Ohm's Law
Earth and Space

Ohm's law and resistance

for 14-16

By looking at a number of examples of non-ohmic behaviour, students can learn to distinguish between the definition of resistance (R = V/I) and Ohm's Law (R is independent of I, V).

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Ohm's law without a voltmeter

Ohm's Law
Electricity and Magnetism

Ohm's law without a voltmeter

Practical Activity for 14-16

Demonstration

An approach to Ohm's law in a quick demonstration.

Apparatus and Materials

  • 1.5-volt cells, new stock, 7 (see technical note)
  • Cell holders, 7
  • 50 Ω. resistor, approx value (see technical note)
  • Ammeter (0-1 amp), DC, preferably moving-coil
  • Leads, 4 mm, 6

Health & Safety and Technical Notes

Test the cells beforehand to make sure they are all approximately equal: since students will need assurance of that. Either connect each in turn to a resistance of about 3 ohms and try a voltmeter across it, or arrange all the cells in series with about 50 ohms and try a voltmeter across each cell in turn. Replace any cell that fails to agree with the rest.

The resistor might be a rheostat, or two rheostats connected in series. The aim is to keep the current low.

Read our standard health & safety guidance


Procedure

  1. Set up the circuit shown. In the course of the experiment, restrict the time for which the current flows to a minimum.
  2. Explain to students that we expect a coulomb to make the same energy transfer in every cell. Then we use the effective number of cells as a measure of the energy transferred to each coulomb.
  3. Explain that all the cells will remain in the circuit, to maintain constant resistance.
  4. Record the ammeter reading with all 7 cells facing the same way.
  5. Reverse one cell, and read the ammeter for what is now a 5-cell transfer.
  6. Continue to reverse one more cell at a time until all 7 are reversed.
  7. Plot a graph, which serves as an introduction to Ohm's law.

Teaching Notes

  • Is there a problem of logic in using moving-coil meters in experiments to test Ohm's law? A moving coil voltmeter is made from a high resistance which obeys Ohm's law, and a milliammeter to measure the current through that resistance. The meter's dial is then labelled in volts. So Ohm's law is implicit in the instruments. In this case, that effect is reduced by assuming that each cell provides a standard unit of voltage.
  • The electromotive force is provided by seven 1.5-volt cells all in series, all kept in the circuit throughout to maintain constant resistance. But the effective e.m.f. is varied by reversing 1 cell, 2, 3, ... all the cells - thus obtaining 8 points on a graph. Assuming that each cell transfers the same amount of energy for each coulomb, the algebraic total of cells is used as an ideal voltmeter reading! Students plot that against the ammeter reading with a fixed resistance in the circuit.
  • When one of the cells is reversed, each coulomb receives the usual share of energy from six of the cells. But in the reversed cell it has to pay one share back. (This assumes that the action of the cell can be reversed like that; not exactly true but quite close to true if the current is not driven backwards for much of the time.)
  • Once the experiment has been carried out with only the ammeter in the circuit, ask students what instrument they could use instead of counting the cells. They should know that a voltmeter is a cell counter. A voltmeter is then added to the circuit, arranging it to act as a cell counter which keeps track of what is happening in the resistance alone. When cells are reversed, the voltmeter keeps track of the algebraic number of cells in the circuit. This experiment shows the essential behaviour described by Ohm's law.

This experiment was safety-tested in October 2006

Up next

Ohm's law

Ohm's Law
Electricity and Magnetism

Ohm's law

Practical Activity for 14-16

Class practical

This experiment looks at the relationship between current and potential difference (p.d.) for a length of resistance wire.

Apparatus and Materials

  • Ammeter (1 amp), DC
  • Voltmeter (5 volt), DC
  • Eureka wire (34 SWG), 10-cm length
  • Power supply, low voltage, DC
  • Leads, 4 mm, 6
  • Crocodile clips, 2
  • Rheostat (10 ohms, at least 1A)

Health & Safety and Technical Notes

Low voltage power supplies are not continuously variable. Many have nominal voltages of 1, 2, 4, 6 etc. In this case the current could be 1, 2, 4, 6 A since 10 cm of SWG 34 Eureka is about 1 Ω..

