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## Electrical resistance

Lesson for 16-19

The central idea is that of electrical resistance - what it is, how it can be measured, how it arises and what affects it. We begin by relating resistance to current and voltage through the electrical characteristics of various components (at the same time providing more practice in setting up electrical circuits and using ammeters and voltmeters). This will naturally introduce some of the key factors affecting resistance - choice of material, temperature, light intensity...

Next we investigate the temperature dependence of the resistance of metals and semiconductors and (where relevant) discuss the phenomenon of superconductivity and its applications. An investigation of the dependence of resistance on type of material and dimensions leads to resistivity. The electrical behaviour of different types of material can then be linked back to their microscopic structure.

## Episode 107: Preparation for resistance topic

Teaching Guidance for 16-19

- Level Advanced

Most multimeters can function as ohm meters, for measuring resistance directly. They apply a small voltage to the component being tested and then measure the current it draws. Ohm meters must only be connected directly across the components they are measuring, which must be removed from any other circuits.

You will have to teach your students how to use micrometer screw gauges to measure diameters of thin wires. This can also form the basis of a useful lesson in handling errors in measurements.

Check with your technician or other support staff that you have enough suitable diodes and thermistors, and check also the supplies of bare constantan and nichrome wire. You may also wish to check the availability of conducting paper or conducting putty for the experiments on resistivity, but you can use more conventional wire if they are not available.

Find a table of values of the electrical resistivity of materials (conductors and insulators). This property covers a greater range of values than any other material property.

## Main aims of this topic

Students will:

- measure the
*I*-*V*characteristics of metals, carbon resistors, semiconductor diodes and filament lamps - define resistance
- use an ohm meter
- state and use Ohm’s law
- describe and explain the effect of temperature on the resistance of a metal and of a thermistor
- describe and explain the effect of light on an LDR
- investigate the dependence of resistance on length and cross-sectional area using resistive putty and resistive paper
- make measurements of resistivity
- perform calculations involving resistivity

## Prior knowledge

Students should have previously encountered the equation
*R* = *V**I*
, which defines resistance. They should also be familiar with the idea that metals contain free electrons, which is why they conduct well (both electricity and energy).

## Where this leads

Students will have extended their understanding of the microscopic nature of electrical current in solid materials. This will help later in understanding the internal resistance of cells and power supplies, as well as other currents such as electron beams.

### Up next

### Resistance

## Episode 108: Resistance

Lesson for 16-19

- Activity time 85 minutes
- Level Advanced

The idea of resistance should be familiar (although perhaps not secure) from pre-16 science course, so there is no point pretending that this is an entirely new concept. A better approach is to draw out what they know. The aim of this first episode is to provide a quantitative definition for resistance (*R* = *V**I*) which reinforces the qualitative notion that more resistance means less current. In addition, we will look at Ohm’s law, which is not the same thing as the definition of resistance.

Lesson Summary

- Demonstration: The meaning of resistance (10 minutes)
- Discussion: Defining resistance (10 minutes)
- Worked Example: Calculating resistance (5 minutes)
- Student Questions: Simple calculations (10 minutes)
- Student Experiment: Characteristics of metal wire (40 minutes)
- Discussion: Ohm’s law. (10 minutes)

## Demonstration: The meaning of resistance

Illustrate the idea of resistance with a quick demonstration. It should be clear from the demonstration that, as more resistors are added (in series) the current (and brightness of the lamp) fall whilst the voltage (electrical push) remains constant. Lead them to the idea that resistance determines the number of volts per amp

needed to maintain the current.

Episode 108-1: Increasing resistance decreases current (Word, 27 KB)

## Discussion: Defining resistance

Now define resistance: *R* = *V**I* pointing out that this is the ratio of the pd across a component to the current flowing through it (i.e. literally volts per amp

). Define the ohm ( Ω ) (again point out that 1 ohm is 1 volt per amp).

1 Ω = 1 V A^{-1}

Point out that kilo-ohms (k Ω ) and mega-ohms (M Ω ) are commonly used:

1 k Ω is 1000 Ω ; 1 M Ω is 1000 k Ω , so 1 000 000 Ω .

## Worked examples: Calculating resistance

Calculate the resistance of a lamp when a pd of 10 V makes a current of 2 mA flow through it. (This will give practice in handling powers of 10.)

