Chapter 2: Units and Measurements
Topic: Combination of Errors
Combination of errors is an important concept in Class 11 Physics Units and Measurements, which explains how measurement errors combine when physical quantities are added, subtracted, multiplied, divided, or raised to powers.
This lesson covers the rules, formulas, and important exam points related to combination of errors.
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Class 11 Physics Chapter 2 – Units and Measurement
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Combination of Errors
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Combination of errors is how the errors in measurements combine in various mathematical operations.
1. Errors of a sum or a difference
If two physical quantities A and B have measured values $latex A+\Delta A $ and $latex B+\Delta B $ respectively where $latex \Delta A $ and $latex \Delta B $ are their absolute errors. Let Z = A ± B and absolute error for Z is $latex \Delta Z $ then maximum value of absolute error is
$latex \Delta Z = \Delta A + \Delta B $
Rule: When two quantities are added or subtracted, the absolute error in the final result is the sum of the absolute errors in the individual quantities.
2. Error of a product
If two physical quantities A and B have measured values $latex A+\Delta A $ and $latex B+\Delta B $ respectively where $latex \Delta A $ and $latex \Delta B $ are their absolute errors. Let Z = AB and absolute error for Z is $latex \Delta Z $ then maximum relative error is
$latex \frac {\Delta Z}{Z} = \frac {\Delta A}{A} + \frac {\Delta B}{B} $
Rule: When two quantities are multiplied the relative error in the result is the sum of the relative errors in the multipliers.
3. Errors in Division
If two physical quantities A and B have measured values $latex A+\Delta A $ and $latex B+\Delta B $ respectively where $latex \Delta A $ and $latex \Delta B $ are their absolute errors. Let Z = A/B and absolute error for Z is $latex \Delta Z $ then maximum relative error is
$latex \frac {\Delta Z}{Z} = \frac {\Delta A}{A} + \frac {\Delta B}{B} $
Rule: When two quantities are divided the relative error in the result is the sum of the relative errors in the individual quantities.
4. Error in case of a measured quantity raised to a power
If a physical quantity A has measured value $latex A+\Delta A $ where $latex \Delta A $ is absolute error. Let Z = Ak and absolute error for Z is $latex \Delta Z $ then maximum relative error is
$latex \frac {\Delta Z}{Z} = k \frac {\Delta A}{A} $
Rule: The relative error in a physical quantity raised to the power k is the k times the relative error in the individual quantity.