TL;DR Measure the resistance of a constantan wire at five or more different lengths (20, 40, 60, 80, 100 cm) using an ammeter in series and a voltmeter in parallel. Calculate R=V/I for each length, then plot R (y-axis) against L (x-axis). The graph should be a straight line through the origin, confirming R∝L. The gradient equals ρ/A
Reviewed by
Chee Wei Jie·Academic Advisor (Physics)
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For a wire of uniform cross-sectional area, the resistance R depends on three factors:
R=AρL
where:
R = resistance of the wire, in Ω
ρ = resistivity of the wire material, in Ω m
L = length of the wire, in m
A = cross-sectional area of the wire, in m2
What this tells us
If the material (ρ) and thickness (A) stay constant, resistance is directly proportional to length:
R∝L
Double the length and the resistance doubles. This is the relationship the experiment sets out to verify.
What is resistivity?
Resistivity ρ is a property of the material itself - it does not depend on the shape or size of the wire. Copper has a very low resistivity (about 1.7×10−8Ω m), which is why it is used for connecting wires. Constantan has a much higher resistivity (about 4.9×10−7Ω m), making it easier to measure meaningful resistance values in a school lab.
Why the graph goes through the origin
Rearranging the resistance formula:
R=(Aρ)L
This has the form y=mx, with no constant term. When L=0, R=0. So the R vs L graph should be a straight line passing through the origin.
2 | Apparatus
You will need:
Item
Purpose
Constantan or nichrome wire (SWG 28 or 32, at least 1 m)
The test wire whose resistance is measured
Metre ruler (resolution 1 mm)
Measures the length of wire under test
Ammeter (0--1 A, 0.01 A resolution)
Measures current through the wire
Voltmeter (0--5 V, 0.01 V resolution)
Measures p.d. across the wire
Cell or battery (e.g. 1.5 V or 3 V)
Provides current
Switch
Opens and closes the circuit
Two crocodile clips
Connect to the wire at measured lengths
Connecting wires (at least 5)
Completes the circuit
The ammeter is connected in series with the test wire. The voltmeter is connected in parallel across the section of wire being tested (between the two crocodile clips). For a refresher on these connections, see the ammeter and voltmeter guide.
3 | Step-by-Step Method
Tape the wire along the metre ruler. Stretch the constantan wire taut along the ruler and secure both ends with tape. The wire must be straight - any slack introduces error in the length measurement.
Connect the circuit. Wire the cell, switch, and ammeter in a series loop. Attach one crocodile clip to the wire at the 0 cm mark. The second crocodile clip will be moved to different positions along the wire.
Set the first length. Clip the second crocodile clip at the 20.0 cm mark. Connect the voltmeter leads to the two crocodile clips so it reads the p.d. across the 20.0 cm section of wire.
Close the switch. Read and record the voltmeter reading (V) and the ammeter reading (I) simultaneously.
Open the switch immediately after taking the reading. This prevents the wire from heating up, which would change its resistance.
Move the clip to the next length. Repeat the measurement at L = 40.0, 60.0, 80.0, and 100.0 cm. For each length, reconnect the voltmeter across the new section of wire.
Record all readings in a table with column headings that include the quantity and unit.
Practical tips:
Switch off between every reading - the heating effect is a major source of error.
Press the crocodile clips firmly onto the wire to minimise contact resistance.
Keep the wire taut throughout. If it sags, the actual length between clips is longer than what you measure on the ruler.
If a variable resistor (rheostat) is available, use it in series to keep the current low (below about 0.5 A). This reduces heating.
Take repeat readings of V and I at each length to spot anomalies.
4 | Raw Data Table Template
Record your data in a table like this:
L / cm
V / V
I / A
R=V/I / Ω
20.0
40.0
60.0
80.0
100.0
Column headings must include the quantity and unit separated by a forward slash (e.g. L / cm).
Record ammeter and voltmeter readings to the precision of the instrument (typically 2 decimal places).
Calculate R=V/I for each row and include the result in the table.
5 | Graph Plotting - R Against L
Axes
y-axis: Resistance R / Ω
x-axis: Length L / cm (or m, as long as you are consistent)
What the graph should look like
The plotted points should lie close to a straight line through the origin. This confirms that resistance is directly proportional to length.