*R* = *V**I*

*R* = 10 V2 × 10^{-3} A

*R* = 5000 Ω , or
*R* = 5 k Ω .

## Student questions: Simple calculations

With weak groups it may be worth spending a few minutes letting them calculate resistances from *R* = *V**I* when currents are given in amps, milli-amps and micro-amps. This will save errors later when they measure their own currents and use the results to calculate resistance.

Episode 108-2: Introductory questions on resistance (Word, 22 KB)

## Student experiment: Characteristics of metal wire

This episode concludes by measuring the voltage/current characteristic for a metal (constantan) wire. (This could be included with the other characteristics in the next episode but if it is done prior to those then Ohm’s Law can be used to interpret later results – leading to the ideas of ohmic and non-ohmic behaviour).

Episode 108-3: Electrical characteristics of a metal wire (Word, 63 KB)

## Discussion: Ohm’s law

Most electrical engineers identify the equation *V* = *I* × *R* with Ohm’s Law but this won’t do for post-16 examinations! Historically, Ohm showed that the resistance of a metal under constant physical conditions (particularly temperature) is constant. The experiment above should have demonstrated this by generating a straight line graph that passes through the origin: if *I*
is directly proportional to *V*
(or the other way around) then Ohm’s law is obeyed. Any conductor (metallic or otherwise) that behaves in this way is described as an ohmic conductor

.

It might well be worth spending some time reinforcing the meaning of directly proportional

and emphasising that the graphical characteristic is a straight line graph that passes through the origin.

Episode 108-4: Electrical characteristics of a resistor (Word, 25 KB)

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### Up next

### Electrical characteristics

## Episode 109: Electrical characteristics

Lesson for 16-19

- Activity time 120 minutes
- Level Advanced

In this episode, students measure the current and voltage characteristics for several components, and identify ohmic and non-ohmic behaviour.

Lesson Summary

- Student experiment: Further characteristics (40 minutes)
- Student experiment – alternative version: Further characteristics (40 minutes)
- Discussion: The results (10 minutes)
- Student questions: On characteristics (30 minutes)

## Student experiment: Further characteristics

Students determine the *V*-*I* characteristics for a carbon resistor, semiconductor diode and filament lamp.

This activity is best carried out individually (if space and apparatus allows this) so that each student has to construct and test his/her own circuit. One of the dangers of always working in pairs is that some students who lack confidence in circuit building will always avoid having to do it. This activity gives good practice in building testing and using a circuit designed to measure current and voltage.

They will need a reasonable amount of time to set up, check the circuit and begin to take readings. Make sure they all have correct circuits and that their meters are set to appropriate ranges (many take a long time to come to terms with multimeters). I would suggest about 40 min on the practical work itself. This should allow them all to collect data for all three components.

Some will work much faster than this so it may be worth having some additional activities available (e.g. the characteristic for thermistor).

Data collection can be handled in two ways: Simply record the data into a prepared table, or record directly into Excel or a similar spreadsheet package.

Episode 109-1: Electrical characteristics (Word, 59 KB)

## Student experiment – alternative version

If you have access to datalogging equipment, this is a good opportunity to get students to set up and record results automatically.

If a pc projector is available it is worth collecting one set of data to use at the end of the practical session (you could generate this yourself or else harvest a reliable set from one of the students/groups).

Episode 109-2: Electrical characteristics – datalogging alternative (Word, 31 KB)

## Discussion: The results

In either case it is useful to bring the class together at the end of the practical session (say, 15 minutes before the end of the lesson) to discuss results. If you have collected some sample data you can show them how to process this in real time using Excel and a PC projector. Use this to instruct them about trend lines (don’t join the dots and don’t let Excel take over!). For some or all it may be worthwhile to recommend plotting by hand.

This may be the first time they have plotted graphs in Physics that include points in more than one quadrant, so this can be illustrated and discussed. Use terms such as ohmic

and non-ohmic

and encourage them to do the same. Reinforce the idea that an ohmic conductor is distinguished by a straight-line graph that passes through the origin. Remind them that resistance is the ratio of V to I not the gradient of the graph (particularly important when discussing the filament lamp).

## Student questions: On characteristics

Students will get confused between *V* against *I* and *I* against *V* graphs. Both will be encountered so they should be prepared.

