Voltage/Potential Difference
Electricity and Magnetism

Potential difference

for 14-16

What is it that a voltmeter measures? These experiments will help students to disentangle the concepts of voltage and current, and to distinguish between potential difference and electromotive force.

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Lamp brightness comparison

Voltage/Potential Difference
Electricity and Magnetism

Lamp brightness comparison

Practical Activity for 14-16

Demonstration

This experiment provides an excellent introduction to the concept of potential difference (voltage). Students observe that two lamps with the same current give out quite different amounts of light and this sets off a discussion.

Apparatus and Materials

  • Lamp Brightness Comparison unit (see Technical notes)
  • Multimeter with probes, 2
  • Power supply, low voltage, variable AC, capable of delivering at least 0.5 A
  • Lamp 12 V, 5 W in SBC holder
  • Lamp, 230 V 100 W
  • Leads, 4 mm, 4

Health & Safety and Technical Notes

This experiment should only be done by teachers with good knowledge of mains electricity and the dangers. Do remember that you are working with potentially lethal voltages and take extra care. Students should not come near the apparatus when it is being used.

The Electrosound apparatus reduces the risk of electrocution. It includes the use of a safety mains lamp socket, which has a built in switching system that only allows it to be switched on when a lamp is inserted. Also included are two switches, which must be pressed simultaneously to route the mains current through the low voltage lamp. The switches are sited at opposite ends of the case, requiring two hands to operate them.

The main risk arises from the ammeter and connections. The 2 mm sockets on the unit are at mains potential even when the switches are not pressed. It is essential that a suitable multimeter (on ammeter setting) and connections are used. Connections to the ammeter should be made with the unit disconnected from the mains, and no adjustments made to the ammeter or wires once the unit is plugged into the mains.

The multimeter should be a type rated for 230 V, with shrouded 4 mm socket connectors. The multimeter probes should have shrouded 4 mm plugs for connection to the multimeter, and 2 mm plugs for the unit of a type that when inserted, make accidental contact with the conductors highly unlikely. All plugs and cables need to be rated at least 230 V AC.

The Lamp Brightness Comparison unit must have the appropriate lamps inserted into the holders before the unit is used.

Read our standard health & safety guidance


The Lamp Brightness Comparison unit is obtainable from Electrosound.

Procedure

  1. Set up a simple circuit with the 12 V, 5 W lamp in series with a multimeter set on the 2 amp AC range. Connect this to the low voltage power supply set at 12 V AC.
  2. Switch on the power supply and observe the brightness of the lamp and record the current. Switch off.
  3. Make sure the Lamp Brightness Comparison unit is unplugged from the mains. Insert a 100 W mains lamp and the 12V, 5W lamp into appropriate sockets of the ‘Lamp Brightness Comparison’ unit. Move the black switch to ‘on’. Connect a multimeter set on the 2 amp AC range to the 2 mm sockets, using the multimeter probes. The use of a meter is essential to the correct operation of the circuit.
  4. Connect the mains lead from the Lamp Brightness Comparison unit into a suitable mains socket and switch on. Caution: Remember the meter probes are live. Do not touch. The mains lamp should illuminate. Once again, observe the brightness of this lamp and record the current. Switch off.
  5. Insert the 230 V and 12 V lamps and ask students to predict what will happen (see Teaching notes). Switch mains on again. Connect the two lamps in series by depressing the two black buttons on the sides of the unit, simultaneously.

