Question

Delta R'/R'^2 = Delta R1/R^2 + Delta R2/R2^2. Derive this formula from 1/R'=1/R1+ 1/R2.

Answer 1

Answer:

1/R = 1/R1 + 1/R2

On differentiating (to obtain the approximation for the linear error)

- dR/ R^2 =  -dR1 / R1^2  - dR2 /R2^2

d will be delta.

dR = (R/R1)^2 dR1 + (R/R2)^2 dR2

Using R = R1 R2 /(R1 + R2) , this becomes

dR = 1/(1+R1/R2)^2  dR1 +  1/(1+R2/R1)^2 dR2