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Simple RLC Circuit problem

  1. Oct 16, 2006 #1
    Please help me to solve this RLC circuit problem. I am completely confused.If you give me the direct answer it would be much appreciated.
    For the series RLC circuit in Figure, find the input/output
    difference equation for

    1.[tex] y(t)=v_{R} [/tex]
    2.[tex] Y(t)=i(t) [/tex]
    3.[tex] y(t)=v_{L} [/tex]
    4.[tex] y(t)=v_{C} [/tex]

    I have attached the Circuit diagram in a .jpg file.
     

    Attached Files:

    Last edited by a moderator: Nov 28, 2006
  2. jcsd
  3. Oct 17, 2006 #2

    berkeman

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    Staff: Mentor

    You must show your own work in order for us to help you (PF homework forum rules). Would KCL or KVL be the best way to start?
     
  4. Oct 17, 2006 #3
    Hey first I tried taking the KVL around the loop
    something like
    [tex] -x(t) + v_c(t) + v_L (t) + v_R (t) = 0 [/tex]----(1)
    replaced v_L(t) with first order Ldi_L(t)/dt and make an equation for
    [tex] v_C(t) [/tex]
    and then as its in series I tried to write a function for
    [tex] i_L(t) = \frac {v_R (t)} R [/tex]------(2)
    and for [ tex ] v_R(t)/R=C \frac {dv_c(t)} {dt} [/tex]----(3)
    Then tried sub (3) in (1)
    and got
    [tex] v_C(t) = x(t) - \frac {L} {R} dv_R(t)/dt - v + R(t)[/tex]----(4)
    and then tried sub it i eqn 3. and didnt come up with a satisfactory result.
    Please help.
    Thanks
     
    Last edited by a moderator: Nov 28, 2006
  5. Oct 18, 2006 #4

    SGT

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    In series circuits you should always use [tex]v_C[/tex] as the independent variable (and [tex]i_L[/tex] in parallel circuits).
    Since the current is the same for all elements, write [tex]v_L[/tex] and [tex]v_R[/tex] as functions of the current. Finally write the current as a function of [tex]v_C[/tex].
     
  6. Oct 18, 2006 #5
    Thank you very much for your info SGT, would you please help little bit more.
     
  7. Oct 18, 2006 #6

    SGT

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    Make the substitutions I suggested in your equation 1. More help will only be provided after you show some work.
     
  8. Nov 23, 2006 #7
    I tried And I am not going anywhere. please help
     
  9. Nov 23, 2006 #8

    SGT

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    Post what you have done and I will give you more hints.
     
  10. Nov 27, 2006 #9
    solution so far

    heres what I got so far.. please help after this point..
    thanks
     

    Attached Files:

  11. Nov 28, 2006 #10

    SGT

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    In the second equation don't use the integral term. Keep it as [tex]V_C(t)[/tex].
    In the two other terms replace i by [tex]C\frac{dV_C}{dt}[/tex]. You get a second order equation in [tex]V_C[/tex]
     
  12. Nov 28, 2006 #11
    Would you please not mind to show me please. I have tried this so far. please help after this.
    thanks
     
  13. Nov 28, 2006 #12

    SGT

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    The rules of the forum are that you must do your work. We only give hints. Rewrite the second equation with the suggestions I made and post it here.
     
  14. Dec 6, 2006 #13
    The easiest way to solve any RCL circuit with an input vs(t) is by a difference equation.

    Let curr= (q1-q0)/dt


    q2=2.*q1-q0 + dt**2*( -q1/(L*c) -(R/L)*curr +vs(t-dt) ).

    Then everything else follows ,

    Vc(t) = q2/C , VL = L * ( q2-2*q1+q0)/dt^2 , VR = R*(q2-q1)/dt
    SEE http://www.geocities.com/serienumerica/RCLfree.doc
     
    Last edited: Dec 6, 2006
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