Read our standard health & safety guidance


Procedure

  1. Set up the circuit shown. The length of Eureka wire acts as the resistance in the circuit.
  2. By adjusting the power supply, you can vary the p.d. across the Eureka wire. The ammeter will show corresponding values of the current through the wire. Keep the current small so that the temperature of the wire does not increase. (Adjust the rheostat at the beginning and then keep it constant.) Record a series of values of p.d. and current.
  3. Calculate the ratio p.d./current for each pair of values. Comment on the result.
  4. Draw a graph to represent the same data. From the graph, deduce a value for the ratio p.d./current.

Teaching Notes

  • Students should collect pairs of results for the potential difference across the wire, and current through the wire.
  • A graph is then plotted of current against potential difference. It is a matter of taste whether current is plotted on the y-axis or the x-axis. It normally depends on what the experimenter is trying to find out.
  • The independent variable is normally the potential difference and so it could be plotted along the x-axis. The resultant current, the dependent variable, would be plotted on the y-axis. This would show how the current varies with potential difference. However, the ratio p.d./current is important to us, and so the axes would have to be reversed if the ratio were needed from the slope of the graph.
  • Students should also calculate the ratio p.d./current for all pairs of results. (This is best done in a table.) It will be found that the ratio is constant, and this is defined to be the resistance of whatever we have connected the voltmeter across. The unit of resistance, one volt per amp, is known as the ohm.
  • The straight line graph through the origin indicates that the current is proportional to the potential difference driving it. It is this proportionality which is Ohm's law.
  • V/I = R is a definition of resistance and is NOT Ohm's law. Only if the resistance is constant as the potential difference increases is the material said to be Ohmic.
  • Ohmic materials play only a small part in our lives. Electronic materials such as those based on semiconductors play an increasing role and are non-ohmic: they do not obey Ohm's Law. Ohm's Law assumed a position of great importance in the nineteenth century when telegraph lines were designed and electrical engineering was developing.
  • How Science Works extension:
  • This experiment provides an excellent opportunity to focus on the range and number of results, as well as the analysis of them. Typically it yields an accurate set. The rheostat enables students to select their own range of results. You may want to encourage them to initially take maximum and minimum readings with the equipment and then select their range and justify it.
  • If they don't think of it themselves, suggest that students take pairs of current and voltage readings as they increase the voltage from 0 V to the maximum. They then repeat these readings while reducing the voltage from the maximum to 0 V. This may help them to identify whether the resistance of the resistor remains constant when it is heated. (Turning the equipment off immediately after readings are taken and allowing the resistor to cool provides an alternative to this procedure but will considerably lengthen the time needed for the experiment. It is also possible to put the resistor into a beaker of water to maintain the resistor at a constant temperature.) Students could also change the direction of the current and repeat the other procedures.
  • You can use the fact that resistors are sold with a specified tolerance (and thus a variation in value) as the basis for a discussion about what a true value really means in this case. Compare calculated resistance values with the manufacturer's stated value or value range. Students can also be encouraged to identify the sources and nature of errors and uncertainties in the experimental method.

This experiment was safety-tested in January 2007

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Measuring resistance with a voltmeter and an ammeter

Ohm's Law
Electricity and Magnetism

Measuring resistance with a voltmeter and an ammeter

Practical Activity for 14-16

Class praticals

Determining resistance from measurements of potential difference (p.d.) and current.

Apparatus and Materials

  • Ammeter, 0 to 1 A, DC
  • Voltmeter, (0-15 V), DC
  • Power supply, low voltage, DC
  • Lamp (12 V, 6 W) in holder
  • Resistor (approx 15 ohms, 10 watt)
  • Various other components

Health & Safety and Technical Notes

Read our standard health & safety guidance


Remind the class that the lamp will get hot, so it should only be moved by handling the lamp holder.

