Topic 4.3
Resistance
Investigating resistivity
Aims
In this experiment you will be testing the resistivity equation
=
RA
L
where  is the resistivity, R is the resistance of the conductor, A is its cross-sectional area and
L is its length.
You will be required to design and use a simple circuit to measure the resistance of a
Nichrome wire and plot a graph of your results. You will plot a graph of resistance (y-axis)
against length (x-axis) for a length of wire. This will enable you to use and interpret the graph
to find the resistivity of Nichrome.
Safety
Check electrical equipment for loose wires and connections. Do not allow the current to go
higher than necessary as this will heat up the Nichrome wire. Do not allow the wire to
become too short since this may also cause the wire to overheat.
Equipment, materials and method
1 For this experiment you will need: a length of Nichrome wire and a metre ruler; a
micrometer; a power supply, voltmeter, milliammeter, 2  4 mm plugs to be used as
contacts and electrical wires.
2 Copy and add to the diagram in the Questions section below, showing the arrangement of
the circuit you will use to measure the resistance of the wire. You will need to measure the
voltage (pd) across the wire and the current through it.
3 Measure the pd and the current for a range of lengths of the wire. Use the whole range of
lengths available without allowing the wire to get too short. For each length, touch the
wire with the edges of the 4 mm plugs, take the readings and then remove the plugs. For
each length of wire that you measure, repeat the measurement, allowing the circuit to cool
between readings.
4 Use a micrometer to measure the average diameter of the wire you have used. At each
point take two measurements at right angles to each other. Hence calculate the average
cross-sectional area of the wire.
5 Tabulate your results in a table with appropriate headings (see the Results section below).
On graph paper, plot a scatter graph of resistance against length, using the average value
of resistance for each length. Carefully draw a line of best fit through your points.
6 Measure the gradient of your graph. Hence calculate the resistivity of the wire.
AQA Physics A AS Level © Nelson Thornes Ltd 2008
1
Topic 4.3
Resistance
Questions
1 Copy the diagram below and add to it to show how you will measure the voltage (pd) of
the wire and the current through it.
2 Which of your measurements will have the greatest effect on the accuracy of this
experiment?
3 When you measure the gradient from your line of best fit, you draw a triangle to show the
values you are reading from the graph. Why is it important that this triangle is as large as
possible?
Results
Tabulate your results in a table. Add headings to each column according to the guidance
provided below. Plot all of your repeated results on a scatter graph and draw a line of best fit
through the points.
length / m
pd / V
current / A
resistance / 
average resistance /
 (for each length)
Discussion
Pure Nichrome has a resistivity of 1.10 × 106 Ω m at room temperature. Compare your value
of resistivity with this value by calculating the percentage difference between the two. By
taking 10% as an acceptable error in your experimental technique, comment on whether your
result is reliable.
AQA Physics A AS Level © Nelson Thornes Ltd 2008
2
Topic 4.3
Resistance
Technicians Notes
Equipment and materials required
Each student or pair of students will require the following equipment:
 masking tape
 a length of Nichrome wire SWG 32 approximately 1.1 m long
 a metre ruler (attach the wire to the metre ruler with a short piece of masking tape near
each end)
 2  4 mm plugs to be used as contacts
 6  electrical wires (more may be required depending on their length – see the diagram
below)
 a micrometer
 a power supply or two 1.5 V cells providing an emf of approximately 3 V
 a voltmeter and a milliammeter (or 2 multimeters)
 graph paper
Safety
All electrical equipment should be checked for loose wires and connections.
If a power supply is used, the Nichrome wire may get hot if the current is allowed to get too
high.
AQA Physics A AS Level © Nelson Thornes Ltd 2008
3
Topic 4.3
Resistance
Teachers Notes
Aims
 To design and use a simple circuit to investigate the potential difference across a wire of
varying length, and the current through it.
 To use and interpret a graph / line of best fit to find an average value of the resistivity of
Nichrome wire.
Safety
All electrical equipment should be checked for loose wires and connections.
If a power supply is used, the Nichrome wire may get hot if the current is allowed to get too
high.
Teaching notes
4 This experiment may take up to an hour.
5 Prepare a sheet with a diagram of the correct experimental set-up for students who are not
able to design it for themselves.
6 Ensure that students switch off the power supply in between readings to avoid overheating
the wire.
7 The edges of the 4 mm plugs should be used as the contacts between the circuit and the
wire. Ensure that they are held firmly against the wire in order to obtain a good contact
and a correct measurement.
8 The full range of lengths of the wire should be used.
9 Note that the resistance of the other wires in the circuit and the ammeter, and the current
drawn from the voltmeter, are all assumed to be negligible.
10 When plotting the graph, a larger scale minimises error.
11 This practical may provide an opportunity to teach about systematic error. The graph may
not pass through the origin due to the position of the 4 mm plug. It may not be exactly at
0 mm on the ruler (probably due to the masking tape). You could have it 5 mm from the
end, and get the students to explain why there is a zero error – and why it is not important
in this experiment. (It also stops them just taking one pair of results to get their gradient.)
AQA Physics A AS Level © Nelson Thornes Ltd 2008
4
Topic 4.3
Resistance
Answers to questions
1 The circuit should be set up as in the following diagram:
2 The measurements of length will probably have the greatest effect on the accuracy. This is
due to the ends of the wire not being exactly on the edge of the ruler and the probability
that the wire is not perfectly tight along the length of the ruler. There will also be contact
errors that will affect the measurement of pd across the wire, which may be significant,
depending on the quality of contact made with the 4 mm plugs.
3 The triangle used to calculate the gradient of the graph should be as large as the graph
paper will allow; if necessary extrapolate the line. A larger triangle minimises the
percentage error.
The graph should be a straight line passing through the origin with a positive gradient equal

to
. The resistivity can be found by multiplying the gradient by the cross-sectional area of
A
the wire.
Answers to discussion
To compare the two values, calculate the percentage difference and compare the percentage
difference to the acceptable error value of 10%. Use the manufacturer’s quoted value as the
denominator in the calculation.
Practical assessment opportunities
4 PSA – Selecting and using equipment: 0–3 marks
(Following instructions and group work; organisation and safety assessed at end of
course.)
5 ISA/EMPA preparation:
Practical task – practice in tabulating results, plotting graphs.
Written task Section A – use own results and graph to calculate resistivity.
Written task Section B – use 10% estimate of measurement errors to evaluate resistivity
value obtained.
AQA Physics A AS Level © Nelson Thornes Ltd 2008
5