Determining Uncertainty (Edexcel International AS Physics)

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14 May 2022

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

Percentage uncertainty = $\frac{u n c e r t a i n t y}{m e a s u r e d v a l u e}$ × 100 %

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.

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

2. Calculate the percentage uncertainty

$\frac{0.1}{15}$ × 100 % = 0.67 %

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

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

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.

1. Calculate the mean value

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

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

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

3. Calculate percentage uncertainty

$\frac{u n c e r t a i n t y}{m e a s u r e d v a l u e}$ × 100 % = $\frac{\pm h a l f t h e r a n g e}{m e a n}$ × 100 %

$\frac{0.006}{0.153}$ × 100 % = 3.92 %

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

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

the (exam) results speak for themselves:

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