Question

Propagate the errors in the dimension measurements into the final uncertainty of the calculated resistance.

a. Use the average error of dimensions
b. Sum the absolute errors
c. Square the errors
d. Combine errors using the root-sum-square method

Answer 1

To calculate the uncertainty in the calculated resistance, you can use the root-sum-square method to propagate the errors in the dimension measurements.

Step-by-step explanation:

The uncertainty in the calculated resistance can be found by propagating the errors in the dimension measurements using the root-sum-square method. Here are the steps:

1. Calculate the percent uncertainty in each dimension measurement. For example, if the length has a percent uncertainty of 2% and the width has a percent uncertainty of 1%, the percent uncertainties would be 0.02 and 0.01, respectively.
2. Square each percent uncertainty to get the squared errors. Using the previous example, the squared errors would be 0.0004 and 0.0001.
3. Add the squared errors together.
4. Take the square root of the sum of squared errors to get the final uncertainty.

For example, if the squared errors are 0.0004 and 0.0001, their sum is 0.0005. Taking the square root of 0.0005 gives an uncertainty of approximately 0.0224.