few of the more common examples.

Perfect wires don't switch at all (i.e. they do not switch the electrical working to any other pathway). This is an idealisation, but one that results in models that mimic the laboratory bench behaviour rather closely. It really is very hard to measure a potential difference across a standard connecting wire. This is, of course, planned: the resistance is low because the wire is thick. However, you'd have to make the transmission wires of the National Grid very, very thick for this idealisation to be so good an approximation. This has significant consequences for designing a grid to shift energy from power stations to our homes.

Devices that switch the pathway to or from electrical working are also called transducers.

Lighting is a kind of accumulating

Even up until the end of the First World War, electric lighting was only enjoyed by rich householders. The advantages over lighting with gas or oil were significant, but the early adopters developed into a significant market only after the perfection of the metal filament lamp (1911). Books were written offering advice on lighting your home, praising the advantages of rapid control of mood, achieved simply by throwing a few switches.

The slowly developing understanding of the new technology led to some companies installing signs mounted next to these new-fangled appliances, such as: Do not attempt to light with a match. Simply turn the switch.

Teachers of electric circuit theory at that time probably faced rather different challenges.

A choice in how to accumulate

Nowaways the choice in any lighting retailer is near-overwhelming, and reasonable sized towns may have several shops. There are many different (incompatible!) fittings: bayonet (BC and SBC), screw in (MES, SES, ES, GES…), simple push in, push and lock (GU10…), and end mounts for fluorescent tubes. MES (miniature edison screw – yes, Edison the pioneer of electrical lighting) and SBC (small bayonet cap) fittings are common in school labs. Then there are a variety of mountings: desk lamps; floor lamps; ceiling roses; spotlight arrays; recessed spotlights, to list only a few.

Significant efforts are made to persuade us to part with our money to establish a mood in the home.

Much of this mood is established by the bulbs that provide the light. These were originally glass bulbs enclosing carbon filaments. In many designs there is still an exoskeleton that protects the active part of the light from the surroundings, but often does not protect us from the lamp, as the outside of many kinds of bulb still gets hot. This warmth is not good, and better lights do more lighting and less heating. Typical powers in the pathways vary enormously with the construction of the lamp: filament, fluorescent, compact fluorescent (CFL) or light-emitting diode (LED).

What you want is luminous power: a measure of the brightness of the lamp as seen by us. All too often what you get is radiant power: a measure of the power radiated at all frequencies – whether you can see them or not. The more efficient the lamp, the higher the ratio: luminous powerradiant power.

Power and colour

Different lamps also emit different qualities of light. A room lit by candles looks very different from one lit by filament lamps, or by fluorescent lamps, or by the Sun. These sources emit different ranges of frequencies, and that's how they affect the mood. The colour temperature is a simple description of how the eye notices these differences. Take a special kind of radiator, a black body (more on this in the SPT: Radiations and radiating topic), and heat it to this temperature, and the light emitted will be indistinguishable from the corresponding source.

Here are a few sample colour temperatures: incandescent filament, 2700 K ;halogen filaments, 3000 K ;LED, 3200 K ;CFL (daylight), 3500 K ;moonlight, 4100 K ;daylight, 6000 K .

Each bulb is a typical value only: engineering prowess can alter these significantly to suit different environments.

Change the world – one light bulb at a time

We have all seen this slogan, but does it make a difference? And in terms of the science, surely it's those using filament light bulbs who are keen on changing the world? After all, it's the rate of dissipation of stores that is thought to be a significant trigger for world change, or at least climate change.

The best option of all is, of course, to turn the light off: a circuit containing a break costs nothing to run. Not buying newly made things (manufacturing has significant energy costs) and not depleting energy resources are the most certain ways to avoid depriving future generations.

But there is no doubt that, if we need lighting, filament lamps do the worst job of switching power in an electrical pathway to power in a heating by radiation pathway (this is a bit of a mouthful, so for shorthand we might say switching electrical power to luminous power). This is not the whole story – a more sophisticated audit would include the environmental costs of construction, and of disposal. Both fluorescent and LED lights are much more demanding in these respects. Just looking at the construction of the compact fluorescent and listing the chemicals involved gives an indication of the challenges. However, these differences are more controversial, further from the simple physics story, and harder to quantify rigorously. So here we stick to actually running the lights.

