Determining Uncertainty (Edexcel IAL Physics)

Percentage Uncertainty in Single Readings

• Percentage uncertainty for a single reading (measured value) is defined by the equation:

Percentage uncertainty =$\frac{uncertainty}{measured value}$× 100 %

Worked Example A student measures the potential difference on an analogue voltmeter with resolution 0.2 V as 15 V.

Calculate the percentage uncertainty in the student's reading of the potential difference.

Answer:

Step 1: Determine the absolute uncertainty

• The absolute uncertainty of the reading is half the resolution of the analogue voltmeter

$\frac{0.2}{2}$= 0.1 V

Step 2: Calculate the percentage uncertainty

$\frac{0.1}{15}$× 100 % = 0.67 %

Exam Hint Always make sure your percentage uncertainty is at least one significant figure smaller than the measurement.

Percentage Uncertainty in Multiple Readings

• The percentage uncertainty in measurements from multiple readings (e.g., repeat readings) use half the range of the readings

  • The range of the readings is the difference between the highest and lowest reading

Worked Example A student achieves the following results in their experiment for the angular frequency, ω.

0.154, 0.153, 0.159, 0.147, 0.152

Calculate the percentage uncertainty in the mean value of ω.

Answer:

Step 1: Calculate the mean value

mean ω = $\frac{0.154+0.153+0.159+0.147+0.152}{5}$= 0.153 rad s^–1

Step 2: Calculate half the range (this is the uncertainty for multiple readings)

$\frac{1}{2}$× (0.159 – 0.147) = 0.006 rad s^–1a

Step 3: Calculate percentage uncertainty

$\frac{uncertainty}{measured value}$ × 100 % = $\frac{\pm half the range}{mean}$ × 100 %

$\frac{0.006}{0.153}$× 100 % = 3.92 %

Exam Hint Remember that percentage uncertainties have no units, only the % sign!

You will not be expected to compound percentage uncertainties for AS.