KeterehskyLab: Experiment 1 Introduction To Uncertainty Analysis

Experiment 1 Introduction To Uncertainty Analysis

Topic : Physical Quantities and Units

Title : Introduction to Error Analysis

Objective : To estimate the accuracy of experimental result

Theory :

Error or uncertainties could be caused by limitation of the measuring instruments, nature of
the measured quantities or other external factors. Error can be classified as systematic error
and random error.

Error analysis is a technique used to determine how error propagates through experimental
procedure. This technique is based on combining the uncertainty for each quantity involved
to estimate the accuracy of the experimental result.

Propagation of errors: Assume A and B are two measured quantities in an experiment.

Addition or Subtraction

If the derived quantity

, then

Multiplication and Division

If the derived quantity

, then

$<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>∆</mo><mi>C</mi></mrow><mi>C</mi></mfrac><mo>=</mo><mfrac><mrow><mo>∆</mo><mi>A</mi></mrow><mi>A</mi></mfrac><mo>+</mo><mfrac><mrow><mo>∆</mo><mi>B</mi></mrow><mi>B</mi></mfrac></math>$

$<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>C</mi><mo>=</mo><mfenced><mrow><mfrac><mrow><mo>∆</mo><mi>A</mi></mrow><mi>A</mi></mfrac><mo>+</mo><mfrac><mrow><mo>∆</mo><mi>B</mi></mrow><mi>B</mi></mfrac></mrow></mfenced><mi>C</mi></math>$

The experimental result should be expressed as

The accuracy of the experimental result can be estimated by calculating the percentage error.

Percentage error $<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mo>∆</mo><mi>C</mi></mrow><mi>C</mi></mfrac><mo>×</mo><mn>100</mn><mo>%</mo></math>$