What action could individuals take, and would it make a difference? Would the money they had saved be spent on something else that dissipated even more energy? The answers will not be simple, but physics can provide some insights.

Actually making a difference

A simple set of sums can provide some numbers to help us decide what to do. Changing from an incandescent to a compact fluorescent reduces the switching power to 40 % of the original input power, for the same luminous power. Calculate or estimate the total wattage installed in a typical house. 60 % of that could be saved. Then multiply up by the number of houses. For every 1000 MW, one less major power station.

You can work through the numbers for a city the size of Worcester:

lightbulbs/household, say 30;

average wattage/bulb, say 75 W;

installed wattage is therefore 30  ×  75 W;

power saved/household is therefore 30  ×  75 W  ×  60100;

households, say 40 000;

power saved is therefore 40 000  ×  30  ×  75 W  ×  60100;

Therefore 0.05 power stations saved. So persuade 100 conurbations of this size to change, and we would lose the need for five new power stations.

There are all kinds of simplifications in this kind of calculation. For example, you might want to add a line to estimate the load factor per bulb: it is unlikely that all 30 are on all of the time. Similarly, you might think that persuading the local council to turn the street lights off will make more of a difference. The point is that some calculation is necessary to the argument, and the argument is either made with real numbers or else is of little use.

Across the EU, the average number of bulbs per household is 24, with about 33 % of these being incandescent.

Global estimates put lighting at about 19 % of the total energy switched from the electrical pathway. Some 10 % of the total could be saved by changing to much more efficient lamps.

The financial picture is equally rosy: CFL and LED lamps save the user significant amounts over their lifetimes, due to the savings in electricity bills. But what will they do with the savings? Real-life decisions can be constrained by insights from physics, but in many cases they aren't determined by these insights.

Warming is a kind of accumulating

Good room heaters warm the particles in a room, so they switch pretty much all of the power from the electrical pathway to a heating by particles pathway. Electric grills, ovens, hobs and irons are also very efficient, so the switch from one pathway to another is nearly 100 % efficient.

It might not always be the thermal store that you want that gets filled by the heating by particles pathway, but it will be a thermal store. Maybe the air outside gets significantly warmed because you didn't insulate well enough, or block off enough of those draughts. So you need to allow for this misdirection in the final description to make sure that when you do the calculations, you consider all the things that may be warmed and not just the target output.

Even simpler than electrical bulbs

These devices are also electrically simple: you've met them in circuits as simple resistors. Choosing the resistance, and using mains voltage, so a potential difference of 230 volt, sets the current and therefore the power dissipated. Remind yourself how by looking again at episode 02 if you need to.

Heating by switching power from the electrical pathway is very convenient, but it has a cost. Much electrical power production is driven by the burning of fuels, so why not burn them directly where you want the warmth? This is more efficient, but perhaps less convenient (although cooking on gas is preferred by many, and gas patio heaters are more portable – no trailing wires for the guests to trip over – so the convenience arguments aren't all one-sided).

In generating electrical power, only 20–60 % of the energy extracted from the chemical store is available to the electrical pathway. These are very substantial inefficiencies (more exact information, and techniques for calculating efficiencies, are given in episode 04).

There is another cost. Transmission wires must be long enough that we don't all need localised power stations. Then the wires are no longer perfect: they function as devices that switch some of the power in the electrical pathway to a heating by particles pathway (typically 5–15 %). The more capital you spend on the wire (and therefore also its supports, if you string it up across the countryside), the lower the running costs will be. Thick wires, of highly-conducting, yet stiff and strong, materials, are best.

In practice, the long transmission wires now present a significant resistance, so not all of the potential difference appears across the heating element. In fact, this is a simple circuit with series connections and we have already learnt how to model these so as to find the power dissipated in each resistor (episode 02). This model doesn't mimic how electrical power gets delivered to the householder, but it's an important step on the way to understanding why the system needs to be more complicated. The result of the complications is that the electrical pathway for long-distance transmission is chosen to be of a particular character: large potential difference and small current, rather than the other way round. We come back to this later.

