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CR Circuit Question (Calculus)

  1. Jun 25, 2013 #1
    A capacitor and resistor are connected as shown across a 10V d.c. supply. The voltage across the capacitor will increase at an exponential rate given by the equation
    v = V - Vet/CR
    a) Plot the graph of the capacitor voltage from the equation for values of t between 0 and 24 seconds.
    vc = V (1-et/CR) , V = 10v, Capacitor = 100µF, Resistor = 47kΩ
    CR = 100µF times 47kΩ = 4.7
    done part a. but I need someone to check it for me please?

    (b)From the graph determine its gradient at t = 5 seconds.
    I have done the graph and after calculating it; it gives me a gradient of -10??? I don't know if that's the right answer.

    (c) Using calculus determine the gradient of the equation and from this the gradient when t = 5 seconds.
    I have attempted it my way and I am not getting the right answer. I have been told by the teacher that the answer should be in minus and both gradient answer should be close.
    So, any help would be appreciated.
    thanks
     

    Attached Files:

  2. jcsd
  3. Jun 25, 2013 #2

    Mark44

    Staff: Mentor

    That's not what you show in the attached image, which is -0.1. Is the slope -10 or -.1? The slope is the vertical rise (or drop) divided by the horizontal run.
    Your derivative is incorrect. You are not using the chain rule correctly.

    Also, be consistent with the letters you use. You are using both V and v, which is confusing, since these could represent different quantities.
    One more thing: since this is a calculus problem, it should NOT be posted in the Precalculus section. I am moving it to the Calculus & Beyond section.
     
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