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1.3.1Development of Practical Skills in Physics

Using Appropriate Instruments and Techniques

5 min read 8 parts Lesson 18 of 29 1 quiz Virtual lab

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Lesson summary

1.3.1 Using Appropriate Instruments and Techniques — OCR A Level Physics A notes: Choose a suitable measuring instrument for a task, state its resolution and uncertainty, and use good technique to reduce systematic and random errors.Every measurement starts with a choice of instrument.

  • systematic error
  • zero error
  • repeat readings
  • Avoid parallax
  • Check the zero
  • Measure large multiples of a small quantity

Section 1 of 8Choosing an instrument

Every measurement starts with a choice of instrument.

Two properties matter most.
Range
The range is the largest and smallest value the instrument can show.
Resolution
The resolution (sensitivity) is the smallest change in the quantity that the instrument can display.
A metre rule has a resolution of 1 mm, a vernier caliper 0.1 mm or 0.05 mm, and a micrometer screw gauge 0.01 mm.

The best instrument is the one whose resolution is small compared with the quantity being measured.

1
Measuring a wire of diameter 0.50 mm with a ruler (resolution 1 mm) is useless; a micrometer is the right tool.
2
In contrast, using a micrometer to measure the length of a corridor is both impossible and pointless.
3
A good rule of thumb is that the resolution should give a percentage uncertainty of a few per cent or less.
4
When a question asks you to justify an instrument, state its resolution, compare it with the size of the quantity, and say what percentage uncertainty results.

Other practical factors also matterthe instrument must not disturb what is being measured (a large thermometer in a small volume of water draws heat from it), and it must respond quickly enough for the change being studied.

Section 2 of 8Accuracy, precision, resolution and uncertainty

These words have precise meanings in practical physics and examiners expect them to be used correctly.

Accuracy
Accuracy how close a measurement is to the true value.
Precision
Precision how close repeated measurements are to each other. Precise readings can still be inaccurate if there is a systematic error.
Resolution
Resolution the smallest division the instrument can show.
Uncertainty
Uncertainty the range within which the true value is expected to lie, written as value ± uncertainty.

For an analogue scale the reading uncertainty is usually taken as half the smallest division, or the full smallest division if the scale is hard to read.

Accuracy, precision, resolution and uncertainty
For a digital meter it is normally ± 1 in the last displayed digit.
Where repeated readings are available, half the range of the repeats may be used if it is larger than the instrument uncertainty.
The final uncertainty should be given to one significant figure (occasionally two) and the value rounded to the same decimal place.

Section 3 of 8Systematic and random errors

A systematic error shifts every reading by the same amount or the same factor in one direction.

Systematic and random errors
Zero error
The commonest example is a zero error: a micrometer that reads 0.02 mm when closed.
Correct it by subtracting the zero reading from every measurement (a negative zero reading is added).
A systematic error cannot be reduced by repeating the experiment, and on a graph it shows up as a non-zero intercept where the line should pass through the origin.
Calibrating against a known standard, or measuring a known quantity first, can reveal it.

A random error causes readings to scatter either side of the true value, for example human reaction time when using a stopwatch.

Systematic and random errors
Repeat readings
Random errors are reduced by taking repeat readings and finding the mean.
The spread of the repeats (half the range) gives an estimate of the uncertainty.
Anomalous
Spotting an anomalous result, one far from the others, and repeating that measurement is part of good practice; do not discard it silently.

Section 4 of 8Good technique

Good technique
Avoid parallax
Avoid parallax view the scale at right angles, with your eye level with the pointer or the meniscus. Mirrored scales on meters help.
Check the zero
Check the zero before starting and record any zero error.
Measure large multiples of a small quantity
Measure large multiples of a small quantity the thickness of one sheet of paper is found by measuring a stack of 100 and dividing. The uncertainty is also divided by 100, so the absolute uncertainty becomes tiny.
Use a fiducial marker
(a pin or a marker at the equilibrium position) when timing oscillations, and time at the centre of the swing where the speed is greatest and the position easiest to judge. Time many oscillations and divide.
Keep other variables constant
Keep other variables constant and change only the independent variable, controlling the others and saying how.
Take enough readings
Take enough readings at least six different values of the independent variable over as wide a range as is practical, with repeats at each.
Safety
Safety consider the specific hazard (hot water, falling masses, lasers, mains voltage) and one sensible precaution.

Section 5 of 8Percentage uncertainty

The percentage uncertainty compares uncertainty with the size of the measurement:

percentage uncertainty = (absolute uncertainty / measured value) × 100%

It is the percentage uncertainty that tells you whether a measurement is good enough.

1
A length of 2.0 cm measured with a ruler uncertain by ± 0.1 cm has a 5% uncertainty, while 80.0 cm measured the same way has only 0.1 / 80.0 × 100% = 0.125%.
2
When quantities are combined, percentage uncertainties are added for products and quotients, and multiplied by the power for powers.
3
Practical planning questions often ask which single measurement dominates the final uncertainty: it is the one with the largest percentage uncertainty.
4
Improving that measurement, for example by using a micrometer instead of a rule, has the greatest effect on the quality of the experiment.

This lesson links directly to analogue reading (1.3.2), digital instruments (1.3.3) and the calipers and micrometer (1.3.5), where the details of resolution and zero error for each tool are developed.

Section 6 of 8Worked examples

  1. A student measures the diameter of a wire with a micrometer and gets 0.62 mm. With the jaws closed it reads 0.03 mm. The resolution is 0.01 mm. Give the corrected diameter and its percentage uncertainty.

  2. The thickness of a stack of 50 identical card sheets is 6.5 mm measured with a ruler of resolution 1 mm (take the uncertainty as ± 1 mm). Find the thickness of one sheet with its uncertainty.

  3. Five timings of a trolley are 2.31 s, 2.40 s, 2.28 s, 2.35 s and 2.36 s. Find the mean time and an estimate of the uncertainty from the spread.

Section 7 of 8Key terms

TermMeaning
ResolutionSmallest change in a quantity that an instrument can display.
RangeInterval between the lowest and highest values an instrument can measure.
AccuracyCloseness of a measurement to the true value.
PrecisionCloseness of repeated measurements to each other.
Zero errorA systematic error where the instrument does not read zero for a true zero.
Parallax errorApparent shift in a reading caused by viewing the scale from an angle.
Percentage uncertaintyAbsolute uncertainty divided by the measured value, times 100%.

Section 8 of 8Exam technique

1
Confusing accuracy and precisiontightly grouped readings may all be wrong by the same zero error.
2
Forgetting to subtract a zero error, or subtracting when it is negative (a negative zero error must be added).
3
Quoting the uncertainty to more significant figures than the measurement, or claiming a resolution smaller than the instrument can show.
4
Thinking repeats remove systematic errorthey only reduce random error.
5
Giving an absolute uncertainty when asked for a percentage, or vice versa.
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