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Math Help - Calculus Spreadsheet for an RC circuit

  1. #1
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    Calculus Spreadsheet for an RC circuit

    Calculus
    I have recently been given the following question but I have no idea how to differntiate the equation or plot the equations. Can you please help me?

    Capacitor = 100 nF
    Resistor = 47 kΩ
    Supply voltage = 5 V
    Charging characteristic for a series capacitive circuit:


    v=V(1- e-^(1/T)) where T=CR



    n Use a spreadsheet to plot the charging curve over the range 0 to 20 ms (milliseconds).
    n Differentiate the charging equation and find the rate of change of voltage at 6 ms.
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  2. #2
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    re: Calculus Spreadsheet for an RC circuit

    Quote Originally Posted by maali5 View Post
    Calculus
    I have recently been given the following question but I have no idea how to differntiate the equation or plot the equations. Can you please help me?

    Capacitor = 100 nF
    Resistor = 47 kΩ
    Supply voltage = 5 V
    Charging characteristic for a series capacitive circuit:


    v=V(1- e-^(t/T)) where T=CR



    n Use a spreadsheet to plot the charging curve over the range 0 to 20 ms (milliseconds).
    n Differentiate the charging equation and find the rate of change of voltage at 6 ms.
    corrected equation ... voltage across the capacitor is a function of time.
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  3. #3
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    Re: Calculus Spreadsheet for an RC circuit

    hint on how to differentiate the equation: V and T are constants. we can re-write the equation as:

    v = V - Ve^(-t/T).

    the first term in this difference disappears in the derivative, so we only have to take the derivative of -Ve^(-t/T).

    the -V in front is just a constant, so v'(t) = (-V)(d/dt)(e^(-t/T))

    and e^(-t/T) is of the form e^(at), where in this particular case, a = -1/T.
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    Re: Calculus Spreadsheet for an RC circuit

    Skeeter: Thanks, I made a spelling mistake


    Question: Use a spreadsheet to plot the charging curve over the range 0 to 20 ms (milliseconds)

    T=CR

    T=0,1 x 47000
    t=0.00470



    Answers:

    T v=V(1- e-^(t/T)) How can I draw the spreadsheet when answers =5?

    0 v=5(1- e-^(0/T)) 0
    1 v=5(1- e-^(1/T)) 5
    2 v=5(1- e-^(2/T)) 5
    3 v=5(1- e-^(3/T)) 5
    4 v=5(1- e-^(4/T)) 5
    5 v=5(1- e-^(5/T)) 5

    6 Etc,
    ..
    ...
    ...
    20 v=5(1- e-^(20/T)) 5





    Deveno: Cheers for the hints
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  5. #5
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    Re: Calculus Spreadsheet for an RC circuit

    Quote Originally Posted by maali5 View Post
    Skeeter: Thanks, I made a spelling mistake


    Question: Use a spreadsheet to plot the charging curve over the range 0 to 20 ms (milliseconds)

    T=CR

    T=0,1 x 47000
    t=0.00470



    Answers:

    T v=V(1- e-^(t/T)) How can I draw the spreadsheet when answers =5?

    0 v=5(1- e-^(0/T)) 0
    1 v=5(1- e-^(1/T)) 5
    2 v=5(1- e-^(2/T)) 5
    3 v=5(1- e-^(3/T)) 5
    4 v=5(1- e-^(4/T)) 5
    5 v=5(1- e-^(5/T)) 5

    6 Etc,
    ..
    ...
    ...
    20 v=5(1- e-^(20/T)) 5





    Deveno: Cheers for the hints
    time is in milliseconds, not seconds ...

    t should be 0, .001, .002, .003, ... , .020
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    Re: Calculus Spreadsheet for an RC circuit

    Genius! but can you explain how to calculate it.

    I know 1 seconds is 1000millisecond.
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    Re: Calculus Spreadsheet for an RC circuit

    I have done the graph and have the attached to the page.

    Is it correct?

    Sooory to bother you with questions
    Attached Files Attached Files
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    Re: Calculus Spreadsheet for an RC circuit

    Quote Originally Posted by maali5 View Post
    Genius! but can you explain how to calculate it.

    I know 1 seconds is 1000millisecond.
    sure ...

    V(.001) = 5 \left(1 - e^{-\frac{.001}{.0047}} \right) = 0.95282...

    ... and so on. You should do some research on how to do it in a spreadsheet ...

    how to generate a graph in excel - Google Search
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