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RLC circuit, finding relations and forming a differential equation

  1. Dec 5, 2012 #1
    Hello. I'm having a hard time solving this homework question, even though I know I shouldn't... but well.

    Here's the problem :

    jabbfa.png

    -The K switch is closed for a long time, so as to be in a steady state.
    What's the electric charge of the capacitor ? Infer vs tension from this.
    Which current is crossing the inductor ?

    My guess : Charge is 0 because it is totally decharged. The tension of the capacitor is equal to vs so vs=0. The current from the generator is crossing the inductor.

    -At t=0 we open the switch. Find five relations between i, ic, ir, q, and vs, and form a differential equation with vs

    So we have
    i=ic+iR

    I am not sure about tensions... let uc=capacitor tension, ur= resitance r tension, uR = resitance R tension

    is E=ur+uL=uc=uR ?

    if yes then we have E=vs+Ldi/dt and I could find a differential equation with i=ic+ir and replacing ic and ir by ic=C*uc/t and iR=uR/R but it would be useless since E=uc=vs...

    to make it short, I don't get how I can find these relations, please help me.. thanks
     
  2. jcsd
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