Simple RLC Circuit problem

  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. berkeman

    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. 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.
    Last edited by a moderator: Nov 28, 2006
  5. SGT

    SGT 0

    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. Thank you very much for your info SGT, would you please help little bit more.
  7. SGT

    SGT 0

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

    SGT 0

    Post what you have done and I will give you more hints.
  10. solution so far

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

    Attached Files:

  11. SGT

    SGT 0

    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. Would you please not mind to show me please. I have tried this so far. please help after this.
  13. SGT

    SGT 0

    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. 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
    Last edited: Dec 6, 2006
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