Practical Skills & Uncertainties
Units 3 and 6 are written papers about experiments. There's no practical exam, but you get questions on planning an experiment, taking readings, spotting what an inexperienced student did wrong, and processing real results. The skills on this page are the same for every topic, so learning them once picks up marks in every unit.
Unit 3 (WPH13)
Practical skills from Units 1 and 2: planning, implementing and processing results. You need percentage uncertainties from a single reading or from repeats, but you are not expected to combine (compound) uncertainties.
Unit 6 (WPH16)
The same skills applied to Units 4 and 5, plus compounding percentage uncertainties, logarithmic graphs, and the words precision, accuracy and sensitivity.
The language of measurement
Edexcel uses these words in a precise, scientific way (from the ASE's The Language of Measurement). Exam answers that use them loosely, like "the results were accurate because I repeated them", lose marks. Repeating improves precision, not accuracy.
| Term | What it means |
|---|---|
| Validity | A measurement is valid if it measures what it is supposed to be measuring. This depends on both the method and the instruments. |
| True value | The value you'd get from an ideal measurement. Apart from fundamental constants, it is considered unknowable. |
| Accuracy | How close a result is judged to be to the true value. It can't be given a number, and it is affected by both random and systematic errors. |
| Precision | How closely repeated measurements agree with each other (how tightly they cluster). Only random effects affect it. |
| Repeatability | Precision when the same person uses the same method and equipment over a short time. |
| Reproducibility | Precision when different people use different apparatus or methods. A harder test than repeatability. |
| Uncertainty | The interval within which the true value can be considered to lie, e.g. 20 °C ± 2 °C. |
| Error | The difference between the measurement and the true value. It is not a mistake. |
| Resolution | The smallest measuring interval of an instrument, and the source of uncertainty in a single reading. |
Random and systematic errors
Readings scatter unpredictably either side of the true value: reaction time with a stopwatch, a fluctuating meter, judging when a pendulum passes a point. They reduce precision.
Reduce it by repeating and averaging, timing many oscillations rather than one, or using a light gate or data logger instead of a human.
Every reading is wrong by the same amount or the same proportion in the same direction: a zero error, a stretched tape measure, always reading a scale from above (parallax), heat lost to the surroundings. They reduce accuracy, and repeating does not help at all.
Reduce it by checking zero before you start, calibrating, and using a set square or eye-level reading to avoid parallax. Using a graph's gradient also cancels a constant offset.
Reading instruments
You need to know the resolution of the instruments you'd choose. A metre rule reads to 1 mm, vernier calipers to 0.1 mm and a micrometer screw gauge to 0.01 mm. In the exam you may be shown a picture of one and asked for the reading to the correct number of significant figures.
| Instrument | Resolution | Typical use |
|---|---|---|
| Metre rule | 1 mm | Lengths of a pendulum or wire, heights, extensions over 1 cm |
| Vernier calipers | 0.1 mm | Diameter of a ball bearing or cylinder, internal diameters, depths |
| Micrometer screw gauge | 0.01 mm | Diameter of a wire (CP3, CP7), thickness of a sheet |
| Stopwatch | 0.01 s (but human reaction time ≈ 0.1–0.3 s) | Timing 10 or 20 oscillations |
| Light gate + data logger | ~0.001 s | Short times and speeds (CP1, CP9) |
| Digital meters | the last digit shown | Current, p.d., mass (top-pan balance) |
Vernier calipers
The sliding vernier scale has 10 divisions that span 9 mm, so each one is 0.9 mm long. Every vernier line is 0.1 mm shorter than a main-scale millimetre, so when the jaws open by an extra 0.1 mm, the next vernier line lines up with a main-scale line. To read it:
- Read the main scale at the vernier's zero: whole millimetres.
- Find the vernier line that lines up exactly with a main-scale line. Its number is the tenths of a millimetre.
- Add them, and check the zero reading with the jaws closed (zero error).
Micrometer screw gauge
One full turn of the thimble moves the spindle 0.50 mm, and the thimble has 50 divisions, so each division is 0.01 mm. Read the sleeve (millimetres and the half-millimetre marks below the line) and add the thimble division on the datum line × 0.01 mm. Always use the ratchet so you don't squash the wire, and check the zero.
When measuring a wire's diameter, take readings at several places along the wire and at right angles to each other (in case it isn't perfectly round), then average. Write it in the method; it's an easy mark in almost every planning question.
Uncertainties
Uncertainty in a single reading or in repeats
- Single reading (or all repeats the same): uncertainty = half the resolution. A ruler marked in mm reads to ± 0.5 mm. A digital ammeter showing 0.4 A (resolution 0.1 A) is ± 0.05 A.
- Repeated readings: uncertainty = half the range of the repeats. Edexcel also accepts the difference between the mean and the reading furthest from it.
- Systematic offset (e.g. a known zero error): don't add it to the uncertainty, subtract it from each reading.
Percentage uncertainty
The diameter of a canister is measured three times with a ruler: 66 mm, 64 mm and 61 mm. Give the diameter with its uncertainty and its percentage uncertainty.
Show solution
Mean = (66 + 64 + 61)/3 = 63.7 mm. To the resolution of the ruler that's 64 mm.
\[ \text{uncertainty} = \tfrac{1}{2}(\text{range}) = \tfrac{1}{2}(66 - 61) = 2.5\ \text{mm} \] \[ \text{percentage uncertainty} = \frac{2.5}{64} \times 100\% = 3.9\% \approx 4\% \]So the diameter is 64 mm ± 2.5 mm (± 4%). The radius has the same percentage uncertainty, 4%, even though its absolute uncertainty is halved to 1.25 mm.
Combining uncertainties Unit 6
When you calculate something from several measurements, their uncertainties combine. There are just three rules:
Add the absolute uncertainties.
\[ (102.8 \pm 0.3) - (101.4 \pm 0.1) = 1.4 \pm 0.4\ \text{mm} \]Add the percentage uncertainties.
\[ \%\,\rho = \%\,m + \%\,V \]Multiply the percentage uncertainty by the power.
\[ \%(d^2) = 2 \times \%\,d \]Subtracting two nearly equal measurements is dangerous: the absolute uncertainties still add, but the result is small, so its percentage uncertainty is huge. In the pipe example above, 0.4 mm on 1.4 mm is a 29% uncertainty from two readings that were each better than 0.3%.
Recording results and significant figures
- Column headings carry the quantity and unit, separated by a solidus: length / m, time for 10 oscillations / s. Never put units in the body of the table.
- Raw readings go to the resolution of the instrument, with the same number of decimal places all the way down a column (write 0.50 m, not 0.5 m, if the rule reads to 0.01 m).
- Processed values (like \(T^2\) or \(1/V\)) usually go to 3 significant figures, about what you can plot on a graph. A final answer should have the same number of s.f. as the least precise data used, normally 2 or 3.
- Take enough readings: usually at least 6 different values over as wide a range as possible, with repeats, and look for any anomalous result to repeat.
A student times 10 oscillations of a pendulum four times: 15.2 s, 15.6 s, 15.3 s and 15.5 s. What is the period, with its uncertainty?
Mean of 10T = 15.4 s with half-range uncertainty (15.6 − 15.2)/2 = 0.2 s. Dividing by 10 gives T = 1.54 s ± 0.02 s. Timing 10 oscillations divides the reaction-time uncertainty by 10, which is exactly why we do it.
Straight-line graphs
Almost every experiment ends with a straight-line graph, because a straight line is easy to recognise, a line of best fit averages out random error, and its gradient and intercept give you the constant you're after. The trick is to rearrange the physics equation into the form
\[ y = m\,x + c \]and then plot whatever plays the role of \(y\) against whatever plays the role of \(x\).
| Equation | Plot y | against x | Gradient | Intercept |
|---|---|---|---|---|
| \(h = \tfrac{1}{2}gt^2\) (CP1) | \(h\) | \(t^2\) | \(g/2\) | 0 |
| \(R = \rho l / A\) (CP7) | \(R\) | \(l\) | \(\rho/A\) | 0 (contact resistance if not) |
| \(V = \varepsilon - Ir\) (CP8) | \(V\) | \(I\) | \(-r\) | \(\varepsilon\) |
| \(T = 2\pi\sqrt{m/k}\) (CP16) | \(T^2\) | \(m\) | \(4\pi^2/k\) | 0 |
| \(pV = NkT\) at fixed \(T\) (CP14) | \(p\) | \(1/V\) | \(NkT\) | 0 |
| \(V = V_0 e^{-t/RC}\) (CP11) | \(\ln V\) | \(t\) | \(-1/RC\) | \(\ln V_0\) |
- Choose scales so the points fill more than half the grid in both directions, with sensible steps (1, 2 or 5 per square; never 3).
- Plot points as small crosses to within half a small square. Draw one thin straight line of best fit with roughly equal numbers of points either side. Don't force it through the origin, and never join the dots.
- Find the gradient from a large triangle (at least half the length of the line) using points on your line, not data points. Show the triangle on the graph.
- A line that should pass through the origin but doesn't suggests a systematic error. A large scatter of points suggests large random errors.
Logarithmic graphs Unit 6
Two kinds of relationship can't be straightened just by squaring or inverting, because you don't know the power yet, or the variable sits in an exponent. Taking logs turns both into straight lines.
Take logs (base 10 or base e, as long as you are consistent) of both sides:
\[ \log y = \log(k x^n) \]Use \(\log(ab) = \log a + \log b\) and \(\log(x^n) = n\log x\):
\[ \log y = n\,\log x + \log k \]Compare with \(y = mx + c\): plotting \(\log y\) against \(\log x\) gives a straight line with
\[ \text{gradient} = n, \qquad \text{intercept} = \log k \]So a log–log graph tells you the power directly. For example, plotting \(\log T\) against \(\log l\) for a pendulum gives a gradient of 0.5.
