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Ambiguity in finding errors using natural logarithm method

  • #1

Homework Statement


[/B]
I was reviewing this stuff and although I excelled at it once, I seem to forget some of it.
For example, please consider this:

Homework Equations



[itex]R_C=\frac {R_1R_2} {R_1+R_2} + R_3[/itex]

Here's the correct formula for its error:

[itex]\Delta R_C=\frac {R_1R_2} {R_1+R_2} \left[ \frac {\Delta R_1} {R_1} +\frac {\Delta R_2} {R_2}
+\frac {\Delta R_1 + \Delta R_2} {R_1+R_2}\right] + \Delta R_3[/itex]

While mine would be this and I don't know what happened to the [itex]\Delta R_3[/itex] in the formula above:

[itex]\Delta R_C=\frac {R_1R_2} {R_1+R_2} \left[ \frac {\Delta R_1} {R_1} +\frac {\Delta R_2} {R_2}
+\frac {\Delta R_1 + \Delta R_2} {R_1+R_2} + \frac {\Delta R_3} {R_3}\right][/itex]

Another equation is:

[itex]I_1=\frac {R_3V_1+R_2(V_1+V_2)} {R_1R_2+R_2R_3+R_3R_1}[/itex]

Which I don't know the correct solution to finding its error, but here's my attempt at a solution:

The Attempt at a Solution



[itex]\Delta I_1= I_1 \left[ \frac {\Delta R_3 \Delta V_1+\Delta R_2 \Delta V_1+ \Delta R_2 \Delta V_2} {R_3V_1 + R_2(V_1+V_2)} + \frac {\Delta R_1 \Delta R_2+ \Delta R_2 \Delta R_3+ \Delta R_3 \Delta R_1} {R_1R_2+R_2R_3+R_3R_1}\right] [/itex]

Is this correct, if not, why?

Thank you in advance.
 

Answers and Replies

  • #2
rude man
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For random errors in R1, R2 and R3,
in general dF(x,y,z) = ∂F/∂x dx + ∂F/∂y dy + ∂F/∂z dz
where x, y and z are independent variables.
Apply this to your F(R1,R2,R3).
Fractional error is dF/F.
 
  • #3
haruspex
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Here's the correct formula for its error:
Are you sure? I think it has a sign error.
While mine would be this
I have no idea how you end up with the ΔR3 inside the bracket.
, if not, why?
Impossible to say without seeing your working.
 
  • #4
Are you sure? I think it has a sign error.
Well, as far as I know, I heard that we don't have any negative signs in error equations... I mean between the delta terms.

I have no idea how you end up with the ΔR3 inside the bracket.
How can I brush up on this topic? I'm studying in a different language than English so I can't find English resources for this topic on the Internet. What is this topic called in English textbooks or on the internet? I'm not sure if I do the beginnings right.
 
  • #5
ehild
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How can I brush up on this topic? I'm studying in a different language than English so I can't find English resources for this topic on the Internet. What is this topic called in English textbooks or on the internet? I'm not sure if I do the beginnings right.
Browse "error propagation".
Calculating the absolute error of a function of several independent variables, F(x, y, z...) take the partial derivatives, multiply each with its error and add the absolute values, or add the squares and take the square root of the sum.
The relative error is (ΔF)/F.
In case of multiplication or division, you can add the individual errors, in case of other function you need to determine the partial derivatives.
 
  • #6
haruspex
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Well, as far as I know, I heard that we don't have any negative signs in error equations... I mean between the delta terms.


How can I brush up on this topic? I'm studying in a different language than English so I can't find English resources for this topic on the Internet. What is this topic called in English textbooks or on the internet? I'm not sure if I do the beginnings right.
Posts #2 and #5 have explained how to figure out the expressions. Follow those and post your working.
 

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