One final cost, often not included, is that the fuel used in the power stations may not be sourced from anywhere near that power station – it might be cheaper to pay miners in another country to dig up the coal and ship it to a power station in this country than to pay the miners closer to the power station. Working out exact efficiencies from chemical store to thermal store depends on accurate information about the larger picture.

Radiating is a kind of accumulating

There are times when remote and directed warming is wanted – a microwave or therapeutic infrared lamp – and here switching is from the electrical pathway to the heating by radiation pathway. These devices are not so simple, electrically, but the energy descriptions are still simple.

The energy descriptions provide both an overview of what the device does and a focus for the engineer trying to improve the design. She can see where the inefficiencies are by studying the Sankey diagram. It then requires considerable skill and cunning to improve the performance of the device. That's where an understanding of the detailed physics comes in useful. The energy description remains helpful, because it provides limits on what can happen, and it offers a mechanism-free overview of the whole process. Doing physics well is often a question of having the experience to select the appropriate point of view, and then developing that description in order to understand what is going on in the process.

Mechanical working is a kind of accumulating

Controlling motion by switching from an electrical pathway to a mechanical pathway happens everywhere. Try counting the electrical motors in your home (washing machine, blender, hard disk, vacuum cleaner…). Then add to this total the number of loudspeakers, because these also switch between the same pathways, and they are examples where control over the switching is paramount. Life without these devices would be very different. As with the more complicated heating devices, the details are often complex but the energy story remains clear and simple.

Power accumulates energy in the kinetic store, by mechanical working, as the object speeds up or slows down. Energy can be shifted by mechanical working because of the switch in the power from electrical working.

Motors and loudspeakers come with many different working powers, showing the maximum rate at which energy can be shifted – the maximum power that the device can switch. Usually failure is as a result of excess dissipation in a thermal store – often the coil of wire that forms an essential part of the design of these devices. The coil melts.

Loudspeakers

Loudspeakers reproduce sounds by turning the to-and-fro movements of electrical currents, which encode the sound, into the to-and-fro movements of air. Power is switched from an electrical working pathway at the loudspeaker. (Another switch, to the electrical working pathway occurs at the ear, but this may not be so helpful a way of thinking about the ear—so not worth emphasising, but it is defensible).

What happens over here affect what happens over there, so it is a kind of remote working, and it is mechanical: pressure differences and forces on the ear and the loudspeaker are connected by the mechanical working pathway.

Place a wire in a magnetic field and alter the current in it. There is a force acting on the wire that changes as the current alters, even reversing in direction as the current reverses. Force changes motion, so the wire's movements change in response to the changing current. Now you need some careful engineering so that the moving wire sets enough air in motion for people to hear, and to ensure that the movement of the wire follows the changes in the electric current exactly. Attach the wire to a cone of paper. As the wire moves, so the paper will move, in turn shifting the air.

The to-and-fro motion can be accounted for in terms of a current in a wire in a magnetic field:

The motion can also be acounted for by describing one of the coils as a varying magnet:

Improving loudspeakers

The first improvement is rather easier than the second. Rather than making the current travel once through the magnetic field, make it travel through the field many times by winding the wire into a coil. An extra force, equal in magnitude and direction to the original, is acting on each transit of the wire. Add these contributing forces (one acting on each transit of the wire) to get the resultant force on the coil. This resultant force can be increased further by altering the shape of the magnetic field so that a greater length of the wire is in the field – in fact the whole of the coil. This resultant force can now drive a large surface area to-and-fro, causing significant changes in density of the air over a large enough volume for people to hear.

The prices that some are willing to pay for their speakers in search of fidelity is evidence that the second improvement is not an easy quest, and that complete success is likely to be both elusive and controversial. There's much debate about the quality of sound produced by speakers, and refining this quality is a subtle art, linking together physics with psycho-acoustics.

