Solve the problem.
-The resistance $R$ produced by wiring resistors of $R _ { 1 }$ and $R _ { 2 }$ ohms in parallel can be calculated from the formul $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } } .$
If $R _ { 1 }$ and $R _ { 2 }$ are measured to be 10 ohms and 6 ohms respectively and if these measurements are accurate to within $0.05$ ohms, estimate the maximum possible error in computing R.
A) 0.032
B) 0.016
C) 0.021
D) 0.027

Question

Quizplus · Accepted Answer

The maximum possible error in computing $R$ can be estimated using the formula for the derivative of the function $R = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}}$. The error in $R$ can be approximated by the sum of the absolute values of the partial derivatives of $R$ with respect to $R_1$ and $R_2$, each multiplied by the maximum error in $R_1$ and $R_2$ (0.05 ohms). The calculation yields a maximum possible error of approximately 0.027 ohms.

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