Class 11 Physics Chapter 2 – Units and Measurement
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Combination of Errors
[Watch Video for Detailed Explanation & Numerical]
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.