Drawing the best-fit line
Use a transparent ruler.
Draw a single straight line of best fit through the data points and the origin (since theory predicts R=0 when L=0).
The line should have roughly equal numbers of points above and below it.
Finding the gradient
Pick two points on the line (not data points) that are far apart:
gradient=ΔLΔR=L2−L1R2−R1
The gradient has units of Ω/cm (or Ω/m if you plotted length in metres). From the resistance formula:
gradient=Aρ
So if you know the cross-sectional area A, you can calculate the resistivity:
ρ=gradient×A
For a detailed walkthrough of gradient calculations, axis-labelling conventions, and common graph errors, see the graph skills guide.
6 | Worked Example
Suppose you collect the following data using a constantan wire of diameter 0.28 mm:
L / cm
V / V
I / A
R=V/I / Ω
20.0
0.16
0.30
0.53
40.0
0.31
0.30
1.03
60.0
0.47
0.30
1.57
80.0
0.63
0.30
2.10
100.0
0.78
0.30
2.60
Step 1 - Plot the graph
Plot R (y-axis) against L (x-axis). Use sensible scales: y-axis from 0 to 3.0 Ω, x-axis from 0 to 100 cm. Mark each point with a small cross.
Step 2 - Draw the best-fit line
The points lie close to a straight line through the origin. Draw a best-fit line passing through the origin.
Step 3 - Calculate the gradient
Choose two well-separated points on the best-fit line:
Point A: (L1,R1)=(0,0)
Point B: (L2,R2)=(100,2.60)
gradient=L2−L1R2−R1=100−02.60−0=0.0260Ω/cm
Converting to SI units: 0.0260Ω/cm = 2.60Ω/m.
Step 4 - Calculate resistivity
The wire diameter is 0.28 mm = 0.28×10−3 m, so the radius is 0.14×10−3 m.
A=πr2=π×(0.14×10−3)2=6.16×10−8 m2
ρ=gradient×A=2.60×6.16×10−8=1.60×10−7Ω m
This is in the right order of magnitude for constantan (the accepted value is about 4.9×10−7Ω m). Differences arise from contact resistance and systematic errors in the current/voltage readings.
Summary of results
Quantity
Value
Gradient of R vs L
2.60 Ω/m
Cross-sectional area A
6.16×10−8 m2
Resistivity ρ
1.60×10−7Ω m
7 | Sources of Error and Improvements
For the generic circuits-experiment error bank (how to tell a systematic zero error on the ruler apart from random parallax on the ammeter), see our O-Level Physics sources of error guide.
Source of error
Effect
Improvement
Wire heats up when current flows
Resistance increases with temperature, giving readings that are too high for longer wires
Switch off between readings; use a low current (add a series resistor)
Contact resistance at crocodile clips
Adds extra, variable resistance to every reading
Press clips firmly; clean the wire surface with emery paper; use the same clips throughout
Wire not straight or taut
Actual length between clips is longer than the ruler reading
Tape the wire along the ruler; keep it taut
Zero error on the ruler
All length readings shifted by the same amount
Check that the 0 cm mark aligns with the first clip; record any offset and correct readings
Temperature change in the room
Resistivity of the wire changes slightly
Take all readings in quick succession; note the room temperature
Parallax error when reading analogue meters
Incorrect V or I values
Read the meter at eye level; use the mirror strip if provided
8 | Why Use Constantan or Nichrome?
You might wonder why the experiment uses constantan or nichrome wire rather than copper. The answer comes down to the temperature coefficient of resistance.
Copper
Copper has a relatively high temperature coefficient of resistance. When current flows, the wire heats up and its resistance increases noticeably. This means the resistance you measure depends on how long the switch has been on and how much heat has built up - not just the length. The relationship R∝L becomes unreliable.
Constantan and nichrome
Constantan (an alloy of copper and nickel) and nichrome (an alloy of nickel and chromium) have very low temperature coefficients of resistance. Their resistance barely changes even when the wire warms up during the experiment. This makes the results more consistent and the R vs L graph more likely to be a clean straight line.
Additionally, constantan and nichrome have higher resistivity than copper, so you get measurable resistance values even with short lengths of thin wire. If you used copper wire of the same dimensions, the resistance might be too small to measure accurately with a school voltmeter.
