1. Limited time only! Sign up for a free 30min personal 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!

Circuit Analysis with Laplace Transforms

  1. Nov 2, 2016 #1

    gmm

    User Avatar

    1. The problem statement, all variables and given/known data
    circuit1.png

    2. Relevant equations
    V=IR
    All of them actually

    3. The attempt at a solution
    So I Started off by transforming the voltage source into the 's' domain
    vs(s) = (4/s) -(4/s)*e-.5t

    I know the initial conditions are zero, in other words at t=0, the voltage and currents at the capacitors are all 0. which means that that my capacitor 1 can be expressed as an impedance: 106/s. and capacitor 2 as : 3*105/s. All the resistors stay the same.
    So now the circuit is transformed into the 's' domain which basically means its comprised of one voltage source and 5 impedences?
    This is kind of where I'm stuck... I know that for a Capacitor in the 's' domain the voltage is Ic/sC + vc(0-)/s.. in this case Initial conditions are zero so for both capacitors Vc = Ic/sC ... I now need to find the current I at each capacitor right?
    If so I'm not sure how to go about this, all of the examples in my book only show steps for circuits that have components either all in series or all in parallel. Node Voltage Analysis? Current Mesh Analysis? Whats my next step??
     
  2. jcsd
  3. Nov 2, 2016 #2

    gneill

    User Avatar

    Staff: Mentor

    Node voltage analysis (nodal analysis) looks like a good choice: There's only one essential node.

    The Laplace impedance of a capacitor is ##\frac{1}{sC}##.
     
  4. Nov 2, 2016 #3

    Hesch

    User Avatar
    Gold Member

    Calculate the transfer functions v1(s)/vs(s) and v2(s)/vs(s).

    ( Calculate the current, I(s), through the 4 rightmost components. Then v(s) = Z(s) * I(s) for both RC pairs. )

    Knowing e.g. v2(s)/vs(s) → v2(s) = v2(s)/vs(s) * vs(s).

    Then inverse Laplace transform.
     
  5. Nov 3, 2016 #4

    rude man

    User Avatar
    Homework Helper
    Gold Member

    I suggest labeling your components C1, C2, R1 etc rather than working with numbers up front. Then you can also use dimensional analysis for checking the math. Otherwise you're on the right track.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted