Free Pearson Edexcel International A Level Physics lesson
Measurement, uncertainty and honest records
Record what the instrument resolves and what the method can justify.
What you’ll learn
- Read and correct scale measurements including vernier and micrometer examples.
- Use half-resolution and half-range estimates with their assumptions.
- Maintain clear raw and processed tables without hiding anomalies.
Read the scale and check its zero
Select an instrument whose range accommodates the object and whose resolution is suitable for the quantity. For this course a typical vernier caliper is read to 0.1 mm and a micrometer screw gauge to 0.01 mm, while actual instruments should be checked rather than assumed identical. A vernier reading combines the main-scale value immediately before the vernier zero with the extra fraction identified by the aligned vernier division.
A micrometer reading combines the visible sleeve scale, including any half-millimetre mark, with the thimble contribution. Use the ratchet or specified gentle technique rather than crushing a soft specimen with the screw. Check the closed reading and correct a known zero offset: if the closed instrument reads +0.02 mm, subtract 0.02 mm from each measured reading. An offset of unknown stability contributes uncertainty rather than a perfectly known correction.
Avoid parallax by viewing a scale in the intended direction and align the instrument with the dimension being measured. Measure wire diameter at several positions and orientations to assess nonuniformity or ovality. This is different from repeatedly squeezing the same point until a preferred value appears. A corrected fine-scale reading is still limited by the measurement method, specimen condition and calibration; precision of the display is not proof of accuracy.
Corrected reading = indicated reading − known zero reading; micrometer total = sleeve + thimble contribution.
Symbols and units
- xindicated, xzero and xcorrected are readings in the same length unit
- instrument divisions must first be converted to their stated units.
How the equation explains the idea
- An additive zero error contributes to every indication, so xindicated = xtrue + xzero. Subtract the measured zero to recover xcorrected.
- If a closed micrometer reads +0.03 mm and a specimen reads 1.28 mm, the corrected value is 1.25 mm. A negative zero error must instead be subtracted as a negative number.
Worked example
A micrometer with a positive zero
- The sleeve shows 2.50 mm and the thimble adds 0.37 mm.
- The indicated reading is 2.87 mm.
- With a closed zero reading of +0.02 mm, the corrected result is 2.85 mm.
Subtract a positive zero reading; include the sleeve’s half-millimetre mark.
Keep this idea. Combine all scale contributions, then apply a checked zero correction with the correct sign.
Use a stated uncertainty model
Every measurement has uncertainty from its instrument and method. For a single reading, Unit 3 asks for an estimate using half the instrument resolution where that model is appropriate. A scale marked every 1 mm then gives a single-reading estimate of ±0.5 mm. This convention does not automatically include every practical effect: reaction time, alignment or unstable input can be larger than the display contribution.
For repeated readings, calculate the mean and use half the range as a simple estimate of the spread where appropriate. With maximum xmax and minimum xmin, that estimate is (xmax − xmin)/2. Percentage uncertainty is 100 times absolute uncertainty divided by the measured magnitude. Quote enough digits to communicate the scale of uncertainty, not a misleading string of calculator decimals. This is a classroom estimate, not a claim of a formally established statistical confidence interval.
Repeated agreement shows precision under the chosen conditions, not guaranteed accuracy. A common calibration error may remain in every reading, and a new operator or method may reveal a reproducibility issue. Investigate an anomalous observation and repeat it rather than deleting it simply to shrink the range. Unit 3’s explicit processing scope does not require compounding percentage uncertainties; the more advanced combined-uncertainty methods belong in Unit 6 and are not needed to answer these single-measurement questions.
Single-reading estimate = half resolution; repeat estimate = (maximum − minimum)/2; percentage uncertainty = 100 δx/|x|.
Symbols and units
- δx is positive absolute uncertainty in the units of x
- |x| is measurement magnitude
- percentage uncertainty is dimensionless and reported as percent.
How the equation explains the idea
- For a stated resolution-only model, a scale step of 0.2 mm gives δx = 0.1 mm. Repeat half-range uses the observed spread and measures a different source of uncertainty.
- For 4.0 mm with δx = 0.1 mm, 100δx/|x| = 2.5%. Combining or choosing uncertainty estimates requires the stated experimental model, not automatically taking half the range for every instrument.
Worked example
A repeated travel time
- Times are 1.42, 1.46 and 1.44 s, giving mean 1.44 s.
- Half range = (1.46 − 1.42)/2 = 0.02 s.
- Percentage uncertainty ≈ 100 × 0.02/1.44 = 1.4%.
Report 1.44 ± 0.02 s with the half-range method stated.
Keep this idea. Name the uncertainty estimate and its limitations; distinguish repeat scatter from systematic bias.
Keep raw evidence distinct from processing
Prepare a table before measuring, with clear quantity names or symbols and units in the column headings. Record raw readings to the resolution of the instrument, keeping consistent decimal places for one measured quantity. Do not add unjustified digits to make the results look more exact, and do not round away a digit that the instrument genuinely resolves. Record repeats separately so another reader can inspect their spread.
Processed values such as resistance, reciprocal length or a mean should be recognisable as calculated quantities, not raw readings. Retain extra digits during calculation and round the recorded result to a sensible consistent precision, often about three significant figures for graph plotting when the data support it. A unit conversion must occur before combining quantities; square and reciprocal columns also need their transformed units, such as s² or m⁻¹.
An honest record includes relevant conditions, instrument ranges, corrections and any unusual observations. If a result is corrected later, preserve enough information to reconstruct the original reading and correction. A neat table is not useful if it conceals which measurements were repeated, which were estimated or which were removed. Recording immediately reduces transcription and memory errors, while an independent check of one processed row can expose a formula or unit error affecting the whole dataset.
Example processed columns: R/Ω = (V/V)/(I/A); t²/s²; (1/L)/m⁻¹. Raw resolution and processed significant figures are different choices.
Symbols and units
- V is potential difference in V
- I is current in A
- R is resistance in Ω
- t is time in s
- L is length in m.
How the equation explains the idea
- A table heading R/Ω means each entry is the numerical value of resistance in ohms. Compute R = V/I from unrounded or adequately precise readings.
- Squaring time also squares its unit, giving t²/s². Taking reciprocal length gives (1/L)/m⁻¹. Keep raw measurements so another reader can repeat the processing.
Worked example
One transparent processed row
- Record raw V = 2.40 V and I = 0.160 A in separate labelled columns.
- Calculate R = 2.40/0.160 = 15.0 Ω.
- Keep a separate resistance column and retain the raw pair so the calculation can be checked.
The processed value is traceable to the original measurements.
Keep this idea. Record raw readings with units and resolution, then show traceable processing with justified precision.
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