Teaching Notes

  • In step 2, the current through the 12 V lamp will be about 0.4 A.
  • In step 4 , the mains lamp is connected directly to the mains (230 V in the UK) and should operate normally. It is useful at this stage to compare the two current readings. The current through the 100 W mains lamp will also be about 0.4 A.
  • In other words, the two lamps are each carrying approximately the same current. The question for students is why is the mains lamp brighter? Stress the fact that the current reading alone does not give enough information to enable the amount of radiation (infra-red and light) from a lamp to be predicted.
  • Before going on to step 5, get students to predict what would happen if the 230 V lamp and the 12 V were connected in series to the 230 V supply. Would anything happen? Would one or both of the lamps blow or explode? Involve as many students as possible in thinking about this before proceeding.
  • In step 5, when the two lamps are connected in series with the mains, both lamps operate normally. This will come as a great surprise to most students. (Just a few will notice that the mains lamp is fractionally dimmer than it was, and that the current is slightly reduced.)
  • Point out that the energy transferred (radiated) every second by the mains lamp is greater than the 12 V lamp, for the same current. The higher the voltage, the more energy is radiated by a lamp (for the same current).
  • Introduce the concept of potential difference V, as the energy E transferred by each unit of charge Q flowing through the circuit.
    • Potential difference (volts) = energy transferred (joules) / charge (coulombs)
    • V = E / Q
    • '1 volt' means 1 joule is transferred by each coulomb of charge.
  • Alternatively, you could point out that the rate of energy (power, P) transferred at the mains lamp is much greater than the rate of energy (power, P) transferred at the 12 V lamp, for the same current, I. The ratio of power to current at a transducer has a name: potential difference (voltage, V). In symbols,
    • V = P / I
    • This is the same as the ratio of energy E transferred per unit charge Q, or,
    • V = E / Q,
    • since V = P / I = (E/ t ) / (Q/ t ) = E / Q
    • The advantage of introducing potential difference in this way is that it makes sense of something puzzling but easily observed. By contrast, the energy transferred by each unit charge cannot be observed, and is not generally of interest.
    • You may want some students to note what this means about the rate of energy transferred: it is the product of current x voltage.
  • With intermediate and advanced students, you may want to go on and introduce the idea of a potential divider, i.e. resistances in series share out the voltage in proportion to their relative size.
    • Consider the resistance of the lamp filaments.
    • Resistance = Potential difference/Current, so the resistance of each filament can be calculated from the measurements taken.
    • Using a rough calculation (which may be a little out because of the characteristics of various lamps*), the resistance of the 100 W lamp is 529 ohms and that of the 5 W lamp is 28.8 ohms.
    • You might re-calculate the resistance from the relationship
    • Resistance = (potential difference)2/Power.
    • See the note from Electrosound (see below)
  • There are further questions you might ask at advanced level, related to the effect of temperature on resistance of a metal wire. Using a multimeter to read the resistance of the lamp shows that the resistance is lower than calculated previously. Why should this be? What effect would this have on the current flow? Why do mains lamps most often blow when they are first switched on, rather than when they have been on for some time?

Acknowledgement: with thanks to Phil Walsh at Electrosound for devising this apparatus and enabling a valuable experiment to get back into school use.

This experiment was safety-tested in March 2007

Resources

Download the support sheet / student worksheet for this practical.

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Lamps in parallel

Voltage/Potential Difference
Electricity and Magnetism

Lamps in parallel

Practical Activity for 14-16

Demonstration

The current flowing in a circuit increases as more lamps are added in parallel with each other.

Apparatus and Materials

  • Lamps (12 V 6 W) in holders, 4
  • Switches, single-pole, 4
  • Ammeter, 0 - 5 A (a demonstration one would be good for this)
  • Power supply, low-voltage

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Connect the ammeter and the four lamp holders with the switches to the low voltage supply.
  2. Note the current as first one, then two, then more, lamps are switched on.

Teaching Notes

  • Any energy that you transfer can be measured in joules. As long as a power supply maintains the electric current through the lamp, you continue to obtain a stream of energy which can be measured:
    • by catching the light radiation on light-sensitive paper
    • by warming up water
    • by measuring the energy delivered by a motor.
  • So you can find out how many joules of energy are being transferred per second from the power supply to some other component.
  • As more lamps are connected across the power supply, the amount of energy transferred by the lamps to the environment in joules/second increases. So does the current in coulombs per second, registered by the ammeter. The rate of energy transfer increases in proportion to the current drawn from the power supply.

This experiment was safety-tested in October 2006

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Use of a voltmeter

Voltage/Potential Difference
Electricity and Magnetism

Use of a voltmeter

Practical Activity for 14-16

Class practical

Experimenting with a voltmeter leads to a discussion of the meaning of potential difference or voltage.

Apparatus and Materials

  • Power supply, low-voltage
  • Lamp (12 V, 6 W) in holder
  • Ammeter, (0-1 A), DC
  • Voltmeter, (0-15 V), DC

Health & Safety and Technical Notes

Choose a low voltage power supply so that the meters are unlikely to be damaged, e.g. use 2 x 1.5 V cells.

Read our standard health & safety guidance


Procedure

  1. Connect up a simple series circuit using the battery, a lamp in its holder, and an ammeter.
  2. Now add the voltmeter to the circuit. Use it to measure the voltage across the lamp.

