Combining uncertainties
Choose when to add absolute uncertainties, add percentages or include powers.
Resistivity practical questions
Process wire measurements, find resistivity from a resistance–length graph and evaluate uncertainty.
Practise
Read wire diameterRead the wire diameter in mm from the micrometer. Assume the micrometer has no zero error.
Practical setup and assumptions
A uniform wire of circular cross-section is measured at a fixed temperature. The ammeter is in series and the voltmeter measures the wire plus a constant contact/lead resistance.
The graph follows R = (ρ/A)L + R₀. The contact and lead resistance R₀ is constant, so it affects the intercept rather than the gradient.
Readings for this dataset
| L / m | V / V | I / A |
|---|---|---|
| 0.2 | 0.09 | 0.1 |
| 0.4 | 0.15 | 0.1 |
| 0.6 | 0.21 | 0.1 |
| 0.8 | 0.27 | 0.1 |
| 1 | 0.33 | 0.1 |
The linked tasks use the same readings. These are generated practice data: treat them as exact unless an uncertainty is stated. Use the stated uncertainty rather than estimating it from scatter.
Scale text alternative
Last visible sleeve mark: 0.00 mm. Thimble division at the reference line: 45.
Larger micrometer
Hint
Add the last visible sleeve mark to the thimble division × 0.01 mm.
Worked solution
- Indication = 0.45 mm; zero correction is zero.
Work through this dataset
- Read wire diameter (current)
- Cross-sectional area
- Process V and I
- Choose graph axes
- Resistance–length gradient
- Calculate resistivity
- Interpret the intercept
- Diameter and area uncertainty
- Propagate resistivity uncertainty
- Control wire heating
These tasks keep the same readings. Another question starts a new dataset. Your answers are checked separately.
Question type: Read wire diameter
Report a problem
Calculate resistivity from wire measurements
A wire has resistance 2.0 Ω, length 1.0 m and diameter 0.40 mm. Radius is 0.20 mm = 2.0 × 10⁻⁴ m. Area = πr² = 1.26 × 10⁻⁷ m². Resistivity ρ = RA/L = 2.51 × 10⁻⁷ Ω m, keeping the area unrounded in the calculation.
The area formula uses radius, or πd²/4 if using diameter. Convert mm to metres before squaring. Resistivity depends on material and temperature; resistance also depends on length and area. A uniform-wire calculation assumes the stated diameter represents the tested length.
From diameter to resistivity
Convert wire diameter d to metres, then A = πd²/4. Calculate each measured resistance from V/I. For a uniform wire at fixed temperature, Rwire = ρL/A.
Use the gradient when there is a series contribution
The supplied model includes a constant contact/lead contribution: Rmeasured = (ρ/A)L + R₀. Plot R vertically against L. Its gradient is ρ/A, so resistivity is gradient × area. A single Rmeasured/L ratio would include R₀/L.
Uncertainty and evaluation
Under the stated first-order maximum method, area’s percentage uncertainty is twice the diameter percentage. Add that to the gradient percentage for resistivity. Check zero error, measure diameter at several positions and orientations, and control heating. Repeats can reveal variation; they do not automatically remove systematic error.
These are synthetic ideal readings with a supplied line, not a full laboratory procedure or noisy best-fit exercise.
A-level relevance
AQA 7408: 3.5.1.3; required practical 5 (selected); OCR A H556: 4.2.4(a) (selected). Tasks cover the selected skills listed above.
AQA electricity specification · OCR A specification · AQA practical handbook · OCR practical skills handbook