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Finding the absolute error for equation of total resistance

  1. May 29, 2017 #1
    1. The problem statement, all variables and given/known data
    Prove the equation for ΔRC. (See the first attachment with the circuit schematic inside)

    2. Relevant equations
    (The equation for RC, in both attachments)

    3. The attempt at a solution
    You can see my attempt at a solution in the second attachment. I'm stuck at the step shown in the picture. Maybe that needs a bit algebra, or my attempt was incorrect.
     

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  2. jcsd
  3. May 29, 2017 #2

    BvU

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    I already have difficulty with the first step: If ##R_C = R_{//} + R_3 ## then it certainly is not so that ##\log R_C = \log R_{//} + \log R_3 ## !
    And then the ##\Rightarrow## is also unjustified.

    I suggest you try to find ##\Delta R_{//}## on its own...
     
  4. May 29, 2017 #3

    mfb

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    ln(a+b) and ln(a) + ln(b) are not the same (first -> second line and also within the second line) and the result is wrong.
     
  5. May 30, 2017 #4
    Thanks a lot, dear BvU! I tried your suggestion and it worked! :smile:
    Yes, I had a big mistake in my first attempt as you mentioned.

    What do you mean by this:
    Is that because of my mistake in taking logarithms or it's generally not considered right to use in these equations?
     
  6. May 30, 2017 #5

    BvU

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    Transition from first line in attachment to second line was in error.
    The transition from before the ##\Rightarrow## to after was also in error, hence my remark.
    $$\ln{R_1 R_2\over R_1+R_2} =\ln R_1+\ln R_2-\ln(R_1+R_2) $$
     
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