Error Propagation Homework: Wheatstone Bridge

In summary, the conversation is about a lab involving a Wheatstone bridge to find an unknown resistance using a resistance box and a slide wire. The formula for finding the unknown resistance is given, and the individual is seeking help with applying the propagated error equation for their measurements. They are unsure if they have done it correctly and if there should be one value or three values for error propagation.
  • #1
Yatty33
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0

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)[tex]\sqrt{}((1/(x(1-x)))^2(\sigma x)^2 + (\sigma Rs/(Rs))^2))[/tex]

With [tex]\sigma whatever[/tex] 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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  • #2
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1. What is error propagation in the context of a Wheatstone Bridge?

Error propagation in a Wheatstone Bridge refers to the process of determining the uncertainty or error in the final calculated value based on the uncertainties of the individual components of the bridge, such as resistors and voltage sources. This is important in accurately measuring and analyzing data in experiments involving Wheatstone Bridges.

2. How is error propagation calculated in a Wheatstone Bridge?

Error propagation in a Wheatstone Bridge is calculated using the law of propagation of uncertainty, which takes into account the individual uncertainties of the components and their relationship with each other to determine the overall uncertainty in the final calculated value. This can be done using mathematical formulas or through simulation and data analysis.

3. What factors can contribute to error propagation in a Wheatstone Bridge?

There are several factors that can contribute to error propagation in a Wheatstone Bridge, including the precision and accuracy of the measuring instruments, variations in the resistance and voltage values of the components, and environmental factors such as temperature and humidity. It is important to carefully control and account for these factors to minimize error propagation.

4. How can error propagation be reduced in a Wheatstone Bridge?

Error propagation in a Wheatstone Bridge can be reduced by using high-precision and calibrated measuring instruments, carefully selecting and controlling the components used in the bridge, and repeating measurements multiple times to improve accuracy. Additionally, using statistical analysis techniques can help identify and minimize sources of error propagation.

5. What are the practical applications of understanding error propagation in a Wheatstone Bridge?

Understanding error propagation in a Wheatstone Bridge is essential in many scientific and engineering fields, such as electronics, physics, and materials science. It allows for more accurate and reliable data analysis and can help identify and troubleshoot potential sources of error in experiments. This understanding can also be applied to other measurement techniques and systems beyond the Wheatstone Bridge.

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