Question

The measured values of two quantities are A ± A and B ± B, ∆A and ∆B being the mean absolute errors.
Show that, if Z = A/B
∆Z/Z = ∆A/A + ∆B/B​

Answer 1

Step-by-step explanation:

we know...

errors are added.....

so, maximum relative error in Z will be the sum of relative error in A and B....

so, ∆Z/Z = ∆A/A + ∆B/B

.....( relative error in A = ∆A/A

relative error in B = ∆B/B )

hope it helps......

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Answer 2

Answer:

Suppose Z = AB and measured values are (A +- ∆A) and(A +- ∆B)

then Z +- ∆Z = (A +- ∆B) (A +- ∆B)

= AB +- A∆B+-B∆A+- ∆A∆B

dividing L.H.S BY Z and R.H.S by AB we get

(1+- ∆Z/Z) = [1 +- ∆B/B+- ∆A/A +- ( ∆A/A ) ( ∆B/B)]

Since ∆A/A and ∆B/B are very small we shall neglect their product. Hence maximum relative error in Z is

∆Z/Z = ∆A/A + ∆B/B

Hence proved¡¡