Simple direct current motors

Simple electric motors spin, but arranging magnets and currents in wires to obtain this motion is not straightforward.

Place a wire carefully in a magnetic field, connect a battery to drive current through the wire, and a force is acting on the wire, catapulting it out of the magnetic field at right angles to both the field and the current (That's just like a loudspeaker). This is a one-time effect and only the start of arranging for the motor to spin.

As with the loudspeaker, arranging for the wire to make multiple transits of the field increases the resultant force. To achieve this, wind the wire into a coil. The charge travels up one side of the coil and back down the other – two significant transits for each turn of the coil. This time, don't reshape the magnetic field – a near-uniform field works well for simple motors. As the current reverses in direction on the return journey down the second side of the coil, so the force on the current in the wire is reversed. The wires on one side of the coil get thrown upwards; those on the other side get thrown downwards.

How the turning happens

Explaining the spinning can be doen in one of three ways, shown below:

coil as magnet, between magnets (top row) wire between magnets (middle row) fields exerting force on wires (bottom row) In each case there is a cross-section through the motor, and a magnified diagram of the commutator, which switches the current as the brushes make and break contact with the exposed opposite ends of the wire on the coil, which are the commutator.

The first quarter turn is achieved by adding an axis to the middle of the coil for it to spin round.

With the coil now at right-angles to the magnetic field, the forces on the wires simply stretch the coil – they no longer act so as to spin it. But neither do they slow it down. That happens as soon as the coil, which is already moving, spins so that the out and back wires swap sides. The forces now act so as to return the coil to its position after the first quarter turn, at right angles to the field.

To continue the spin, simply reverse the direction of the current in the wires as the coil reaches this quarter-turn position. Now, as the wires swap sides, the force acting on the current also reverses by 180 degrees. The result is that whichever wire is on one side will always be pulled down, while the wire on the other side will always be pulled up. The wire coil is kept spinning. To reverse the direction of the current, use a split-ring commutator – a simple position-dependent reversing switch made of two brushes and a sliced ring that encases the axle of the coil.

Further improvements

You can, of course, switch the magnetic field rather than the current to alter the direction of the force, but this is rather harder to do quickly. Reshaping the magnetic field by curving the poles makes the field near radial and so keeps the out and back transits of the wire at right angles to the field for longer.

You can add more coils, cutting the split-ring commutator once for each coil that you add. This makes the motor smoother, just as adding more cylinders to a car motor produces a smoother torque to drive the car.

Permanent magnets attract and repel

One magnet exerts a force on another. Magnetic field line patterns (see the SPT: Magnetism topic episode 01 for an introduction) also change when you place magnets close to each other. There should be a connection between these two representations, so that interpreting a pattern of field lines will enable you to predict the forces.

Connections between field lines and changes in motion

To explore the connection, start with the simplest situation. Pull a pair of attracting magnets apart and the field lines get stretched – the field lines extend. Release one magnet and it flies back – there is a force acting on that magnet. The force produces a change in motion that shortens the field lines. Of course, it doesn't matter which magnet you let go of – the interaction is represented by a force acting on one magnet and exerted by the other. There is an equal and opposite force on the other magnet of the pair (Newton's third law).

Perhaps situations where movement of the magnets reduces the length of the field lines will always be those where the magnets experience a force that will cause that change in movement. Check out this speculation by pushing together a pair of magnets that are arranged to repel. Now when the magnets are released they fly apart, and the field lines are shortened, mostly by straightening.

There is a general rule: where field lines can be shortened by movement, there will be a force acting on the magnets to cause exactly such a change.

Currents in wires attract and repel

A current-carrying wire is surrounded by a magnetic field. Place two wires close to each other and the field lines will become longer. Your experience with permanent magnets should lead you to expect a pair of forces, one acting on each wire to create movement that shortens the field lines again. There are two simple cases: in both the wires are parallel.

Principles and rules of thumb

If the currents in the wires are in the same direction then the wires attract.

If the currents in the wires are in opposite directions then the wires repel.