Procedure

  1. Set up the circuit shown. Turn the power supply up until the p.d. across the lamp is 12 V (the normal operating voltage).
  2. Take readings of the p.d. and current.
  3. Calculate the resistance of the lamp at its running temperature.
  4. Now, for several different values of p.d., measure the current through the lamp. Plot a graph of your results; this graph is known as the voltage-current characteristic of the lamp.
  5. Replace the lamp in the circuit with the resistor. Repeat the experiment and calculate its resistance. Take sufficient readings to allow you to plot the voltage-current characteristic.

Teaching Notes

  • This series of experiments should give students practice in taking a pair of current and potential difference readings for various components so that the resistance of the component can be calculated from V/I = R.
  • It can also be extended so that students plot the current/potential difference characteristics for components such as a carbon resistor, a diode, a light-emitting diode (LED), a thermistor, motor armature, electric fire element (12 V supply only!) and so on. Students will need to be able to select appropriate meters, as the current through some of these devices may be very small. Each member of the class could tackle one component and present their results to the class, or produce a wall display.
  • Some things which appear not to obey Ohm's law might, in fact, do so; for example, the tungsten filament of a lamp. Tungsten's resistance increases as the lamp gets hotter, but if it could be maintained at a constant temperature then its resistance would be constant.
  • For suggested graphs, see below

This experiment was safety-tested in January 2007

Resources

Download the support sheet / student worksheet for this practical.

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Relationship between volts and amps for electrolytes

Ohm's Law
Electricity and Magnetism

Relationship between volts and amps for electrolytes

Practical Activity for 14-16

Demonstration

Solutions may show ohmic or non-ohmic characteristics.

Apparatus and Materials

  • Power supply, low voltage, DC
  • Ammeter, 1 A
  • Voltmeter, 10 V
  • Gas voltameter (see technical note)
  • Copper voltameter (see technical note)

Health & Safety and Technical Notes

Saturated copper sulfate solution is harmful. Wear eye protection and keep it off the skin. Eye protection is also needed for the electrolysis of water, since the bursting gas bubbles may spray into eyes.

Read our standard health & safety guidance


A typical copper voltameter consists of two clean copper electrodes held to the sides of a rectangular glass jar by bulldog clips, and each fitted with a soldered terminal. This arrangement facilitates easy replacement in the same place. Copper sulfate solution is used as the electrolyte (saturated, with 5% IM sulfuric acid added).

The gas voltameter referred to is equipment for the electrolysis of acidified water. At its simplest it need only be a beaker of water with a little sulfuric acid in it and carbon rod electrodes. A little acid is added to provide plenty of hydrogen ions, but it is the water which is used up and produces the gases; the original acid remains. (NB Oxygen attacks the carbon electrode, giving CO2 and loose carbon granules.)

Procedure

  1. Connect the copper voltameter into a simple series circuit as shown. Alter the power supply to give voltages across the voltameter of 2 V, 4 V.... up to 10 V, and record pairs of readings, p.d. and current. Plot a graph of potential difference (y axis) against current (x axis).
  2. Repeat this procedure using the gas voltameter.

Teaching Notes

  • The graph of potential difference against current for the electrolysis of copper sulfate solution with copper electrodes is a straight line almost through the origin. This shows that it is an ohmic material with constant resistance.
  • In blue copper sulfate solution, the current is carried by positively charged copper ions and negatively charged sulfate ions. The copper ions give the solution its blue colour. The copper ions drift slowly across to the negative electrode, and the positive ions drift slowly towards the positive electrode. Although the ions drift slowly, the current starts as soon as the battery is connected. This is because the whole liquid is full of a dense population of ions which start drifting immediately.
  • The graph of potential difference against current for water electrolysis (part b) will show a straight line, but it does not go through the origin. It needs a small potential difference before it will begin to conduct. This suggests the existence of a back e.m.f.
  • When the potential difference applied to the cell is small, some of the hydrogen bubbles produced at the cathode by electrolysis adhere to and soon coat this electrode. Likewise, oxygen bubbles adhere to and soon coat the anode. This process is known as polarization. The electrodes then behave as if they are made of hydrogen and oxygen, reversing the current in the cell and so giving a back e.m.f.
  • When a larger external potential difference applied to the cell, it supplies or removes electrons from the electrodes at a sufficient rate to overcome this effect.

