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Explain error of a sum or a difference. |
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Answer» Solution :Let two physical QUANTITIES A and B has measured value `A+-DeltaA and B+- AB` where, (1) For addition : Let Z is quantity obtained by addition of A and B. `:.Z=A+B` Let ERROR is Z be`DeltaZ` `Z+-DeltaZ=(A+-DeltaA)+(B+-DeltaB)` `A+B=Z` `:. +-Z=+-DeltaA+-DeltaB` For maximum absolute, error `DeltaZ = DeltaA+DeltaB` (ii) For Subtractio n : Let diference of A and B is Z. `:.Z=A-B` [ Let `A GT B]` `Z+-DeltaZ=(A+-DeltaA)-(B +-DeltaB)` `=(A-B)-(+-DeltaA+-DeltaB)` `A-B=Z` `+-DeltaZ=+DeltaA+- DeltaB` For maximum error in Z, `DeltaZ=DeltaA+DeltaB` 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. |
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