Depending on the ability and experience of your students you may need to spend time reviewing their previous knowledge and rehearsing the language that will be needed to cope with what follows.

Lesson Summary

• Demonstration and discussion: Talking about circuits (30 minutes)
• Student activity: How current flows (20 minutes)
• Demonstration: Using multimeters.(15 minutes)

Discussion and demonstrations: Talking about circuits

One way to review your students’ existing understanding of simple circuits would be to ask questions about a concrete example (e.g. the circuit shown above) and correct misunderstandings.

Set up the circuit using batteries and three identical resistors. At the same time, show the circuit diagram. Give a running commentary as you connect up: Position the components as shown in the diagram. Starting from the – of one cell, connect up in a clockwise direction....

(Note that you could use lamps instead of resistors, but remember that resistance changes with temperature so filaments with equal cold resistance will not have equal resistance when different currents flow through them.)

Point out that there is little to be seen with a circuit like this, but they already know quite a lot about how to describe the invisible processes which are going on. Pose some questions about the circuit; here are some suggestions:

• Get them to imagine charge carriers moving around the circuit – what happens at a junction? (Current divides, re-combines.) At this stage, don’t worry about the distinction between conventional current flow (from + to – ) and electron flow
• Rehearse flow analogies – people queuing to go through two turnstiles/traffic at a junction/water in a central heating system etc. (Be aware that each analogy has its pitfalls!). The key point is that charge has to be accounted for (i.e. it is conserved)
• Give values of current at a particular point (e.g. leaving the cell or in one of the parallel arms) and ask them for values at other points
• How would they measure these currents? (Check they know how to add an ammeter to the circuit.)
• Ask students to make up sentences relating to the circuit using the terms series and parallel. (Two of the resistors are connected in parallel with each other. The cells are connected in series, etc.) Relate these terms to current flow. (Series: same current flows through one component then the next. Parallel: current divides up, or is shared.)
• Give them pds across the cell and the single resistor and ask for the pd across the parallel resistors. How would they measure these pds? (Check they know how to add a voltmeter to the circuit.)
• Vary the circuit by having two resistors in one arm and one in the other
• A tricky question: How do charge carriers know how much resistance is ahead of them? They don’t, but charge density adjusts very rapidly – like traffic on a motorway that backs up for a long distance before road works or an accident constricts the flow. (Again, be aware of the limitations of this analogy)

Student activity: How current flows

If your students are unfamiliar with your standard electric circuit equipment (they may have come from another institution), give them a short activity to allow them to familiarise themselves with such components as power supplies, connecting wires, ammeters, resistors and lamps.

Ask them to set up a circuit which will demonstrate some aspect of how current flows. Then they should be able to demonstrate what their circuit shows to the rest of the class. They should accompany their description with a circuit diagram.

(Some can be expected to show that current is the same around a series circuit, and others that it divides in a parallel circuit. However, you could initially leave them to decide for themselves what they will show.)

Demonstration: Using multimeters

If you expect your students to make use of multimeters, it is worth taking the time to explore them now. There are a wide range of multimeters in use in school physics faculties. Make sure you are familiar with the ones that will be used. It is valuable, prior to using them for measurements, to give out meters (e.g. in pairs) and take your class through the rules for connection. With a weaker group you may find it is worthwhile providing a pictorial instruction sheet. Most multimeters are fused. Make sure you know what currents are likely to be drawn and insist that student use an appropriate range. Otherwise you are likely to end up with a lot of blown fuses and confused students. If you have access to a PC projector a webcam and a laptop you can demonstrate the use of the meter and project an image of the connections.

Here, you are trying to illustrate the idea of electric charge and its relationship to a flow of current.

Lesson Summary

• Demonstration: Spooning charge (15 minutes)
• Worked example: Calculating numbers of electrons (10 minutes)
• Demonstration: The shuttling ball (15 minutes)
• Worked example: Calculating charge per second (10 minutes)
• Discussion: Defining current, the coulomb (10 minutes)
• Student questions: On charge and current (30 minutes)

Demonstration: Spooning charge

Start by reminding your students of the nature of electric charge. They should be familiar with the concept of charge from pre-16 science course. Remind them that this is a fundamental property of some types of particles (e.g. protons and electrons) and that there is a law of force: like charges repel, unlike charges attract. These are the forces that push charges around electric circuits.

Use the Spooning Charge demonstration to reinforce the idea that charge can be taken from one place to another and does not just disappear.

Episode 102-1: Spooning charge (Word, 38 KB)

Worked examples: Calculating numbers of electrons

Remind them that charge is measured in coulombs and tell them that the size of the charge on an electron is a tiny fraction of a coulomb (1.6 × 10^-19 C). A quick calculation will confirm that even tiny charge transfers on our scale involve enormous numbers of electrons.

