1.1 Basic Physics

Uncertainties: Practical Applications

Absolute Uncertainty

Absolute uncertainty is calculated by subtracting the smallest measurement from the largest measurement and dividing by two. In more detail, absolute uncertainty is a measure of the potential range of error in a measurement.

It can be represented as X ± Y. E.g. ±0.1 cm

Percentage Uncertainty (%) / Precision

It is useful to calculate the percentage uncertainty as this will help us to combine uncertainties later on.

Method:

  1. Find the arithmetic mean of all the values given.

  2. Find the absolute uncertainty of the values ( ½ larger value-smallest value)

  3. Plot numbers into formulae P = ( absolute uncertainty / mean) x 100

E.g. R = 3.4 Ω ± 3%

Combining Uncertainties

This section tells you how to combine, or propagate, uncertainties in A-level Physics.

Adding and subtracting

To find the absolute uncertainty in the sum or difference of two quantities, add the absolute uncertainties.

E.g. if Z=A+B, where A=(4.0±0.1)Ω and B=(1.0±0.2)Ω, then Z=(5.0±0.3)Ω

Multiplying and Dividing

To find the relative uncertainty in the product or ratio of two quantities, add the relative uncertainties.

E.g. if Y=C/D, where C=30.0m±2% and D=3s±4%, then Y=10ms ^−1 ±6%

Powers

To find the relative uncertainty in a quantity that has been raised to a power, multiply the relative uncertainty by the power.

E.g. if F=5.0Hz±4%, then F2=25s−2±8%