Laplace Transform in an RC Circuit

Discussion in 'Homework Help' started by juicebox4158, Nov 18, 2012.

  1. juicebox4158

    Thread Starter New Member

    Nov 18, 2012
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    Homework and i have no idea how to attack this... please help me!?!
    i am soo lost that i dont known what u4 is for... if someone could walk me thought this. please... see attachment if the problem.

    consider the RC circuit shown below with an exponentially decaying voltage source. The voltage is a
    function of time as given below.




    The voltage source turns on with a voltage of 2 at time t = 4 and then decays exponentially as t increases.



    The differential equation for the voltage across the capacitor is




    ( ).



    Suppose the initial voltage across the capacitor is ( ) . Taking the (unrealistic) values R = 1 and C =
    1/3 and using V(t) given above, we have the initial value problem
     
  2. juicebox4158

    Thread Starter New Member

    Nov 18, 2012
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    0
    i have not taken circuit yet. and the teacher in this class is assuming we know about this stuff already
     
  3. WBahn

    Moderator

    Mar 31, 2012
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    4,796
    So why are you taking a class that assumes you have had Circuits if you haven't?

    But, as I read the problem, I don't see where any knowledge of circuits is expected. You are GIVEN the differential equation that would normally come from performing a circuit analysis. And, like most math folks, completely ignores the fact that these are physical quantities that have units associated with them. But, be that as it may, you are simply being asked to solve a differential equation (the topic of this course) using Laplace transforms.

    As for what u4 is for, that is almost certainly something that was covered in this course. Look it up in your text. Look for something like "unit step function". If you compare the equation for V(t) that they give with the verbal description provided around it, you should be able to figure out what the function u_4(t) has to look like.
     
  4. juicebox4158

    Thread Starter New Member

    Nov 18, 2012
    4
    0
    the class does not have pre or co req of circuits but after playing around with it i think i found that the laplace transform is 2e^4u/s(s-2)^2...?
     
  5. juicebox4158

    Thread Starter New Member

    Nov 18, 2012
    4
    0
    multiping both sides by 3... getting sV'c + 3Vc = 2e^4u/ (s+1)^2... solving for V i would get the right side all divided by (s+3)...
     
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