The underlying principle – that forces on the wires generate movements that shorten the field lines – is what is valuable here as you can apply it often, and it gets you closer to having a physical model of the field, rather like the model used so effectively by Faraday.

Faraday developed his expectations by reasoning about field lines as if they were special elastic tubes that were under longitudinal tension, so were always trying to shorten. He also thought of them as repelling each other radially. The resulting field patterns that Faraday drew were a result of considering the responses to these two opposing tendencies. The electromagnetic changes that he expected as a result of the rearrangement of the field lines led him to many of his most famous experimental results.

Electromagnets: coils and fields

Coils of wire carrying currents produce magnetic fields, and these field patterns are identical to the field patterns of bar magnets. Just as with bar magnets, placing two current-carrying coils near each other produces changes in the fields of both, lengthening the field lines. Moving the coils can shorten the field lines. The direction in which you move to bring about this shortening shows the direction of the force.

Electromagnets: wires and fields

Placing a current-carrying wire between attracting magnets also lengthens field lines. As the field lines shorten, so the wire is thrown out of the space between the magnets. Again, magnetic forces produce a change in movement that shortens the field lines.

This movement is at right-angles to the current in the wire and to the magnetic field lines between the pair of magnets.

Transformers are pervasive, and a bit mysterious

Transformers are devices connecting pathways yet they seem not to switch pathway – one electric circuit is linked to another (completely separate) electric circuit. The inbound pathway is electrical working, as is the outbound pathway. How can this be useful?

The key to their usefulness is that two pathways can be different in character, because the rate at which energy is shifted – the electrical working – is the product of the current and the potential difference. There can be the same power in the pathway for many different currents: smaller currents are compensated for by larger potential differences.

Next, you'll meet the principles for designing transformers to step up, or to step down, the potential difference to allow smaller or larger currents.

Transformers can be built to be very efficient – all of the power appears in the desired output pathway. So the power in the inbound pathway is effectively equal to the power in the outbound pathway:

power_in = power_out

Transformers everywhere

Transformers appear at all scales, from providing small potential differences running all of the electronic devices in the home, to large substations on the National Grid, supplying very large potential differences. In between these two, the domestic supply is set at 230 volt. This is a compromise between improving safety, for which an even smaller potential difference might be preferred, and greater efficiency, for which a larger potential difference would be chosen.

The details are given in episodes 01 and 02. You choose the character of the pathway, constrained by both efficiency and safety.

To change the character of the electrical pathway, use a transformer. This device trades a change in potential difference for a change in current: current_in × pd_in = current_out × pd_out (this must be true, as power_in = power_out).

Stepping up and stepping down

Described from the energy point of view, the transformer is a very simple device. You change the character of the electrical pathway, not the pathway itself. This change in character is fixed by altering the ratio of the number of turns on the two coils.

To step down the potential difference, choose more coils on the input side; to step up the potential, choose more on the output side: V_outV_in = N_outN_in

The ratio of the potential differences is equal to the ratio of the number of turns.

There is more detail about how transformers work later in this episode, but for now note that practical devices work using alternating current. There is no transforming action at all for steady, direct currents.

What is inside

A transformer is rather simple – there are no moving parts.

Two electrical coils are linked by a loop of magnetic material, typically iron. A transformer is just three linked loops, suitably arranged: the electrical loops are at right angles to the magentic loop.

The usefulness of transformers

A transformer transforms potential difference. In particular it can step up or step down the potential difference by a constant multiplier.

But you don't get something for nothing. Energy is still conserved, so the power in the inbound (electrical) pathway is nearly exactly equal to the power in the outbound (electrical) pathway. The transformer doesn't accumulate energy, having no stores of energy associated with it – the transformer is just a device. In fact the engineering can be so good that nearly all of the power stays in the electrical pathway – very little gets diverted to different pathways (less than 1 % for large transformers).

Different characters of pathway

However, the character of the electrical pathway can be altered – you can switch a small potential difference, large-current pathway to a large potential difference, small-current pathway. The same power is carried in the pathway, but there are advantages to pathways of particular character, which were explored earlier in discussions about the choice of 230 volt as the domestic supply.

