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International A LevelPhysicsEdexcelRevision Notes3. Practical Skills in Physics IPractical Skills I: Processing ResultsDetermining Uncertainty

Determining Uncertainty (Edexcel International A Level Physics)

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Katie M

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Katie M

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Percentage Uncertainty in Single Readings

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

Percentage uncertainty = fraction numerator u n c e r t a i n t y over denominator m e a s u r e d space v a l u e end fraction× 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

fraction numerator 0.2 over denominator 2 end fraction= 0.1 V

Step 2: Calculate the percentage uncertainty

fraction numerator 0.1 over denominator 15 end fraction× 100 % = 0.67 %

Examiner Tips and Tricks

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 = fraction numerator 0.154 thin space plus thin space 0.153 space plus thin space 0.159 thin space plus thin space 0.147 space plus thin space 0.152 over denominator 5 end fraction= 0.153 rad s–1

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

1 half× (0.159 – 0.147) = 0.006 rad s–1a

Step 3: Calculate percentage uncertainty

fraction numerator u n c e r t a i n t y over denominator m e a s u r e d space v a l u e end fraction × 100 % = fraction numerator plus-or-minus h a l f space t h e space r a n g e over denominator m e a n end fraction × 100 %

fraction numerator 0.006 over denominator 0.153 end fraction× 100 % = 3.92 %

Examiner Tips and Tricks

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

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

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    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.