This experiment was safety-tested in January 2007

Up next

Voltage/current relationship for a gas

Ohm's Law
Electricity and Magnetism

Voltage/current relationship for a gas

Practical Activity for 14-16

Demonstration

Gases conduct electricity, but they have to be ionised first.

Apparatus and Materials

  • Neon indicator lamp (230 V, 10 mm MES type with integrated resistor)
  • Power supply, HT, 0-300 V, (current limited to less than 5 mA.)
  • Voltmeter, 300 V, DC
  • Ammeter, 5 mA., DC
  • Leads, 4 mm, 5

Health & Safety and Technical Notes

This must be a teacher demonstration because an HT supply is being used. The lamp holder must be in an insulating box.

Read our standard health & safety guidance


To prevent excessive currents, the neon lamp should be provided with a ballast resistor (of about 2,000 Ω.) in the base.

Leads with shrouded plugs (sprung or fixed) are advantageous but not essential here.

Procedure

  1. Set up a series circuit consisting of the power supply, the neon lamp, and the 5 mA. meter. Connect the voltmeter across the lamp and 100 mA. meter.
  2. Apply increasing voltages from 0 to 200 V, recording both the current and the voltage at each stage.

Teaching Notes

  • Take a set of potential difference and current measurements, and draw the characteristic graph (p.d. against current). The graph is a straight line once the current gets going, but it takes a potential difference of more than 60 V to get it started.
  • The conduction of gases is complicated, but on a simple level the gas has to be ionised and so energy is need to do this. Once the ions are formed, they can drift to the electrodes in the same way as in liquids. As the potential difference is raised, a glow will start abruptly and then continue as the potential difference increases.
  • The striking potential, for a neon lamp is about 60 V. The glow will be extinguished when the voltage applied is reduced to about 50 V.

This experiment was safety-tested in January 2007

Up next

A transistor as a current amplifier

Ohm's Law
Electricity and Magnetism

A transistor as a current amplifier

Practical Activity for 14-16

Class practical

A minute current in the base-emitter circuit is used to control a much larger current in the collector-emitter circuit.

Apparatus and Materials

For each student group

  • NPN transistor (mounted if possible)
  • Ammeters, 0-100 mA., 2 (depending on the transistor)
  • Cell, 1.5 V in holder
  • Cells, 1.5 V in holder, 4 (or stabilized low voltage DC supply)
  • Rheostat
  • Resistor (680 ohms, 1 W)
  • Lamp in holder, 6 V 60 mA.
  • Leads, 4 mm, 10
  • Crocodile clips, 3 (if necessary)

Health & Safety and Technical Notes

It will help if the transistor is mounted on a base with three 4 mm terminals. Otherwise, make connections to it using crocodile clips.

