The gradient of an R-against-L graph is (1.80 +/- 0.05) ohm m−1. The mean wire diameter is (0.360 +/- 0.005) mm. Calculate rho = gradient x pi d2 / 4 and its absolute uncertainty.
[5 marks]
Total for this question: 5
A-level Physics required practicals
Resistivity of a wire
AQA 3.5.1.3 · RP5
A-level Physics (7408) · Required practical 5 — method, techniques, safety, analysis and uncertainty. Includes errors documented in examiner reports.
Board and spec code confirmed against AQA 7408 · registry checked 2026-07-11How this checking works
Determine the resistivity of a metal wire from its diameter and the variation of resistance with measured length.
Apparatus
- Long uniform test wire fixed beside a metre rule
- Micrometer screw gauge
- Low-voltage DC supply, switch and protective resistor
- Ammeter in series and voltmeter across the selected test-wire length
- Fixed contact and movable crocodile clip or sliding contact
- Connecting leads
Apparatus & techniques (AT)
AT a · analogue measurement
The metre rule provides the analogue wire-length readings from the fixed contact to the movable contact.
AT b · digital instruments
Digital ammeter and voltmeter readings are paired to calculate resistance for each selected wire length.
AT e · calipers/micrometers
A micrometer measures the small wire diameter repeatedly before cross-sectional area is calculated.
AT f · circuit construction
The series ammeter, parallel voltmeter, switch and protective resistor are connected into a working low-voltage circuit.
Safety
Hazard
The test wire or protective resistor can become hot at high current.
Control
Use a low-voltage supply and current-limiting resistor, close the switch briefly and open it between readings.
Hazard
A long taut wire or loose leads can snag or cause cuts.
Control
Secure the wire and route leads away from the bench edge and walkways.
Method
- 1With the circuit open, use the micrometer ratchet to measure the wire diameter at several positions and in two perpendicular directions; calculate the mean diameter.
- 2Connect the ammeter in series and the voltmeter only across the selected test-wire length; include a protective resistor and switch.
- 3Set a measured length from the fixed contact to the movable contact, close the switch briefly and record V and I once stable.
- 4Open the switch between readings, choose several well-spaced lengths and repeat each V-I pair without allowing the wire to heat appreciably.
- 5Calculate R = V/I for each length and plot R against L.
CPAC focus (editorial)
This is an editorial study focus, not an AQA mapping of fixed CPAC competencies to this practical.
- CPAC 2: Editorial focus: select an effective length range and current that give resolvable resistance changes without heating.
- CPAC 3: Editorial focus: limit current and switch-on time so the wire and contacts remain safe.
- CPAC 4: Editorial focus: record repeat diameter readings and matched V, I and L values with units and instrument resolution.
- CPAC 5: Editorial focus: interpret gradient and intercept, then propagate gradient and area uncertainty into rho.
Variables
Independent
Length L of test wire between the voltage contacts
Dependent
Resistance R = V/I of that selected wire length
Control
- Wire material and diameter
- Wire temperature and measurement current
- Contact method, meter ranges and the fixed reference end
Results & processing
- Fit R = (rho/A)L + R0; multiply the R-against-L gradient by area A to obtain resistivity rho.
- A non-zero intercept can represent lead or contact resistance and should not be silently removed by forcing the line through the origin.
- Report rho in ohm metres and propagate gradient and diameter uncertainty through rho = gradient x pi d squared / 4.
Analysis skills
- Calculate R = V/I for each length and obtain rho from the gradient of R against L multiplied by A.
- Use the intercept to diagnose lead/contact resistance and max/min acceptable gradients for uncertainty.
Uncertainty
Sources
- Micrometer resolution, zero error and diameter variation along the wire
- Voltmeter and ammeter resolution plus fluctuating contact resistance
- Uncertainty in the effective contact positions and resistance change caused by heating
Calculations
- For rho = gradient x pi d squared / 4, add percentage uncertainty in the gradient to twice the percentage uncertainty in d.
- Find gradient uncertainty from best and max/min acceptable lines that remain consistent with all error bars.
Interpretation
- A stable positive intercept is consistent with extra series resistance; curvature or drifting readings suggest heating or poor contacts.
- Repeated voltage readings do not correct a micrometer zero error or a systematically mislocated length contact.
Exam angles
- Place the ammeter and voltmeter correctly and explain why the switch is opened between readings.
- Use the micrometer ratchet and repeated orientations when measuring diameter.
- Calculate rho from the correct graph gradient, attach the unit ohm metre and construct valid max/min gradient lines.
Where students lose marks
Turning the micrometer thimble hard instead of using the ratchet.
Fix: Close with the ratchet until it slips so the wire is not compressed and the contact force is repeatable.
- Examiner report: P3-24 · PDF p. 3
Substituting one measured resistance divided by one length when a graph gradient is required.
Fix: Use the best-fit R-against-L gradient after calculating each R from its matched V and I reading.
Drawing max/min gradients through only part of the error bars or quoting resistivity in ohms per metre.
Fix: Use acceptable extreme lines consistent with every error bar and finish with the resistivity unit ohm metre.
Improve the method
- Use a long wire and a wide range of lengths so the resistance change is large compared with meter resolution and contact resistance.
- Use low current, close the switch briefly and allow cooling so resistivity is not changed by heating.
- Repeat micrometer readings across positions and rotations, check zero error and calculate area from the mean diameter.
Source references
- Specification: PSpec 3.5.1.3 · PDF p. 28
Try it — exam-style
Hard
ORIGINAL
Medium
ORIGINAL
An R-against-L graph has a straight best-fit line with a positive resistance intercept. Give one plausible cause and explain why forcing the graph through the origin is poor analysis.
[2 marks]
Total for this question: 2
Questions are written in the style of past AQA papers — never copied from them.
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