Question

If the measured values of two quantities
are A + AA and B AB, AA and AB
being the mean absolute errors. What is
the maximum possible error in A I B?
Show that if z = 2
А A
B
AZ
ΔΑ ΔΒ
Z AB​

Answer 1

Answer:

Error in A + B = ±ΔA ±ΔB

max error in A + B = ∆A + ∆B

Explanation:

Z = A/B

=> Z ± ∆Z = (A±ΔA / B±ΔB)

=(A/B) (1 ± ∆A/A)/(1 ± ∆B/B)

=> 1 ± ∆Z/Z = (1 ± ∆A/A)(1 ± ∆B/B)^-1

=> 1 ± ∆Z/Z= (1 ± ∆A/A) (1 -+ ∆B/B)

=> ± ∆Z/Z = ± ∆A/A -+ ∆B/B

=> ∆Z/Z = ∆A/A + ∆B/B