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Units And Measurement

Question
CBSEENPH11016790

Compute the error in An, if percentage error in the measurement of A is α%.

Solution

Here, X =A
Let ∆A and ∆X be the absolute errors in A and X respectively.
Therefore the above equation with error can be written as


space space space space space space space space space space space space space space space space space space open parentheses straight X plus-or-minus ΔX close parentheses equals open parentheses straight A plus-or-minus ΔA close parentheses to the power of straight N
rightwards double arrow space space space space space space straight X open parentheses 1 plus-or-minus ΔX over straight X close parentheses equals straight A to the power of straight n open parentheses 1 plus-or-minus ΔA over straight A close parentheses to the power of straight n

rightwards double arrow space space space space space open parentheses 1 plus-or-minus ΔX over straight X close parentheses equals space space open parentheses 1 plus-or-minus straight n space ΔX over straight X close parentheses

rightwards double arrow space space space space space space space ΔX over straight X equals straight n ΔA over straight A 
Multiplying both sides by 100, 
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i.e. Maximum possible %age error in X = n (Maximum possible %age error in A)