The device plays a crucial role in any large-scale electrical supply system, where its role is to alter the character of the pathways to reduce losses by reducing switching to other pathways in the transmission wires.

Households contain many transformers, because small electronic devices – which are very common as a part of larger appliances (do you have an LCD display on the washing machine, dishwasher, or oven?) or on their own (the computer, alarm clock, electric shaver, or music player) – need small potential differences to work and don't work well on 230 volt. If 230 volt were used, the resistances would have to be huge to prevent large currents where they weren't needed, and so the compact and handy devices that we have now wouldn't have been developed.

However, not everything that appears in a small black cube on the end of a socket must contain a transformer – there are electronic devices that can now bypass this process but will still change the character of the pathway, so care is needed.

In systems for shifting energy across large distances, there will typically also be many transformers. The cost of running electrical power lines at 400 kilovolt (much of it associated with mitigating danger to people) is only justified if there are great distances to be covered and if the power in the pathway is huge (e.g. linking a large power station to large conurbations). For local distribution, say across a town, power lines can be at a smaller potential difference, perhaps 11 kV, so the pylons and other devices designed to keep people from being part of a circuit containing such a large potential difference can be smaller, with smaller capital costs as a consequence. Remember that we are comparatively safe – particularly with dry skin – with a potential difference of 230 V across us. However, factories and other industries may be supplied with much larger potential differences and, as a result, be subject to much more careful safety procedures.

As there will be several different compromises, depending on the distances from generating stations, and the power demands and safety needs of end users, there will need to be many transformations of potential difference, each likely to have its own transformer.

Some high-voltage systems do use direct current, but these have to rely on devices other than the transformer to change the character of the pathway.

Three linked loops make up the transformer

A coil of current-carrying wire produces a steady magnetic field, just like a bar magnet. Link this magnetic field to a second coil by placing that second coil near the first. You'll get a good link when the strength of the magnetic field inside the second coil is as big as possible. Use what you know about the shape of the magnetic field produced to guide the placement in order to maximise the linkage. The linkage between the coils can be improved further by using a soft iron loop, because this provides a preferred route for the magnetic field, just as copper wire does for the electrical current.

The linkage between the coils can be improved further by using a soft iron loop, because this provides a preferred route for the magnetic field, just as copper wire does for the electrical current.

The magnetic effect propagates round this loop, just as electrical effects flow round copper loops, but nothing magnetic flows. So now you have two interlinked loops: the electrical loop and the magnetic loop. But nothing is happening in the second coil – a steady current in the first electrical loop produces a steady magnetic field in the iron loop, which doesn't induce any activity in the second coil.

It took the persistence and genius of Faraday, working with his hand-made apparatus, to show that only a changing magnetic field induced electrical activity in the third loop.

What each loop does

Changing the current in the first coil produces a changing magnetic field. An alternating current produces an alternating field. You can drive an alternating current through the first coil by applying an alternating potential difference across this input coil. The electrical current in the input coil sets the value of the magnetic field produced by that input coil.

The simplest kind of change to explore is where the current changes steadily with time, say increasing at 0.1 ampere inverse second. This steadily increasing electrical flow round the input electrical loop will produce a steadily increasing magnetic effect in the magnetic loop.

Now we turn to the second electrical loop – the output coil – to explore the experimental findings of Faraday.

Steady changes induce constant outputs

A steadily increasing magnetic effect in the second coil induces a constant potential difference across the second coil. So the second coil acts as if it is a battery of constant potential difference. As a result, the second coil, if connected into an electrical loop with a resistor, has an electrical current driven around it (I = VR). So a steadily increasing electrical flow in the input coil produces a steadily increasing magnetic effect, which induces a constant potential difference in the linked output coil.

A constant electrical flow in the input coil produces a constant magnetic effect, which induces no potential difference in any linked output coils.

However, a steadily decreasing electrical flow in the input coil, driven by a steadily decreasing potential difference across that coil, produces a steadily decreasing magnetic effect. Any linked output coils now have a constant negative potential difference induced across them, resulting in a reversed constant electrical flow in completed electrical loops.

