1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solve RC Circuit Using Laplace Transforms

  1. Dec 30, 2007 #1
    Find v(t) at t=800ms for the circuit in Figure 1.

    Ans: 802mV



    Writing a single node equation we have

    [tex]\frac{v(t)-2tu(t)}{5}+0.1\frac{dv}{dt}=0.[/tex]

    Taking the Laplace transform we have

    [tex]L\left\{ \frac{v(t)-2tu(t)}{5}+0.1\frac{dv}{dt}=0\right\} .[/tex]

    [tex]tu(t)\Rightarrow\frac{1}{s^{2}}[/tex]

    [tex]\frac{df}{dt}\Rightarrow sF(s)-f(0^{-})[/tex]

    [tex]\frac{V(s)}{5}-\frac{2}{5s^{2}}+0.1sV(s)-0.1v(0^{-})=0[/tex]

    Assume that [tex]v(0^{-})=0[/tex] we have

    [tex]\frac{V(s)}{5}-\frac{2}{5s^{2}}+0.1sV(s)=0[/tex]

    multiplying through by 10 and combing like terms

    [tex]V(s)\left(2+s\right)=\frac{4}{s^{2}}[/tex]

    Solving for V(s) we have

    [tex]V(s)=\frac{4}{s^{2}(s+2)}[/tex]

    Applying the method of residues we have

    [tex]\frac{4}{s^{2}(s+2)}=\frac{A}{s^{2}}+\frac{B}{s+2}[/tex]

    Multiplying throught by [tex]s^{2}[/tex] we have

    [tex]\frac{4}{s+2}=A+\frac{Bs^{2}}{s+2}[/tex]

    [tex]A=\frac{4-Bs^{2}}{s+2}\mid_{s=0}=2[/tex]

    Multiplying through by s+2 we have

    [tex]\frac{4}{s^{2}}=\frac{A(s+2)}{s^{2}}+B[/tex]

    [tex]B=\frac{4-A(s+2)}{s^{2}}\mid_{s=-2}=1[/tex]

    Substituting A and B back into the equation we have

    [tex]V(s)=\frac{2}{s^{2}}+\frac{1}{s+2}[/tex]

    Applying the known Laplace transform pairs we have

    [tex]v(t)=2t+e^{-2t}[/tex]

    [tex]v(800ms)=2(0.8)+e^{-2(0.8s)}=1.802V[/tex]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Dec 30, 2007 #2
    I haven't checked all the details, but you seem to have the right idea.

    What is the question?
     
  4. Dec 30, 2007 #3
    Well my answer is different from that given in the book. My answer is too high by 1V.
     
  5. Jan 8, 2008 #4

    CEL

    User Avatar

    Your partial fraction expansion is wrong. You should have:

    [tex]\frac{4}{s^{2}(s+2)}=\frac{A}{s^{2}}+\frac{C}{s}+\frac{B}{s+2}[/tex]
    Using the residues you have A = 2 and B = 1 as you have found.
    Rewrite the second member with the common denominator and equate the numerator to 4.
    You will find C = -1. This is what you need to find the correct answer.
     
  6. Jan 13, 2008 #5
    Thanks for not giving up on my question.

    Kevin
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Solve RC Circuit Using Laplace Transforms
Loading...