Teaching Notes

  • Allow students to decide for themselves how to connect the voltmeter. They should be allowed to connect the voltmeter in series in the circuit. They will soon discover that there appears to be no current left in the circuit. This is because the voltmeter has a very high resistance.
  • Putting the ammeter across the lamp could damage the ammeter. Make sure that it can withstand the shock if students do it accidentally! The reason for this is that the ammeter has an extremely low resistance, and so most of the current takes the easy route and avoids the lamp.
  • When considering how fast energy is transferred in an electric circuit, the output energy is directly proportional to charge, or current x time, or the number of coulombs that pass, measured by ammeter and clock.
  • However, charge cannot be the only factor. You also need a device that shows how many joules of energy are delivered by each coulomb going through the lamp. That device is called a voltmeter.
  • Just as a mass of one kilogram can transfer more energy if the cliff it falls off is 100 metres high than if it is only 10 metres high, so a coulomb of electricity delivers more energy if it falls through a potential difference of 100 volts than if it falls through a potential difference of 10 volts. Also, more obviously, more energy is transferred by several kilograms or coulombs than by one. Analogies of helter-skelters or loaves of bread on delivery vans may help to get the idea across.
  • An analogy for a voltmeter might be the following.
  • The flow of coulombs in a circuit can be likened to the flow of cars along a main road. Suppose that every driver arrives at point A on the road with the same amount of money in his pocket and has spent all of it at point B. To find out how much money that is, you need not hold up every car and examine the driver's finances. Instead you could arrange to divert just a few cars out to a lay-by at A and back onto the main road again at B. Somewhere along the lay-by install a hold-up gang who empty the pockets of each driver in the diverted stream. That is a model of a working voltmeter (actually a milliammeter in disguise).
  • The water circuit with its pressure gauge as a model for a voltmeter could also be used here. The pressure gauge is connected across the tubes to measure the pressure difference between the two sides.
  • Whatever explanation you give, end up by saying that the voltmeter measures the energy transferred to the lamp by each coulomb, as it passes through part of the circuit across which the voltmeter is connected.
  • The voltmeter is connected across the lamp so that it can measure the joules per coulomb transferred to the lamp. The ammeter measures how many coulombs per second pass through the lamp.
  • Hence the energy transferred to the lamp = potential difference (measured in volts) x charge (measured in coulombs).
  • Energy transferred = V x Q joules
  • = V x I x t joules
  • Energy transferred per second = power = V x I watts
  • where V volts is the potential difference across the lamp, Q coulombs is the charge flowing through the lamp, I amps is the current through the lamp and t seconds is the time for which the charge flows.
  • In discussing this experiment with students, continue to reinforce these new ideas at every opportunity:
  • 5 volts means 5 joules per coulomb: a volt is just shorthand for joules per coulomb which is itself an abbreviated form of joules of energy transferred from the energy supply to a component in a circuit for every coulomb passing through it. So 5 volts (joules per coulomb) carried by a current of 2 amps (coulombs per second) transfers 10 joules of energy per second or 10 watts of power.

This experiment was safety-tested in January 2007

Up next

The voltmeter as a cell (battery) counter

Voltage/Potential Difference
Electricity and Magnetism

The voltmeter as a cell

Practical Activity for 14-16

Class experiment

A voltmeter, by measuring the voltage across several 1.5 V cells in series, can count the cells.

Apparatus and Materials

For each student group:

  • Cells, 1.5 V, 3
  • Lamp with lamp holders, 3 (e.g. 1.25 V, 0.5 A)
  • Leads, 4 mm, 9
  • Voltmeter, 0 to 5 V, DC
  • Ammeter, 0 to 1 A, DC

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Set up a circuit with three cells and three lamps all in series, as in the diagram.
  2. Switch on the lamps.
  3. Attach two long, flexible leads to the voltmeter.
  4. Connect the voltmeter leads across one cell, then across two cells, then across three. Record the reading of the voltmeter each time.
    • How many cells are needed to light one lamp fully?
    • How many cells to light two lamps fully? Three lamps fully?
    • What does the voltmeter tell you? What does it count?
    • Is the voltmeter connected in series with the lamps or in parallel?
    • What does an ammeter count?
  5. Connect the voltmeter leads across one lamp, two lamps, and then three lamps.

Teaching Notes

  • Students connect the voltmeter across each cell, and so measure the energy per coulomb transferred by each cell to the circuit.
  • They then connect the voltmeter across all three cells, and show that the total potential difference across three cells is three times that across one cell. The potential differences add up, and so does the energy transferred per coulomb. The voltmeter is a cell counter.
  • In part 10, students connect the voltmeter across each of the lamps in turn, and then across all three lamps. This shows that the energy per coulomb transferred from the cells is equal to the energy per coulomb transferred from the lamps to the environment.
  • This is evidence for the conservation of energy.

