If the measurement errors in all the independent quantities are known, then it is possible to...

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If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x,y and z are Ax, Ay and Az, respectively, then The series expansion for variables are always added. So the error in z will be Consider the ratio r= (A) *= A== X=A* - *(1+)(1+4)* x+ Ax Ay = y Ay y x (C) (1+^) ".. to first power in Ay/y, is 1 F (Ay/y). The relative errors in independent The above derivation makes the assumption that Ax/x < 1, Ayly 1. Therefore, the higher powers of these quantities are neglected. (1 + a) 2Aa (1-a) Az = Ar Ay x measurement of a is Aa (A a la < 1), then what is the error Ar in determining r? 2 (B) (1+a) y (1-a) to be determined by measuring a dimensionless quantity a. If the error in the (1+ a) (D) (1-a) If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x,y and z are Ax, Ay and Az, respectively, then The series expansion for variables are always added. So the error in z will be Consider the ratio r= (A) *= A== X=A* - *(1+)(1+4)* x+ Ax Ay = y Ay y x (C) (1+^) ".. to first power in Ay/y, is 1 F (Ay/y). The relative errors in independent The above derivation makes the assumption that Ax/x < 1, Ayly 1. Therefore, the higher powers of these quantities are neglected. (1 + a) 2Aa (1-a) Az = Ar Ay x measurement of a is Aa (A a la < 1), then what is the error Ar in determining r? 2 (B) (1+a) y (1-a) to be determined by measuring a dimensionless quantity a. If the error in the (1+ a) (D) (1-a)

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