9 | Paper 3 Planning Question Angle
If you are asked to plan this experiment in Paper 3, structure your answer using these headings. For the full marking breakdown, see the Paper 3 marking guide.
Diagram
Draw a clear, labelled circuit diagram showing the battery, switch, ammeter (in series), test wire with two crocodile clips, voltmeter (across the test wire), and connecting wires. Use standard circuit symbols. Show the metre ruler alongside the wire.
Independent and dependent variables
Independent variable: Length of wire L (changed by moving the crocodile clip).
Dependent variable: Resistance R, calculated from R=V/I.
Controlled variables
Same wire used throughout (same material, same diameter).
Same ammeter and voltmeter.
Temperature of the wire kept approximately constant (switch off between readings; use a low current).
Method summary
State that you will measure at least 5 different lengths (e.g. 20, 40, 60, 80, 100 cm), record V and I at each length, calculate R=V/I, and plot R (y-axis) against L (x-axis).
Analysis
State that the graph should be a straight line through the origin.
The gradient equals ρ/A.
If the cross-sectional area is known, resistivity can be calculated.
Safety
Switch off between readings to prevent the wire from overheating.
Do not use excessively high currents - the wire can become hot enough to burn.
10 | Common Exam Mistakes
These are the errors examiners see most often in Paper 3 and Paper 2 questions on this topic:
Forgetting to switch off between readings. The wire heats up and its resistance changes. This is both a practical error and a planning mark that examiners specifically look for.
Measuring length from the wrong end of the ruler. Always measure the length of wire between the inner edges of the two crocodile clips. If your ruler does not start at zero, account for the offset.
Not keeping the wire taut. If the wire sags, the actual length is greater than the ruler reading, giving a lower resistance per centimetre than expected.
Confusing R∝L with R∝1/L. Resistance increases with length, not decreases. If your graph slopes downward, something has gone wrong.
Forgetting units on the gradient. The gradient of an R vs L graph has units of Ω/cm or Ω/m. You must state the unit when giving the value.
Not plotting the line through the origin. Theory predicts that R=0 when L=0. Your best-fit line should pass through the origin (unlike the EMF/internal resistance experiment, where the y-intercept carries meaning).
Using data points instead of points on the line for the gradient. The gradient should be calculated from two well-separated points that lie on the best-fit line, not from raw data points.
Connecting the voltmeter across the whole circuit instead of across just the test wire. The voltmeter must be connected in parallel across the section of wire between the two crocodile clips only.
11 | Frequently Asked Questions
Why does resistance increase with wire length?
A longer wire means free electrons must travel a greater distance through the metal lattice. They collide more often with the vibrating metal ions, losing more energy. Each additional centimetre of wire adds more obstacles, so the total opposition to current (resistance) increases proportionally.
Can I use any wire for this experiment?
You can use any metallic wire, but the experiment works best with constantan or nichrome. These alloys have high resistivity (giving measurable resistance values) and a low temperature coefficient (so heating does not significantly change the results). Copper wire has very low resistance per centimetre, making accurate measurements difficult with school equipment.
What if my graph does not pass through the origin?
A non-zero y-intercept usually indicates systematic error - most commonly contact resistance at the crocodile clips or a zero error on the ruler. Mention this in your evaluation and suggest cleaning the wire surface and checking the ruler alignment as improvements.
How do I measure the diameter of the wire?
Use a micrometer screw gauge. For a step-by-step guide, see our vernier caliper and micrometer reading guide. Measure the diameter at three different positions along the wire and take the mean. This accounts for any slight variation in thickness. The cross-sectional area is then A=π(d/2)2, where d is the mean diameter.
Does temperature affect the results?
Yes. When current flows through the wire, it heats up and its resistance increases (even constantan has a small temperature coefficient). This is why you must switch off between readings and use a low current. If the wire gets noticeably warm, wait for it to cool before taking the next reading.
What is the difference between resistance and resistivity?
Resistance (R, measured in Ω) depends on the length, cross-sectional area, and material of a specific wire. Resistivity (ρ, measured in Ω m) is a property of the material itself - it does not change with the dimensions of the wire. Two wires made of the same material have the same resistivity but different resistances if they differ in length or thickness.