This experiment was safety-tested in October 2006

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The water circuit: modelling current and potential difference

Voltage/Potential Difference
Electricity and Magnetism

The water circuit: modelling current and potential difference

Practical Activity for 14-16

Demonstration

Current can be modelled by the flow of water; potential difference corresponds to water pressure.

Apparatus and Materials

  • Water circuit board
  • Power supply, low voltage, variable (to match pump)
  • Fluorescein solution or methyl orange solution (see CLEAPSS Recipe Cards)
  • Pressure gauge
  • Small piece of cork

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Set up the water circuit board vertically. Connect the electric motor, which drives the water pump, to the terminals of the low voltage supply. (Ensure that the supply is matched to the pump: correct voltage, DC or AC.)
  2. Fill the tubes with water: a little fluorescein or a few drops of methyl orange can be added to make the water more clearly visible. The water is conveniently poured in at the funnel.
  3. The pump will drive water round the circuit of glass tubing attached to the board, the pressure being dependent on the voltage applied to the motor.
  4. At one point, the tube divides. The two sections represent different resistances: one tube has a much finer bore than the other.
  5. Clips enable one or other or both sections to be opened at once: thus the effect on the current of different resistances can be seen.
  6. Where there is a break in the circuit, the funnel catches the water flowing down from the tube above. The rate of flow of water is apparent and this indicates the current. Alternatively, if there is a pool of water in the funnel, the faster the flow of water the more rapid the swirling motion in the funnel. A small piece of cork floating on the water in the funnel acts as an indicator of the rate of swirling, which thus shows the current.
  7. In this demonstration, do not use the pressure gauge at first. Add it later. It consists of a U-tube connected as illustrated and filled with coloured water. This enables you to demonstrate the change in current with pressure (voltage).

Teaching Notes

  • The water circuit is a demonstration which can be referred to at many points in a course of elementary electricity teaching.

This experiment was safety-tested in January 2007

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Potential difference and e.m.f.

Electromotive Force
Electricity and Magnetism

Potential difference and EMF

Practical Activity for 14-16

Demonstration

Opening up discussion of the difference between potential difference (p.d.) and electromotive force (e.m.f.).

Apparatus and Materials

  • 12-volt battery or power supply
  • Lamps (12 V 6 W) in holders, 2
  • Ammeter, 0-1 A
  • Voltmeter, 0–15 V
  • Demonstration meters OPTIONAL

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Connect the battery, ammeter and lamps in series as shown. Arrange them in positions to match the circuit diagram.
  2. Support the voltmeter below the battery and connect it first across lamp 1, then across the ammeter, then across lamp 2, then across the three together (between P and Q). Note the potential difference in each case.
  3. Hold the voltmeter above the battery - a purely didactic move - and connect it across the battery. Ask for a new interpretation (EMF).
  4. With a very fast group it may be worth repeating this demonstration with a supply possessing internal resistance - e.g. a low-voltage d.c. supply with a 100 Ω. resistor in series hidden in a box.
  5. The voltmeter is connected to terminals on the outside of the box. More lamps can be added in parallel to increase the current and so reduce the terminal potential difference.

Teaching Notes

  • Encourage students to think, as follows:
  • "Potential differences are electrical pressure differences between the ends of some part of a circuit where energy is transferred to a lamp or other component. Voltmeters are devices to measure energy transfer for each coulomb passing through that part of the circuit."
  • When you apply the voltmeter across the battery, it is effectively the same as applying a voltmeter across the rest of the outside circuit. What happens if there is only the battery and no outside circuit? The voltmeter gives a reading and, if the voltmeter is a good one (very high resistance), then it may read slightly higher than when the battery is connected across a circuit. When the battery is disconnected from the circuit the voltmeter is reading the electrical potential difference between the ends of the battery. We call that the EMF of the battery. It is the 'uphill push'...
  • uphill push


