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elihid98

Error propagation issue

Hey guys, I need some serious help...

So I am doing my physics IA on the infinite ladder resistor and when I try to propagate uncertainty I get ridiculously big numbers (i.e. 150300%). How can I do it?

This is the problem I am approaching--> n1eIX.jpg (I am adding more and more loops to see if it reaches the golden ratio)

In order to do this, the next resistance is in theory given by the expression attached. So I am propagating uncertainty by adding percentage uncertainties by that expression because I cannot work out the absolute uncertainty of Rn as it is composed of several loops (In order to get more loops you have to multiply, add, etc). However if I add the percentage uncertainty of R0 which is 1,1 three times and I add the percentage uncertainty of Rn (2 times as it appears in the expression) to get the percentage uncertainty of Rn+1, uncertainty becomes cumulative and ridiculously big...

How do I approach this? I only know the value of R0 and its uncertainty which would potentially be R in the diagram shown above. 

Please help!!! please please

 

 

Screen Shot 2016-03-22 at 20.32.21.png

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@elihid98 I'm not sure I understand exactly what you're asking. Yes, I know that you are trying to compute the uncertainty. But the uncertainty for what? Is it for the value of Z (the total resistance)?

If I'm not mistaken, then the goal of your experiment is to figure how the value of Z changes as you keep adding more and more resistors onto the ladder (theoretically Z would approach the golden ratio). And I guess the most straight-forward way to do this is to measure Z directly using an ohmmeter. But then doesn't that mean that the uncertainty of Z is simply the uncertainty of the ohmmeter itself? In other words, I don't really get why you have to do the propagation of error in order to figure out the uncertainty for Z, especially if you have directly measured the value of Z yourself....

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You can't always add the percentage uncertainties. You have to find an expression for error of Rn by using n = 2 onward. This should be more feasible by using a spreadsheet. You can eventually find uncertainty in Rn if you assume all resistors have some same resistance, such as 1 ohm or something. Every time you add, you use absolute uncertainties, and every time you multiply/divide you use percentage uncertainties. Note that with all identical resistors, there should be an expression for Rn. Eventually you should see the uncertainty approach some expression of n as n tends of infinite (this gets more mathematical perhaps more than you were hoping). 

Alternatively you can use the quadratic (root mean squared) formula of calculating error, http://chemwiki.ucdavis.edu/Core/Analytical_Chemistry/Quantifying_Nature/Significant_Digits/Propagation_of_Error. This will result in a much smaller error because it only accounts for data one standard deviation (1 +/-) away. This is derived using definition of standard deviation and multivariable calculus, and the mechanics of using this method is slightly more complicated by the use of the square root, than adding absolute or percentage uncertainties. You should only use this once you are certain you are not making any mistakes using the normal version of propagating errors. 

 
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