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Modelling Help

  1. May 16, 2009 #1
    1. The problem statement, all variables and given/known data
    The transient behaviour of a capacitor has been studied by measuring the voltage from across the device as a function of time. The following data has been obtained.

    Time (s)/Voltage (v)
    0 / 10
    1 / 6.1
    2 / 3.7
    3 / 2.2
    4 / 1.4
    5 / 0.8
    6 / 0.5
    7 / 0.3
    8 / 0.2
    9 / 0.1
    10 /0.07
    12 /0.03

    2. Relevant equations

    The following relationship for the change in voltage, V, with time, t, has been proposed:

    DV/DT = -k fcn(v)

    Where k is a constant and fcn(v) could have one of the following forms:

    1. fcn(v) = c (where c is a constant)
    2. fcn(v) = V
    3. fcn(v) = V2

    (fcn is an abbreviation of the term "a function of")

    I am to derive three corresponding expressions for V as a function of time.

    3. The attempt at a solution

    I am having trouble with where to start. I believe the aim is to find which equation, using the data, creates a linear relationship. Any help on how to derive the equations would be much appreciated.
     
  2. jcsd
  3. May 16, 2009 #2
    Have you drawn a plot of voltage vs time? Try using a spreadsheet application such as Excel - where you can use the trend line feature.
     
  4. May 16, 2009 #3

    Doc Al

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    Staff: Mentor

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