An induced battery

Coils linked to a changing magnetic loop can be induced to act like electrical batteries.

If the magnetic effect is increasing then the polarity of the battery is in one sense (one end of the coil acts as a positive terminal, the other as a negative terminal); if the magnetic effect is decreasing, then the terminals of the battery have to be switched.

Now add a resistor, or any other load, to the output coil to make a complete loop.

Lenz's law

The conservation of energy is a very fundamental principle: the energy shifted from one store is equal to the energy shifted to other stores.

Power in pathways also respects this principle, in that no device can do more than switch pathways: the output power can be no more than the input power.

If you propose a process where more power emerges than you put in, you are certain to be wrong. So, if there are only two possibilities, and you eliminate one, the other must be true. This is how to decide about the relationship between the direction of flow in the output coil and the changing flow in the input coil. We show that one possibility violates the conservation of energy, and then conclude that the other possibility must be true.

So to work: describing what turns out not to be possible.

Arguments about the conservation of energy

Consider the input electrical loop with an increasing flow and so producing an increasing magnetic effect in the linking loop. The output electrical loop will have a constant potential difference induced across it. This can only be in one of two directions. This potential difference will drive an electrical current that also produces a magnetic field, and so a magnetic effect. One direction will produce a magnetic effect that adds to the existing effect, produced by the input coil. In this case, a change in magnetic effect induces a potential difference that drives a current that increases the magnetic effect, so leading to a greater potential difference being induced, and therefore to a larger driven current in the output. The positive feedback loop continues without limit. Now the output coil has a growing potential difference and a growing current, so there is more power in the pathway P = I × V). This is without making any changes to the input. You're now getting something for nothing, and there is no longer compensation in changing the character of the pathway: both the output potential difference and the output current are growing.

Conclusion: the opposite case must be true. The potential difference across the output must be of such a polarity that the current driven produces a magnetic effect that decreases the inducing magnetic effect.

Starting with a decreasing electrical flow in the primary changes all of the signs in the argument, and again leads to the conclusion that the magnetic effect produced by the current driven by the induced potential difference in the output loop must be in such a direction that it opposes any changes in the magnetic effect.

This result is know as Lenz's law, but now you can see that it is really just the conservation of energy. In further studies we'd just write:

induced potential difference = — constant × change in magnetic effect.

Sometimes a simple minus sign represents a lot of physical reasoning.

Inputs and outputs for transformers

An alternating potential difference is one that repeatedly changes polarity, driving electrical current first one way and then the other. Tracing out the variation over time can give any number of patterns, while still being alternating (sawtooth, ramps and square waves are all possibilities).

The mains supply is sinusoidal, so it's worth thinking about how this works in a transformer. We think it's best to choose a few instants to think about, to predict how the changing linkage will affect the induced potential difference.

When the current in the input electrical loop is small, but growing rapidly, the magnetic effect in the linking loop is also growing rapidly, so the induced potential difference is large and negative.

Current in one electrical loop related to potential difference across the second

When the current in the input electrical loop is at its maximum positive value (no longer growing), the magnetic effect in the linking loop is also large, but no longer growing, so the induced potential difference is zero.

When the current in the input electrical loop is small, but shrinking rapidly, the magnetic effect in the linking loop is also shrinking rapidly, so the induced potential difference is large and positive.

When the current in the input electrical loop is at its maximum negative value (no longer growing), the magnetic effect in the linking loop is also large, but no longer growing, so the induced potential difference is zero.

Certain of these points, we can now fill in the graph, to show that the induced potential difference is also sinusoidal (so the current in the output electrical loop will be too), but that it does not peak at the same time as the input. We say that the input current is out of phase with the induced potential difference.

What generators do

Transformers use the principle that a changing magnetic effect linked to a coil induces a potential difference. This potential difference can then be used to drive a current. In transformers a changing current produces the changing magnetic effect.