    ...which the battery can give to a coulomb before it slides downhill in the rest of the circuit.
  • Some energy is needed to transfer the coulomb through the battery. This is measured as the difference between the EMF of the battery when no current is flowing, and the potential difference between the terminals of the battery when it is connected to a circuit and a charge is flowing. The bigger the internal resistance then the bigger the energy loss, or dissipated, in the battery.
  • Part 4 is an extension to the experiment. Use a battery with artificially increased internal resistance concealed in a box. Add more and more lamps in parallel, and note the potential difference between the terminals. As the current increases through the cell, the terminal potential difference (PD) falls.
  • Car batteries have a very low internal resistance and so high currents can be taken from them. However, when you start a car with the lights switched on, then the lights dim. This is because the starter motor takes a current of more than 100 amps, and so the amount of potential difference needed to produce this current through the battery is high. The potential difference between the terminals of the 12 V battery drops to as low as 4 V and so the lights are dim. Power supplies, especially school ones, have a high internal resistance and as more and more current is taken from the power supply then the potential difference at the terminals drops. This is why it is wise to monitor the terminal potential difference (PD) with a voltmeter even though there is a scale marked on the power supply.
  • There are many terms used in energy discussions in electricity, and they all have historical roots.
    • Cavendish, Watson: the idea of an electrical pressure
    • Volta: electric tension, electromotive force (EMF) used now in LT, HT, and EHT supplies
    • Poisson, Green: electric potential
    • Lagrange, Gauss: potential energy
  • The definition of the volt now comes from the Josephson junction. When there is a steady direct current and a sinusoidal alternating current of frequency, f, then the average potential difference = nhf/2e across the junction.

This experiment was safety-tested in January 2007

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From galvanometer to voltmeter

Voltage/Potential Difference
Electricity and Magnetism

From galvanometer to voltmeter

Practical Activity for 14-16

Class Practical

Adding a multiplier in series with a galvanometer converts it to a voltmeter with a higher range.

Apparatus and Materials

For each student group

  • Galvanometer
  • Voltmeter, 0 to 5 V, DC
  • Cells, 1.5 V in holder, 4
  • Selection of high-value resistors, see technical note

Health & Safety and Technical Notes

Read our standard health & safety guidance


You will need to select suitable resistors according to the resistance and full-scale-deflection (f.s.d.) of your galvanometers. If the galvanometer has f.s.d. 1 mV and resistance 10 Ω., and you want to increase this to f.s.d. 10 V, you will have to provide 100 kΩ. resistors.

Procedure

  1. The ordinary commercial voltmeter that you use in the laboratory is really a trickle meter. It measures the tiny trickle of current which the potential difference drives through a high resistance inside the voltmeter's case.
  2. To convert your galvanometer to a voltmeter reading, say, 5 V when the pointer is at the end of the scale, you must add a large resistance in series, as in the diagram. The galvanometer itself has only a small resistance, perhaps 10 Ω., and it gives a full scale reading when the voltage across it is 1 mV. So the p.d. across the extra resistance must be 4.999 V.
  3. You can discover the right resistance to add by trying it out. Choose the largest high resistance you are offered. Connect it in series with the galvanometer and connect to a 1.5 V cell, just for an instant. Does your voltmeter read 1.5 V, as you wished? If it reads more, you do not have enough resistance in it: add more resistance. If it reads too little, try less resistance in it.
  4. When you have adjusted the resistance, try your voltmeter on two 1.5 V cells in series. Also test those with a commercial voltmeter to make sure yours now reads as you wish.
  5. Convert your voltmeter to one with twice that range, 0-10 V; and try that on a 6 V battery.

Teaching Notes

  • A voltmeter is always connected across the component whose potential difference is to be measured. It therefore taps off a trickle of charge from the main circuit. The higher the resistance of the voltmeter and its multiplier, the less the circuit is disturbed by this measurement. The resistance of the multiplier has to be high enough so that only a small current passes through the galvanometer.
  • Students can either calculate the resistance needed or do it by trial and error, beginning with the largest resistance possible in series with the galvanometer.
  • The commercial voltmeter enables students to adjust their home-made one to read as they wish, by trial instead of by calculation.
  • NB. Digital voltmeters work quite differently.

This experiment was safety-tested in October 2006

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Internal resistance of a potato cell

Internal Resistance
Electricity and Magnetism

Internal resistance of a potato cell

for 14-16

Class practical

An introduction to the concept of internal resistance, using a more interesting example than a battery.

Apparatus and Materials

For each student group

  • Digital multimeters, 2
  • Leads, 4 mm, 5
  • Cells, 1.5 V type C, 4
  • Resistors of a range of values from 10 ohms to 100 ohms
  • Crocodile clips, 10 pairs

Health & Safety and Technical Notes

Biology teachers should note the potato cell in this experiment refers to a whole potato not an individual potato cell.

