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Calculating charge uncertainty

  1. Jul 15, 2006 #1
    Problem 1
    Given: 2 capacitors in a series, each capacitor's farad & voltage across.
    Voltage uncertainty 1%, capacitor uncertainty 5%
    C1: 1019microFarads C2: 553microFarads
    V1: 3.58 volts V2: 6.56 volts
    Uncertainty: 5% for CAPs & 1% for Volt

    Find Q for each: Q1=3648 Coulombs Q2=3627 Coulombs
    Find Q's +/-(variance): SQRT(.05^2 + .01^2) = .051
    Q1 Variance: 186 Q2 Variance: 185

    Now for the question:
    find Q.total Q.total=C.eq * V.total => 3634.84
    What is the Uncertainty of Q.total??

    Does anyone know how to find Q.total's variance?
    I've looked through my text and online, still no luck.

    If anyone could make a suggestion, I'd be very appreciative.

  2. jcsd
  3. Jul 28, 2006 #2
    Hmm.. you should consult a book on statistics. I think that Gauss proved something about how to calculate the variance.

    For example, if you have the forumla Q = A * B and you know the variances of A and B, then the variance of Q can be calculated. If I am not mistaken you find it with
    Var(Q) = dQ/dA * Var(A) + dQ/dB * Var(B)
    and this forumla applies generally.

    I might have confused the variance with the standard deviation or something so there might be a squareroot over the whole right hand side...
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