Another possibility is to use the power in another pathway to change this magnetic effect and link these changes in effect to an output coil. This new device switches from the other pathway to the electrical pathway. Such devices are called electrical generators. Electrical charge is set in motion everywhere in an electrical loop connected to such a generator. It's just as if you'd inserted a battery to complete a circuit.

Here we'll focus on generators that switch from the mechanical pathway because these are quite common.

Large-scale power stations, whether nuclear, geothermal, fossil fuel or wind powered, all make a turbine spin, and this turbine is used to rotate an arrangement that varies the effect in the magnetic loop.

More details about which energy stores are depleted in achieving the spinning are given in the SPT: Energy topic.

Modelling a generator from what we know about a transformer

To explore an arrangement that can vary the magnetic effect, start with the transformer. The input coil has a constant current driven through the coil in order to make an electromagnet. The constant magnetic effect is converted to a changing magnetic effect by spinning the coil or magnet.

Careful design of the coils and the iron can make the whole process much more efficient by optimising the magnetic linkage between the two electrical loops (input and output). This is the essential design of the generators in many power stations.

Spinning a coil changes the magnetic field clinked to that coil

You don't have to spin the magnet – you could have a stationary permanent magnet and spin the coils. What you do need is a changing magnetic effect through the output coil.

The combination of a spinning coil and stationary permanent magnets is the way in which a generator is most likely to be introduced in the laboratory. First make an electric motor. Then disconnect the power supply and connect an ammeter. Spin the coils and you have a direct current generator.

Why direct current? That's because of the split-ring commutator – the position-reversing switch introduced in explaining the motor. Here it functions exactly as before, serving to connect the side of the coil moving upwards to one terminal of the motor, and the side of the coil moving downwards to the other.

A less useful, but perhaps simpler, generator

You could have an oscillating permanent magnet moving in and out of the output coil. This has so far proved impractical as a large-scale design but is often used to introduce electromagnetic induction in the laboratory. Again, it's the changing magnetic effect that's important. You could simply rotate the permanent magnet – or the coil. Either will produce a change in the linkage between the magnetic link and the electrical loop, and so a change in magnetic effect, and this will in turn induce a potential difference.

Not all generators use magnetic fields …

As Earth has a magnetic field, you might think that rotating a coil would change the magnetic effect through the coil by changing the linkage. On this basis you might expect an induced potential difference. You'd be right! But you need the most sensitive meter in the school laboratory to detect the very small potential difference and a coil with a very large number of turns to convert the small rate of change of magnetic effect into even this tiny potential difference. (You could also try spinning the coil faster, but then you'd need a sensitive AC voltmeter: not so common.)

The principles you learnt about the magnetic loop linking input and output electrical loops when studying the transformer also apply to generators.

The more the current in the input loop, the more the magnetic effect. The greater the rate of change of magnetic effect, the larger the induced potential difference.

The more turns on the output coil, the larger the induced potential difference.

Not all generators switch from mechanical working to electrical working.

Solar photovoltaic cells are generators that switch from the heating by radiation pathway to the electrical working pathway as they absorb the incident photons of light and provide a potential difference. Usually this involves carefully layered semiconductors. Nothing has to get hot and make steam, unlike the solar energy stations that concentrate sunlight to boil water, and then drive a conventional turbine.

Thermoelectric generators are still largely in the development laboratories, except for specialised applications, but they mostly switch from the heating by particles pathway to the electrical working pathway. Again, semiconductors are involved and development continues, but so far the power made available to the electrical pathway is only small.

Devices and pathways

Devices switch pathways, allowing you to change the power in the pathways connected by the device. Often these devices are very carefully engineered, requiring detailed knowledge beyond the principles outlined in this episode.

The power in one pathway is switched to power in another by a device

Here is a summary of the devices introduced, listed with the switching for which they were designed:

• Light bulb: electrical working switched to heating by radiation (visible radiations only – that is, the range of frequencies we're interested in).
• Heater: electrical working switched to heating by particles or, for radiant heaters, heating by radiation.
• Motor: electrical working switched to mechanical working.
• Transformer: electrical working to electrical working.
• Generator: mechanical working switched to electrical working.