Read our standard health & safety guidance


Procedure

  1. Make your potato cell. Insert the copper and zinc electrodes at either end of the potato. Attach a 4 mm lead to each electrode using a crocodile clip.
  2. Set up the circuit as shown. Set the resistance substitution box to 4.7 kΩ.. This is the load resistance. Record the current and potential difference values in a suitable table.
  3. Change the load resistance and record the values of current and potential difference. Repeat this process to gather data for a range of load resistances. You will have to change the range of your ammeter. Take care not to confuse amps with milliamps or microamps!
  4. Plot a graph of V against I. Describe the trend.

Teaching Notes

  • This experiment can be used for a number of purposes – as an introduction to the concept of internal resistance, an interesting example of internal resistance or an example of a simple cell. If standard resistors are available it is possible to vary the load resistance in smaller steps.
  • The VI graph line will surprise students who have not been introduced to the concept of internal resistance. Those students familiar with the equation V=εIr should be able to interpret the data in terms of the internal resistance of the potato cell. However, many students find internal resistance a difficult concept and may find the Internal resistance of a shoe box cell experiment a useful support activity...
  • Internal resistance of a shoe box cell


  • If readings are entered into a spreadsheet it is easy for interested students to plot further graphs, including load resistance/power dissipated in resistor. Such a graph will show a peak power output when the load resistance is equal to the internal resistance of the cell.

This experiment comes from AS/A2 Advancing Physics. It has been re-written for this website by Lawrence Herklots, King Edward VI School, Southampton. This experiment was safety-tested in June 2007

Up next

Internal resistance of a shoe box cell

Internal Resistance
Electricity and Magnetism

Internal resistance of a shoe box cell

Practical Activity for 14-16

Class practical

Finding an internal resistance of a supply from the power dissipated by a load resistance.

Apparatus and Materials

For each student group

  • Digital multimeters, 2
  • Leads, 4 mm, 5
  • Cells, 1.5 V type C, 4
  • Resistors of a range of values from 10 ohms to 100 ohms
  • Crocodile clips, 10 pairs

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. The shoe box cell contains a 6 V supply with an unknown resistor in series. The unknown resistor acts as the internal resistance in the shoe box cell. Your challenge is to find the value of the internal resistance without opening the box!
  2. Choose a value for the load resistance R and set up the circuit as shown. Record the current and potential difference values. E is the e.m.f. of the equivalent perfect cell of internal resistance r.
  3. Change the load resistance and once again record the values of current and potential difference values.
  4. Repeat this process for about ten values of load resistance.

Analysis

  1. Calculate the power dissipated by the load resistance by using the equation P=IV.
  2. Plot a graph of power dissipated against load resistance.
  3. The power dissipated by the load resistance is a maximum value when it equals the ‘internal resistance’ of the shoe box cell. Use this fact to estimate the resistance in the box.
  4. The cells in the box have a total internal resistance of about 4 ohms. How does this fact change your answer?

Teaching Notes

  • The resistance in the box needs to be about 50 ohms if a clear peak is to be found when the load resistance varies between about 10 ohms and 100 ohms. This will give a minimum current of about 40 mA. using 4 x 1.5 V cells.
  • Resistors can be labelled and clipped together to give a good range of total resistance values.
  • Students familiar with V=εIr should be able to interpret the data in terms of the internal resistance of the shoe box cell. This experiment can also be interpreted as an example of a potential divider. The internal and external resistances are in series, so the e.m.f. is divided between them.
  • Some students will be able to complete the analysis more quickly using a spreadsheet.
  • This experiment submitted by Lawrence Herklots, King Edward VI School, Southampton.

This experiment was safety-tested in April 2006

Up next

Hill diagram as a model for potential difference

Voltage
Electricity and Magnetism

Hill diagram as a model for potential difference

Teaching Guidance for 14-16

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

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

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

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

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

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

Up next

Models of electric circuits

Electrical Circuit
Electricity and Magnetism

Models of electric circuits

Teaching Guidance for 14-16

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

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

Misconceptions common among students

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

Teachers' models

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

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

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

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

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

Bring out the analogy between:

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

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

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

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

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

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

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

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

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Quantitative ideas in electricity

Electrical Circuit
Electricity and Magnetism

Quantitative ideas in electricity

Teaching Guidance for 14-16

Introductory level ideas

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

Intermediate level ideas

Defining current

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

Defining Potential difference

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

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

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

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

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

Advanced level ideas

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

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

Developing electrical knowledge – from introductory to advanced level

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

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

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

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