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
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For a uniform wire at constant temperature, 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. For a product-specific copper-nickel example, Kanthal lists Cuprothal 49 resistivity at 20°C (equivalent to 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
Example apparatus is listed below. Check the actual wire, meter ranges, resolution and supply limits before choosing the setup:
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
Low-voltage supply or cell, with suitable current limiting
Provides current within the wire and instrument limits
Series resistor or rheostat, unless the supply provides suitable current limiting
Limits initial current and reduces heating
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. With the switch open, connect the low-voltage supply, suitable series current limiter, switch, and ammeter in the main loop. If the supply itself provides suitable current limiting, set it before switching on. 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.
Use suitable current limiting from the start. For a series rheostat, begin at high resistance and use a current low enough to avoid noticeable wire heating. Follow the apparatus limits; a single current threshold is not suitable for every wire diameter and setup.
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 readings with precision appropriate to the actual instrument and question instructions.
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
For a uniform wire at approximately constant temperature and negligible extra voltage drops, points should be consistent with a straight line and an intercept consistent with zero. This supports the proportional relationship; judge it against measurement uncertainty.
Drawing the best-fit line
Use a transparent ruler.
Draw a straight line of best fit to the data. Do not force it through the origin unless the question instructs you to do so. For the ideal wire model, 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). When length is expressed in metres, the resistance formula gives:
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
The following illustrative data demonstrate the calculation for a uniform wire of diameter 0.28 mm. They are not presented as measured constantan data:
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
These illustrative points are consistent with an approximately proportional relationship. Draw a line of best fit to the points; an intercept consistent with zero supports the ideal model, but do not force an experimental fit through the origin without instruction.
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
The calculated value is about one third of the copper-nickel product reference stated earlier (about 4.9×10−7Ω m). These illustrative data do not establish the wire material or the cause of that difference. Do not attribute a discrepancy to contact resistance or instrument errors without supporting measurements.
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
Temperature changes can alter resistance and confound the comparison between lengths; the size and direction depend on the material and setup
Switch off between readings; use a low current (add a series resistor)
Contact resistance at crocodile clips
Can affect the reading if the measured potential difference includes contact voltage drops; the effect depends on where the voltage leads connect
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 (a copper-nickel alloy) and nichrome (a nickel-chromium alloy) are useful resistance-wire materials, but their temperature response depends on the specific alloy grade. The temperature response depends on alloy composition and temperature range. Do not assume that warming has no effect; still control heating during measurements. Keeping the wire at approximately constant temperature 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 further practical guidance, 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.
With length expressed in metres, 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
Check for the following errors when carrying out or explaining this experiment:
Forgetting to switch off between readings. The wire heats up and its resistance changes. Control heating so that temperature changes do not confound the length comparison.
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, its actual length is greater than the ruler reading, so resistance divided by the recorded length is higher than expected for the same wire at constant temperature.
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.
Forcing a best-fit line through the origin. The ideal uniform-wire model predicts a zero intercept, but experimental offsets and uncertainty must be evaluated from the data. Fit the measured points and follow any explicit question instruction. Compare this with the EMF/internal resistance experiment, where the intercept has a physical interpretation.
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?
For a uniform wire of the same material and cross-sectional area at constant temperature, each length segment has a resistance. Joining these segments end to end adds their resistances in series, so total resistance increases in proportion to length.
Can I use any wire for this experiment?
Choose a metallic wire whose material and dimensions suit the instrument and supply limits. Constantan or nichrome can be suitable choices. Their higher resistivity can make resistance easier to measure than copper of the same dimensions. Choose a known alloy grade and control temperature rather than assuming all such wires have negligible temperature effects. 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?
Check whether the fitted intercept is distinguishable from zero given measurement uncertainty. Possible contributors include a length offset or contact voltage drops included by the connection geometry. Investigate the setup rather than assigning a cause from the intercept alone; check ruler alignment and contact quality.
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. Current can heat the wire and change its resistance; the size and direction of the change depend on the material and temperature range. 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 at the same temperature have the same resistivity but different resistances if they differ in length or thickness.
