(28/48/50) Dual Number Functions

[Thomas Klemm]

(02-21-2024 04:34 PM)DavidM Wrote:  Personally, I find threads like this one intriguing. I just lack the mathematical background to make practical use of the concepts.

Consider two resistors with a certain tolerance:

\(
\begin{align}
R_1 &= 3 \pm 4 \varepsilon \\
R_1 &= 5 \pm 6 \varepsilon \\
\end{align}
\)

What is the total resistance and its tolerance if both resistors are in parallel?

3 4 R→C 1/X
5 6 R→C 1/X
+ 1/X

(1.875,2.40625)


Compare this to the calculation if \(\varepsilon = 1e-5\):

3.00004 1/X
5.00006 1/X
+ 1/X

1.8750240625


With each number we include the linearization of its perturbation.