Episode 109-3: Lamp and resistor in series (Word, 41 KB)

Episode 109-4: Using non-ohmic behaviour (Word, 109 KB)

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### Resistance and temperature

## Episode 110: Resistance and temperature

Lesson for 16-19

- Activity time 115 minutes
- Level Advanced

This episode looks at the resistance of a metal and a semiconductor, giving a microscopic explanation of the variation with temperature. There is also a brief look at superconductivity and its applications.

Lesson Summary

- Demonstration and discussion: Resistance and temperature (10 minutes)
- Discussion: Free-electrons in metals (10 minutes)
- Student experiment: Thermistor behaviour (20 minutes)
- Discussion and demonstration: Conduction in semiconductors (5 minutes)
- Discussion: Superconductivity (20 minutes)
- Student activity: Researching superconductivity (30 minutes plus time for reporting back)
- Student questions: Using these ideas (20 minutes)

## Discussion and demonstrations: Resistance and temperature

This episode picks up on the variation of resistance of the filament lamp. Students’ own results should show that the resistance increases with current. Link this to the change of temperature of the wire and remind them that metals obey Ohm’s Law if the temperature is constant. (When they measured the resistance of the constantan wire in Episode 109, the current was always small, so temperature was almost constant.) You can reinforce the idea of resistance change in metals by cooling a wire and showing that its resistance decreases. This can be done using a cooling spray or, more dramatically, using liquid nitrogen (if this is available).

Episode 110-1: Metal resistance decreases as temperature falls (Word, 43 KB)

## Discussion: Free-electrons in metals

It is worth pausing at this point to discuss the mechanism of metallic resistance. Remind students of the model whereby as temperature increases the thermal vibrations in the lattice increase causing more electron scattering. (Be aware that there is more here than meets the eye in terms of quantum, as opposed to classical, free electron theory). This increases the resistance of the metal.

Next consider semiconductors. Students are unlikely to know much about semiconductors so it may be worth giving a brief introduction by saying that, compared to metals, they have only a few free electrons, so resistance (resistivity is the more appropriate term here, but they have not yet met it) is much higher. However, semiconductors such as silicon are central to the electronics industry so it is well worth considering their electrical characteristics. For example, how does their resistance depend on temperature?

## Student experiment: Thermistor behaviour

Students can investigate the temperature dependence of the resistance of a thermistor for themselves.

The results should show a clear decrease of resistance with increasing temperature. This is the opposite of what happened with the metal.

NB These thermistors are n.t.c. types (negative temperature coefficient). Other types exist which have a non-linear positive temperature coefficient.

Episode 110-2: Calibration of a thermistor (Word, 39 KB)

## Discussion and demonstrations: Conduction in semiconductors

Ask whether the atoms in the semiconductor vibrate more at higher temperature. Of course they do – so this contribution to resistance must increase in the same way as for a metal. So what else could make the semiconductor conduct better? The answer is: more charge carriers. Whereas the number of free electrons in a metal is constant the effect of heating a semiconductor frees additional electrons (and holes, but it’s probably not worth mentioning them yet!). For silicon in this temperature range the effect of additional charge carriers outweighs the effect of additional vibrations.

An interesting additional demonstration can be done using a different semiconductor (carbon). This shows that the two effects compete with each other. At lower temperatures the increase in resistance due to vibration dominates, as temperature rises, more and more electrons are freed and the resistance begins to fall.

## Discussion: Superconductivity

Having introduced the idea that metallic resistance is caused by electron scattering from ions as they vibrate you should return to what happens as a metal is cooled down.

You are looking for an argument that runs along the lines of: lower temperature, smaller amplitude of vibration so reduced scattering and therefore reduced resistance. Refer back to the initial demonstration.

## How low can we go?

The students ought to predict that thermal vibrations will eventually stop (at absolute zero on a simple mechanical model). This implies a very low resistance at low temperatures (but not necessarily zero).

Lead into Kammerlingh Onnes’s work and his surprise that mercury’s resistance disappears at a very low temperature (a few degrees above absolute zero: 4.15 K).

This sudden transition was unexpected and is a quantum effect. It occurs for some but not all metals. It has also been observed at much higher temperatures (around 150 K) in certain ceramics. These are called high temperature

superconductors (even though we are still talking about temperatures more than 100 degrees below zero Celsius! The mechanism for high temperature superconductivity is not fully understood and it is hoped that in future we may be able to manufacture room temperature superconductors.