Calculate the number of electrons transferred when you spoon charge and show that this depends on the voltage of the supply. (The result is, of course, linked to capacitance; this could be mentioned for a strong group.)

Demonstration: The shuttling ball

Use the Shuttling Ball demonstration to link charge and current. The greater the rate of transfer of charge the greater the current.

Episode 102-2: Shuttling ball (Word, 54 KB)

Worked examples: Calculating charge per second

Calculate the charge transferred per second in the shuttling ball experiment. To do this, use a coulomb-meter to measure the charge on the ball and then measure the number of transfers in a given time. Alternatively you could work back from the current.

Discussion: Defining current, the coulomb

Define current as rate of change of charge. At this level it might be best to do this graphically. Current is the gradient of a graph of charge transferred against time, leading to I =  Δ Q Δ t or (in the limit) I =  d Q d t. Exactly how you represent this will depend on the requirements of your specification and the mathematical experience of your students. The idea of the gradient can be introduced by asking how the charge transferred by the shuttling ball increases with time – it will go up in a series of steps but, given a large number of transfers, these will approximate to a constant slope. The average current is equal to its gradient. The essential outcome is that they realise that a current of one amp is equivalent to a flow of one coulomb per second. The equation I = Qt (familiar from pre-16 science lessons) is useful but stress that this refers to an average current I and they must take care when I is changing.

Define the coulomb as the charge passed by a current of 1 A in 1  s, i.e. 1 C = 1 A s. (Note that the ampere is an SI base unit, and its definition is beyond requirements at this stage.)

Student questions: On charge and current

Episode 102-3: Introductory questions on charge and current (Word, 26 KB)

There are two main aims for this episode: to present a range of examples involving different types of charge carrier, and to measure currents and link the measured current to rates of flow of charge.

Lesson Summary

• Demonstration: Identifying charge carriers (20 minutes)
• Demonstration: An electron beam (15 minutes)
• Demonstration: Students conducting electricity (15 minutes)

The episode consists of a series of demonstrations which could be set up as a circus before the lesson. The students can then be taken around as each one is discussed.

Demonstration: Identifying charge carriers

Students are used to thinking of metals as good conductors. However, they should appreciate that there are other situations, more or less familiar, in which current flows.

In a filament lamp: Conductor: metal (tungsten). Charge carriers: electrons. Remind them of the free-electron model (i.e. in a metal, there are free electrons which can move about within the metal). Discuss the behaviour of the charge carriers as the supply voltage is increased. (They move faster to make a bigger current.)

A spark through air: The level here is variable. The essential idea involves ionisation. You could ask why air is usually a good insulator and what must happen in order for it to break down and conduct. The charge carriers are positive ions and electrons. These move in opposite directions. Link this to lightning.

A fluorescent tube: Conductor: Plasma. Charge carriers: ions and electrons. Plasma is the 4^th state of matter and is the most common phase of matter in the universe (e.g. in stars).

Electrolysing copper sulphate solution with copper electrodes: Conductor: Electrolyte. Charge carriers: positive (copper) and negative (sulphate) ions.

So both electrons and ions are charge carriers; when they move, a current is flowing.

Episode 103-1: Identifying charge carriers (Word, 39 KB)

Demonstration: An electron beam

Show the path of beam of electrons in a vacuum tube. You will need to practice setting this up; follow the manufacturer’s instructions.

Conductor: charged beam in a vacuum. Charge carriers: electrons. The high speed and low density of charge in the beam can be contrasted with the low speed and high density of charge carriers in a metal (this helps to lead into the derivation of I = nAqv if your specification requires it).

Episode 103-2: Current and charge in electron beams (Word, 53 KB)

Demonstration: Students conducting electricity

This can be used to show the effect of series and parallel circuits. It can also lead to a discussion of electric shock and electrical safety. It takes a few tens of milliampere to kill a person. A car battery can supply hundreds of ampere if it is shorted, but 12 V is not sufficient to push a tangible current through a person. The amount of current depends on the contact resistance and path of the current through the body. We conduct because much of our body is effectively an ionic electrolyte (like salty water).

Episode 103-3: Conduction by students (Word, 122 KB)

In this episode, you can show that charge carriers in good conductors usually move very slowly. You can also derive and use the equation I = nAqv.

