Class 11 Physics Units and Measurement – Combination of Errors

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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 and  respectively where and  are their absolute errors. Let Z = A ± B and absolute error for Z is  then maximum value of absolute error is

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 and  respectively where and  are their absolute errors. Let Z = AB and absolute error for Z is  then maximum relative error is

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 and  respectively where and  are their absolute errors. Let Z = A/B and absolute error for Z is  then maximum relative error is

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 where is absolute error. Let Z = A^k and absolute error for Z is  then maximum relative error is

Rule: The relative error in a physical quantity raised to the power k is the k times the relative error in the individual quantity.

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