Rather than lecture them about superconductors this would be a good opportunity to set them some research tasks which can be reported back to the class. Here is a work sheet that could be used:

Episode 110-3: Researching superconductivity (Word, 27 KB)

## Student questions: Using these ideas

Episode 110-4: Filament lamp and thermistor in series (Word, 31 KB)

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### Semiconductor devices

## Episode 111: Semiconductor devices

Lesson for 16-19

- Activity time 50 minutes
- Level Advanced

Light dependent resistors (LDRs) are probably already familiar. Like thermistors, they are semiconductor devices. Their behaviour can be illustrated by experiment and explained in a similar way to the variation of resistance with temperature for a semiconductor thermistor.

Lesson Summary

- Student experiment: Characteristics of an LDR (30 minutes)
- Demonstration: Semiconductor devices in use (20 minutes)

If your specification requires it, this is a good time to look at semiconductor devices in general.

## Student experiment: Characteristics of an LDR

Students look at the changing resistance of an LDR as the light intensity is varied.

Explain that photons of light absorbed by the LDR free electrons to conduct, reducing the resistance.

Episode 111-1: Variation of resistance of an LDR with light intensity (Word, 25 KB)

## Demonstration: Semiconductor devices in use

If you have plenty of time you could ask the students to construct some of these circuits. Otherwise set them up as a circus of demonstrations and use each one to demonstrate how the components can be used.

Don’t forget to mention the key role of silicon in the electronic and computing industries!

Episode 111-2: Applications of semiconductor devices (Word, 26 KB)

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### Resistivity

## Episode 112: Resistivity

Lesson for 16-19

- Activity time 110 minutes
- Level Advanced

In this episode, students learn how and why the resistance of a wire depends on the wire’s dimensions. They learn the definition of resistivity and use it in calculations.

Lesson Summary

- Discussion: Variation of resistance with length and area (5 minutes)
- Student experiment: Variation of resistance with length and area (30 minutes)
- Discussion: Variation of resistance with length and area (10 minutes)
- Student experiment: Measurement of resistivity (30 minutes)
- Student questions: Using these ideas (30 minutes)

## Discussion: Variation of resistance with length and area

The analogy to water flow will be useful here – ask them how they think the flow rate will be affected if you increase the cross-sectional area or length of the pipe along which the water has to flow. This should lead to two predictions about the resistance of a wire:

- resistance increases with length
- resistance decreases with diameter or cross-sectional area

It will be worth reminding them that doubling the diameter quadruples the cross-sectional area; many students get confused about the distinction and expect a wire of double diameter to have half the resistance.

## Student experiment: Variation of resistance with length and area

You could ask them to do one or both of the following experiments. Both reinforce the idea that resistance depends on material dimensions:

Episode 112-1: How the dimensions of a conductor affect its resistance (Word, 44 KB)

Episode 112-2: Introduction to resistivity using conducting paper (Word, 49 KB)

## Discussion: Variation of resistance with length and area

Follow up with some theory suggesting:

Resistance is proportional to length *l*

Resistance is inversely proportional to cross-sectional area *A*

resistance = constant × lengthcross-section area

The constant is a property of the material used – its resistivity ρ.

*R* = ρ × *l**A*

The units of resistivity can be derived from the equation: Ω m.

Emphasise that this is ohm metre

, not ohm per metre

.

Discuss the great range of resistivities amongst materials. Values for metals are very small. The resistivity of a material is numerically equal to the resistance between opposite faces of a one-metre-cube of the material; although this is not a good definition of resistivity, imagining such a block of metal does indicate why its value should be so low (~ 10^{-9} Ω m).

## Student experiment: Measurement of resistivity

Complete this section by asking your students to measure the resistivity of several metal wires.

This experiment provides an opportunity for a detailed discussion of the treatment of experimental errors.

Episode 112-3: Measuring electrical resistivity (Word, 30 KB)

## Student questions: Using these ideas

Problems involving resistivity.

Students often get confused between cross-section area and diameter.

Make sure they are able to convert mm^{2} to m^{2} for resistivity calculations.

Episode 112-4: Electrical properties (Word, 28 KB)