If this episode is not required by your specification, the demonstration could be added to those of

episode 103

Lesson Summary

• Demonstration: Ions moving (15 minutes)
• Discussion: Deriving I = nAqv (15 minutes)
• Worked example: Using I = nAqv (10 minutes)
• Discussion: Interpreting I = nAqv (5 minutes)
• Student questions: Practice with the equation (30 minutes)

Demonstration: Ions moving

Show the movement of ions when a current flows through a solution. The permanganate ions (negative) carry the distinctive purple colour toward the positive electrode. An estimate of drift velocity (of the order of mm/minute) shows the extremely slow progress of the ions.

Ask whether electrons might move faster in a metal wire. (Students may point out that, for example, a light comes on as soon as the switch is closed. Leave this in the air for now; they will be able to see whether this is a correct interpretation shortly – see the Discussion at the end of this episode.)

Episode 104-1: Conduction by coloured ions (Word, 63 KB)

Discussion: Deriving I = nAqv

You can now derive the equation I = nAqv.

It is worth exploring the meaning of this equation before trying numerical examples.

If a material has a large density of charge carriers, (large n), then v will be relatively low (for a given current).

The thinner the wire (for the same current) the faster the charge carriers must move.

If current is increased the only term that can increase is v.

Episode 104-2: Derivation of nAvq (Word, 25 KB)

Worked examples: Using I = nAqv

Now make an estimate of drift velocity in a metal by estimating the value of n.

Consider a current of 1 A in a copper wire of cross-sectional area 1 mm².

Assume one free electron per atom. (This is a good estimate.) So we need to find the number of atoms present.

For copper (density 8900 kg m^-3 and atomic mass number 63.5):

In 1 m³ there are 89000.0635 moles of Cu atoms , so 8.4 × 10²⁸ atoms m^-3.

This gives a value of n of order 10 29^{m -3}.

Rearrange the equation to give:

v = In Aq

and substitute values to get;

v = 1 A10 29^{m -3}  ×  1 × 10^-6 m  ×  1.6 × 10^-19 C

v = 6 × 10^-5 m s^-1

(i.e. less than 0.1 mm s^-1.)

This is consistent with the observed drift of ions in the experiment.

Discussion: Interpreting I = nAqv

They should be surprised by this result. Remind them that this is the drift velocity of the electrons inside the metal and is much lower than the actual individual velocities of electrons. This is because of the random motion of the electrons. It is useful to think of a gas of electrons with large random velocities whose nominal centre of mass drifts slowly along the metal tube.

Drift velocities in semiconductors are much larger because they have much smaller values of n (by a factor of at least 10⁶).

Student questions: Practice with the equation

Episode 104-3: Electrons in copper (Word, 22 KB)

It is worth discussing energy transfer in electric circuits and linking this by analogy to other more familiar examples.

Lesson Summary

• Demonstrations: Human and lemon batteries (10 minutes)
• Discussion: Energy and work in an electric circuit (10 minutes)
• Discussion: Quantitative energy transfers (10 minutes)
• Student questions: Practice with the ideas (30 minutes)

Demonstration: Human and lemon batteries

Two fun demonstrations showing that there is nothing special about the chemical substances that are needed to make a battery. The limitation is, of course, the high internal resistance of the cells.

Episode 105-1: The human battery (Word, 24 KB)

Episode 105-2: Making electricity (Word, 27 KB)

Discussion: Energy and work in an electric circuit

Show a cell connected to a lamp. The idea to get across is that charge carriers are pushed around a circuit by the electromotive force (EMF) of the cell. The charge carriers are rather like water in a hydroelectric power station – they do work (e.g. in the lamp) just as the flowing water does work in the turbo-generators. Neither the charge nor the water is used up but the current transfers energy. In the power station, water moves from behind a raised dam to a lower level. In an electric circuit the charge falls from high electrical potential to lower electrical potential.

This can lead to the idea that a cell provides a potential difference and that charges move around the circuit from higher to lower potential (beware of signs here – negative charges fall from  −  to  +  whilst positive charges would fall the other way!). The greater the vertical drop in the hydroelectric station the greater the change in energy per kilogram of water stored gravitationally. In a similar way, the higher the EMF across a power supply the greater the change in energy per coulomb of charge moving between its terminals stored electrically.

Discussion: Quantitative energy transfers

The volt is defined as the energy transfer per coulomb of charge as charges move between two points in a circuit.

V =  Δ E Δ Q

i.e. energy change per unit charge (so that 1 V = 1 J C^-1 )

Introduce the terminology of electromotive force (voltage across an power supply) and potential difference (voltage across a component in which electrical work is done). Stress that, despite its name, EMF is not a force but a voltage, measured in volts.

