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Resistors in Series Calculations including Uncertainties

  1. Aug 26, 2011 #1
    Hey, this is my first post ever on PF, and I have done my best to follow the guidelines on posts asking for help with homework. Please know that I am not after the answer just to cheat and get the questions right, I am after the method so that I could do a similar question myself in the future.

    1. The problem statement, all variables and given/known data

    Three resistors in series are 4.0 Ohms, 9.4 Ohms and again 4 Ohms.
    They all have a tolerance or uncertainty of 10%. What is the total resistance including uncertainties?

    2. Relevant equations

    Total resistance in series = R(1) + R(2) + R(3)

    3. The attempt at a solution

    The first part is easy, 4.0+9.4+4.0= 17.4

    Now, I believe that when calculating uncertainty in this situation, you are meant to calculate the uncertainty for each resistor, and then add.

    10% of 4 = 0.4
    10% of 9.4 = .94
    10 % of 4 = 0.4

    Total uncertainty of all resistors combined = 1.74.

    So am I correct in saying that the total resistance in series = 17.4 Ohms + or - 1.74 Ohms, correct? The thing I am worried about is whether it is +- 1.74, or half; 0.84.

    Again, thanks for the help, and please let me know if I have broken any rules or how I can improve my post.

    Thanks.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 26, 2011 #2

    wukunlin

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    if i remember correctly, when the quantities are added of sutracted,

    the absolute error values (I mean the actually error values, not the percentages) are added together like calculating the hypotenuse of a triangle,

    ie say your error values are x,y,z, the final error value should be:
    sqrt(x^2 + y^2 + z^2)
     
  4. Aug 26, 2011 #3
    Hmm. That's interesting. I will ask my teacher about the best approach in this situation. Thank you very much for your reply.
     
  5. Aug 26, 2011 #4

    phinds

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    does the 10% uncertainty mean "plus or minus 5%" or does it mean "plus or minus 10%" ?

    Seems to me it has to mean plus or minus 10%, so I believe your calculations are the right way to do it AND have the right answer.
     
  6. Aug 26, 2011 #5
    The exact questions says: Three resistors are in series. They have values of 4.0 ohms, 9.4 ohms, and 4.0 ohms. All values have an uncertainty of 10%. What is the total resistance including uncertainties?

    I believe that it means "plus or minus 10%", but I am not sure.

    Thank you for your help.
     
  7. Aug 26, 2011 #6

    vela

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    Wukunlin is correct. The idea here is that the value of each resistor is a random variable, and when you sum them, you form a new random variable. The variance of the new random variable is the sum of the individual variances, where the variance is equal to the uncertainty squared.

    An uncertainty of 10% means "plus or minus 10%".
     
  8. Aug 26, 2011 #7

    Dick

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    Tolerance in this case refers to the standard deviation in a normal distribution of the component values. Not the extreme values. You add standard deviation just like wukinlin said. It's a square root of the sum of the squares.
     
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