Take natural logs (base e) of both sides:
\[ \ln y = \ln\!\left(A e^{-kx}\right) = \ln A + \ln\!\left(e^{-kx}\right) \]Since \(\ln(e^{z}) = z\):
\[ \ln y = -k\,x + \ln A \]Plot \(\ln y\) against \(x\) (only \(y\) is logged): a straight line with gradient \(-k\) and intercept \(\ln A\). This is how you get the time constant from capacitor discharge (CP11) and the decay constant in radioactivity.
Logs have no units, so label the axis ln (V / V) or log (T / s): take the log of the number, not the unit. When reading a gradient on a log graph, use differences in the log values on the axes, not the original numbers.
Drawing conclusions
To decide whether your result is accurate, compare it with the accepted value in one of two ways:
Work out the range your result could lie in. If the accepted value is inside it, the result is accurate. Example: \(g = 10.1\ \text{m s}^{-2} \pm 4\%\) means 9.7 to 10.5 m s⁻², which includes 9.81, so it's accurate.
Find the percentage difference. Less than 5% indicates the result is accurate.
\[ \frac{10.1 - 9.81}{9.81}\times 100\% = 3\% \]Then go further than "it was accurate". Say which measurement had the largest percentage uncertainty, and suggest a specific improvement: "use a micrometer instead of a ruler for the diameter", not "use better equipment". Mention any systematic error suggested by a non-zero intercept.
Planning an experiment
Planning questions are marked against a checklist. Hit every point:
- Variables: state the independent variable (what you change), the dependent variable (what you measure) and every control variable, with how each is kept constant.
- Apparatus with resolution: name each instrument and its resolution, chosen to suit the size of the measurement (micrometer for a wire, metre rule for its length).
- Method: how each variable is measured, including technique details (eye level to avoid parallax, set square, fiducial marker at the centre of an oscillation, timing 20 oscillations, checking zero).
- Range and repeats: at least 6 values over a wide range, repeated and averaged where readings vary.
- Analysis: which graph you'll plot and how the gradient or intercept gives the answer.
- Sources of uncertainty and how to reduce them, plus any safety issue with a sensible precaution (goggles when wires may snap, a sand tray under hanging masses, lead-lined handling tongs for sources).
The 16 core practicals
Each one is covered on its topic page with a virtual version you can run. Click through to revise the method and analysis.
| # | Core practical | Key graph or analysis |
|---|---|---|
| 1 | Acceleration of a freely-falling object | \(h\) against \(t^2\), gradient \(= g/2\) |
| 2 | Viscosity of a liquid by the falling-ball method | Terminal velocity from time between marks, then Stokes' law |
| 3 | Young modulus of a material | Stress against strain, gradient \(= E\) |
| 4 | Speed of sound with a 2-beam oscilloscope | Move the microphone through whole wavelengths, then \(v = f\lambda\) |
| 5 | Frequency of a vibrating string: length, tension, mass per unit length | \(f\) against \(1/l\), or \(f\) against \(\sqrt{T}\) |
| 6 | Wavelength of light with a diffraction grating | \(n\lambda = d\sin\theta\) for several orders |
| 7 | Resistivity of a material | \(R\) against \(l\), gradient \(= \rho/A\) |
| 8 | E.m.f. and internal resistance of a cell | \(V\) against \(I\): intercept \(\varepsilon\), gradient \(-r\) |
| 9 | Force and change of momentum | Impulse \(F\Delta t\) compared with \(\Delta p\) |
| 10 | Collisions between small spheres using ICT | Momentum components before and after |
| 11 | Capacitor charge and discharge on an oscilloscope or data logger | \(\ln V\) against \(t\), gradient \(= -1/RC\) |
| 12 | Calibrate a thermistor in a potential divider as a thermostat | Calibration curve of \(V_\text{out}\) against temperature |
| 13 | Specific latent heat of a phase change | \(L = \Delta E / \Delta m\) |
| 14 | Pressure and volume of a gas at fixed temperature | \(p\) against \(1/V\), a straight line through the origin |
| 15 | Absorption of gamma radiation by lead | Corrected count rate against thickness |
| 16 | Unknown mass from resonant frequencies of known masses | \(T^2\) (or \(1/f^2\)) against \(m\) |
Quick checks
A metre rule has a zero error: it reads 2 mm when it should read zero. What kind of error is this, and what should you do?
A zero error shifts every reading by the same amount in the same direction, so it is systematic. You correct each reading. Repeating can't remove it.
A wire's diameter is measured as 0.50 mm ± 0.01 mm. What is the percentage uncertainty in its cross-sectional area?
% uncertainty in \(d\) = 0.01/0.50 × 100% = 2%. Area \(= \pi d^2/4\), so the percentage doubles to 4%. π and the 4 are exact numbers with no uncertainty.
The intensity of a source falls with distance as \(I = k d^n\). Which graph gives \(n\) as its gradient?
\(\log I = n\log d + \log k\), a straight line with gradient \(n\). Plotting \(I\) against \(1/d^2\) only works if you already know that \(n = -2\).
A student repeats a measurement many times and gets very similar values, but they are all well away from the accepted value. The results are best described as:
Close agreement between repeats means precise. Being far from the true value means not accurate, which points to a systematic error.