Kirchhoff’s second law comes later, but there is no harm in preparing the way here. They will be familiar with the concept of energy conservation and this can be applied to a single charge carrier (or more simply 1 C) as it is followed around any closed loop in a circuit. The essential idea is that the total change in energy stored (e.g. chemically in a cell) equals the total change in energy transferred by components around any loop (leading to sum of EMFs = sum of pds).

This leads on to the basic principle behind the chemical cells shown in the demonstrations. Different metals have different affinities for electrons. This pushes electrons from one to the other through the intervening electrolyte. The accumulation of charge on the cell terminals provides the push that drives charge carriers around the external circuit. Large EMF can be obtained by connecting cells in series. Larger currents can be drawn if they are connected in parallel.

Discuss the energy per coulomb from the human and lemon batteries and compare it with familiar AA cells.

The idea that EMF is energy per coulomb leads to the idea that more charge must pass through the cell to increase the energy transferred to the circuit.

Δ E = V ×  Δ Q

Student questions: Practice with the ideas

Episode 105-3: Measuring potential difference (Word, 40 KB)

Students may need to be reminded of the idea that power is the rate of doing work (or the rate at which energy is transferred).

Lesson Summary

• Discussion: How to calculate electrical power (15 minutes)
• Student questions: Calculations (30 minutes)
• Discussion: Reviewing progress, checking understanding (30 minutes)

Discussion: How to calculate electrical power

Start with some theory, reinforcing the idea of voltage and using the equations:

Δ E = V ×  Δ Q and Δ Q = I ×  Δ t

to derive Δ E = I × V Δ Q

The rate of doing work is the power:

P =  Δ E Δ t

P = I × V

Discuss the significance of this using familiar examples; e.g. a 100 W lamp connected to 230 V (ac) supply; an electric kettle (about 2.0 kW); power station transmitting 1.0 GW along transmission lines illustrating the need to transmit at high voltage in order to reduce losses due to heating.

Episode 106-1: Lamp lighting (Word, 36 KB)

Student questions: Calculations

These questions, which can be used in class or for homework will give you the opportunity to asses your students’ understanding at the end of this introduction to electric circuits – see the discussion below.

Episode 106-2: The power of a torch bulb (Word, 20 KB)

Episode 106-3: Kinds of the light bulbs (Word, 47 KB)

Episode 106-4: Power of appliances (Word, 59 KB)

Discussion: Reviewing progress, checking understanding

In discussing students’ work on this topic, there are a number of things to look out for. Students may fail to discriminate between terms – current and voltage in particular.

Potential difference (pd) versus voltage

pd has the advantage that it emphasises that we are measuring a change between two different points in an electric circuit (rather than flow at one point).

Electromotive force

(emf) is a term for voltages across sources of electrical supplies (cells or power packs).

Cells becoming discharged

charge is not used up, energy is transferred and, usually, dissipated.

This is a good time to reinforce some other ideas:

Conventional current:

This flows (by definition) from positive to negative around the external circuit (inside the cell chemical reactions pump charge carriers to the terminals). Some students may say that physicists got it wrong because we now know that electrons flow the other way. Whilst there would have been some advantages in reversing the definition of current flow (or of sign of charge on an electron) it is really an arbitrary choice. You can illustrate this by discussing current flow and movement of charge carriers in an electrolyte (or an ionised gas). Positive ions go one way, negative ions go the other way, and so however current is defined there will always be examples where current direction and charge carrier movement are opposite.

Current flows all around a circuit

Including through the cell itself.

They will find it hard to believe that charge carriers on average drift slowly and yet the effects of an electric current are transmitted very rapidly (at the speed of light in the medium). It may be worth pointing out that the electrical influence is spread through the field between charges and this travels at the speed of light. At a lower level the analogy of cars moving off when a traffic light changes is good – the influence spreads down the line of cars far more rapidly than the speed of any individual vehicle.

A useful analogy for charge flow – a bicycle chain

The chain is a way of doing work remotely. It allows a cyclist to pedal in one place in order to turn a wheel in another place. Having cycled for ten minutes, the energy stored chemically by the cyclist (the cell) will have gone down. The rate at which links pass any point is constant all round the circuit

i.e. the flow of links (the current) is not used up. Also, the chain itself is not used up (neither is charge) and stops when the cyclist stops pedalling (when the circuit is switched off). The quantity that is 'used up' is the reactants (sugars plus oxygen) in the cyclist (the chemicals in the cell).

Yet another analogy

Skiers (charges) being lifted up a mountain by a ski lift (working mechnically or electrically) and then skiing down a slope (resistor). This is particularly useful for the idea of voltages in parallel circuits. Parallel slopes drop different skiers through the same vertical height (equal voltages across components in parallel).