Read our standard health & safety guidance


Procedure

  1. In the transistor, a minute current in the base-emitter circuit is used to control a much larger current in the collector-emitter circuit. Arrange the components of the circuit as in the diagram, and connect them as follows.
  2. Connect the rheostat to form a voltage-divider across the 1.5 V cell.
  3. Connect the slider terminal to the fixed resistance of 680 Ω., one ammeter (range
  4. 100 mA.) and the base terminal of the transistor.
  5. Connect one end of the voltage-divider to the emitter terminal of the transistor.
  6. Connect the collector terminal of the transistor to the other milliammeter (range 100 mA.), the small lamp and the 6-volt battery and back to the emitter (which is already connected to the voltage-divider).
  7. Now try the following experiments:
  8. Firstly, leave the base circuit open, with no connection to the base. You will see no detectable current in the collector circuit.
  9. Join up the base circuit. The voltage for a suitable base current is less than 1 volt. Start with no voltage from your voltage-divider, and increase the voltage until the lamp in the collector circuit glows.
  10. Read the milliammeter in that circuit.
  11. Look at the other milliammeter, in the base-emitter circuit. Is any current flowing to the base? If there seems to be no current, try switching the supply on and off, and see whether the milliammeter's pointer moves at all.
  12. Your transistor is amplifying current. Comparing the two milliammeter readings gives you an idea of the amplification.
  13. Increase the base current a little, causing an increase in collector current. The ratio of the two currents will remain approximately constant.
  14. The collector current will level off at about 60 milliamps, which is the limit imposed by the lamp in the circuit. Any further increase in the base current will have no further effect.

Teaching Notes

  • Students may not have experimented with transistors previously. You could describe a transistor to them like this:
  • A transistor is a tiny chip of semi-conductor materials. It is rather like a sandwich of a piece of cheese between two slices of bread.
    • The transistor's emitter corresponds to a thin slice of bread
    • The transistor's base corresponds to the cheese
    • The transistor's collector corresponds to a thick slice of bread.
  • The transistor needs a small voltage to cause a base current to flow: less than 1 volt. That is easily obtained from a voltage-divider (potentiometer) across a cell. -You may need to ensure that students are familiar with the use of a three-terminal variable resistor for tapping off a voltage in this way.
  • Students should plot a graph of collector current against base current. This is one of several possible characteristic graphs for a transistor.
  • The experiment could be extended with the addition of voltmeters. Students could then look at, for example, how the base current and collector current depend on the input voltage Vinput.

This experiment was safety-tested in October 2006

Up next

Crossed wires - electrical fault-finding

Electrical Resistance
Electricity and Magnetism

Crossed wires - electrical fault-finding

Practical Activity for 14-16

Class practical

A problem-solving activity, using the concept of resistance in the context of a concert sound system.

Apparatus and Materials

For each student group

  • Fault-finding board (see technical note)
  • Ammeter, 0-1 A
  • Voltmeter, 0–10 V
  • Power supply, low voltage, DC
  • Leads, 4 mm, 5

Health & Safety and Technical Notes

Read our standard health & safety guidance


The fault-finding board simulates a short-circuit in the lead (a pair of wires) from the amplifier to a remote loudspeaker.

A board about 60 cm long and 10 cm wide carries, on one side, two 45 cm lengths of resistance wire (e.g. Eureka, SWG 34). The resistance of each wire should not be less than 3 Ω.

Each of the wires terminates in terminals, providing electrical access from the other side of the board.

Two-thirds of the way along the wires, a soldered link is provided. (You could make a number of boards with wires of different resistances, crossing at different points.) Since Eureka wire is difficult to solder, it may be helpful to twist the wires together first.

The wires have a resistance of about 3 Ω. (end to end) and the fault is so placed that, provided the voltage is less than 2, the maximum current is 1 amp.

Label the ends of the boards ‘stage’, ‘speaker 1’ etc. This will also make it easy to refer to results for different boards.

Procedure

  1. Using an ammeter and voltmeter, measure the resistance of the wires from each of the two ends, and hence, determine the position of the fault.

Teaching Notes

  • The ‘fault-finding board’ has two wires representing long wires connecting the amplifier in a sound system to remote loudspeakers. Unfortunately, they have touched at some point along their path. The students' task is to make suitable measurements which will allow them to deduce the point at which they have crossed.
  • This is a problem-solving activity using ammeters and voltmeters and an understanding of resistance. Students can make measurements of resistance at the stage end and at the loudspeaker end, and from the relative values infer how far away the fault is.
  • Some may ask about the obviously more likely and more difficult problem, which is an open break in one of the wires. This kind of break is much harder to locate, but it can be done with capacitance measurements.

