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Math Help - Percentage Change

  1. #1
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    Percentage Change

    Q: P=I^2R

    If the percentage error in I is 0.75% and R is 0.25%

    What is the maximum Percentage change in P?

    Could anyone please help me out in this one?
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  2. #2
    MHF Contributor
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    P = I^2 R

    Are we to assume that P, I, and R are all functions of a common variable, maybe 't'?

    If so, we have by the Product Rule dP = I^2 dR + 2*I*dI*R

    Relative error:

    I has 0.75%, or dI/I = 0.0075 ==> I = dI/*0.0075
    R has 0.25%, or dR/R = 0.0025 ==> R = dR/0.0025

    Putting it all together

    dP = I^2 dR + 2*I*dI*R = (dI/*0.0075)^2 dR + 2*(dI/*0.0075)*dI*dR/0.0025 = [dR * dI^2 / 0.0075]*[1/0.0075 + 2/0.0025]

    For Relative Error, calculate dP/P and see all the stuff that cancels out.
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    P = I^2 R

    Are we to assume that P, I, and R are all functions of a common variable, maybe 't'?

    If so, we have by the Product Rule dP = I^2 dR + 2*I*dI*R

    Relative error:

    I has 0.75%, or dI/I = 0.0075 ==> I = dI/*0.0075
    R has 0.25%, or dR/R = 0.0025 ==> R = dR/0.0025

    Putting it all together

    dP = I^2 dR + 2*I*dI*R = (dI/*0.0075)^2 dR + 2*(dI/*0.0075)*dI*dR/0.0025 = [dR * dI^2 / 0.0075]*[1/0.0075 + 2/0.0025]

    For Relative Error, calculate dP/P and see all the stuff that cancels out.
    Dude how do you calculate the dP/P??
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