Error Propagation Homework: Wheatstone Bridge

AI Thread Summary
The discussion revolves around using a Wheatstone bridge to determine an unknown resistance and the associated error propagation. The user has derived a formula for the unknown resistance based on measurements from a slide wire and a resistance box. They express uncertainty about calculating partial derivatives and applying the error propagation equation correctly. The user seeks clarification on whether to calculate a single error propagation value for all measurements or separate values for each set of measurements. The inquiry highlights the importance of understanding error propagation in experimental physics.
Yatty33
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Homework Statement



I have completed a lab that uses a Wheatstone bridge to find an unknown resistance utitlizing a resistance box and a slide wire.

This will yield the unknown resistance from the following formula...
Ru = unknown resistance
Rs = known resistance from the resistance box
x = distance from 0 on the slide wire in meters

Ru = (x/(1-x))*(Rs)

So for the unknown resistance, I took 3 values of x, and Rs (because Rs changes on the slide wire as x increases)

So here's my problem. I don't know how to do partial derivatives, except in the most basic way, or how to apply the propagated error equation.

The Attempt at a Solution



My attempt:

Error Ru = (Rs)\sqrt{}((1/(x(1-x)))^2(\sigma x)^2 + (\sigma Rs/(Rs))^2))

With \sigma whatever being the standard deviation.

The question here is, did I do this correctly?

If I did do this correctly, should I get one value for my error propagation for the entire series of measurments or should I get 3 different error propagations (3 different x, 3 different Rs)?

Will there be 3 different values for error propagation then?

Thanks for your help!

P.S. This is my first post, but I have been using PF for physics help the last 2 semesters, awesome website. This is the first time I've ever had to post something on here :)
 
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