This experiment was safety-tested in October 2006

Up next

Temperature change and resistance

Temperature Dependence of Resistance
Electricity and Magnetism

Temperature change and resistance

Practical Activity for 14-16

Class practical

Investigating the changing resistance of a wire as it heats up.

Apparatus and Materials

  • Power supply, low voltage, DC e.g. 12 V, 4 A at least
  • Rheostat (10 - 20 ohms) rated at 5 A at least
  • Aluminium container (e.g. disposable food container)
  • Ammeter, 0 to 5 A, DC
  • Voltmeter, 0 to 10 V, DC
  • Leads, 4 mm, 6
  • Crocodile clips, 2
  • Coil of copper wire (see technical note)

Health & Safety and Technical Notes

The polyurethane-coated wire may release hazardous fumes if overheated. The laboratory windows should be opened to reduce the risk.

Read our standard health & safety guidance


The coil should be loosely wound from 1 m of polyurethane-coated copper wire (30 or 33 SWG). Strip coating from the ends to allow electrical contact via crocodile clips.

Procedure

  1. Set up a simple series circuit with long leads to the loosely wound coil of copper wire.
  2. Adjust the power supply to give a current of about 4-5 amps in the coil. Switch the circuit off, as soon as possible.
  3. After a minute or so, the coil will have cooled to room temperature. Switch the circuit on again. Take readings of the ammeter and voltmeter several times during the next half-minute or so. During this time the coil heats up and the current changes quite rapidly.
  4. Repeat the experiment with the coil of copper wire suspended in water in the container. The water should be kept very well stirred. Take care to avoid short-circuiting the coil by using a wooden lolly stick or spatula as the stirrer.

Teaching Notes

  • Students record pairs of current and potential difference readings with the coil in air, and then plot the current/potential difference characteristic. This is not a straight line showing constant resistance, but rather a curve showing that the resistance of the wire increases with temperature.
  • When the experiment is repeated with the coil in a water bath so that its temperature remains constant, the characteristic graph is a straight line, showing that the resistance remains constant. Pure metals do obey Ohm's law when their temperature remains constant. Wires made from alloys such as Constantan or Eureka wire (consisting of 60% copper and 40% nickel} are designed to have a very small temperature coefficient of resistivity. Therefore, they do not need to be placed in a constant temperature bath in order to show ohmic behaviour.
  • How Science Works Extension:
  • This experiment can be used to teach about the idea of validity of scientific results. Results may be rendered invalid if an uncontrolled factor affects the results. In this case, the temperature of the wire is a factor which affects measurements of its resistance.
  • Discuss how this can be taken account of. One approach is (as discussed above) to keep the wire at a constant temperature by immersing it in a water bath. An alternative would be to use the p.d./current graph above to find the wire’s resistance when no current flows through it, because then there is no heating effect. Explain that the resistance of the wire is equal to p.d. divided by current; i.e. it is the gradient of the line from the origin to the point on the graph. Place a ruler on the graph, through the origin, and passing through the highest point on the graph. The ruler has a large gradient. Move down the graph, from point to point, showing that the gradient decreases. Close to the origin, the graph is almost straight (or you can use the idea of the tangent to the graph). In this way, you can determine the resistance of the wire when it is not heated by the current.
  • This experiment can be extended to include an investigation of the effect of temperature on resistance, between 0°C and 100°C, using a water bath. If students are familiar with the experimental observation of Charles’ law, you could ask them to extrapolate their graph of resistance against temperature to find the approximate temperature at which the wire’s resistance would be zero. For a pure metal, resistance decreases approximately linearly towards a temperature close to 0 K. (The temperature coefficient of resistance of many pure metals is close to 0.004 K-1, so the resistance/temperature graph will extrapolate back to 1/0.004 = 250 K.) You could link this to the idea that the resistance of a pure metal at room temperature is dominated by the vibration of ions, and this will reduce to zero close to 0 K.

This experiment was safety-tested in October 2006

Up next

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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