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Homework Help: RLC circuit with DC

  1. May 21, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-5-21_15-17-45.png

    2. Relevant equations


    3. The attempt at a solution
    I used the loop rule where ##ΣΔV=0## and junction rule.
    From here I get 4 equations
    ##i_3=i_1+i_2##
    ##ε-i_3R_3-i_1R_1-L(di\dt)=0##
    ##ε-i_3R_3-i_2R_2-Q\C=0##
    ##i_1R_1-L(di\dt)+Q\C+i_2R_2=0##

    1-I said Q\C will dissapear since Q=0 at t=0. But what about (di\dt) ? Is (di\dt)=0 ? I think it should be, but If its zero I didnt understand why it asked again since we need to claim its zero to solve the question.If its not zero then I couldnt solve the upper 4 equations.İts like something is missing.
     
  2. jcsd
  3. May 21, 2017 #2

    cnh1995

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    You do not need any equations here.
    Just apply what you know about the behaviour of L and C at the moment of energization i.e. t=0.

    What is the current through the inductor "just before" the switch is closed?
     
  4. May 21, 2017 #3
    Isnt it a time depented value ? Function like I(t)=Awcos(wt)+Bwsin(wt) ? I dont know...
     
  5. May 21, 2017 #4

    cnh1995

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    Yes.
    But you only need to know what happens at t=0.
     
  6. May 21, 2017 #5
    Can you help a bit more..I couldnt see the solution
     
  7. May 21, 2017 #6

    cnh1995

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    There was no source in the circuit before the switch is closed.
    So what can you say about the inductor current "before" the switch is closed?
     
  8. May 21, 2017 #7
    Zero ?
     
  9. May 21, 2017 #8

    cnh1995

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    Yes. So what is the inductor current just after closing the switch?
     
  10. May 21, 2017 #9
    zero ?
     
  11. May 21, 2017 #10

    cnh1995

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    Yes.
     
  12. May 21, 2017 #11
    You could have just say yes.. ? Are my equations wrong ? Cause I need to find currents.
     
  13. May 21, 2017 #12

    cnh1995

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    I just answered your question. You need to be more specific about your problems.
    Only at t=0. As I said, you do not need any of the equations you've written.

    What can you say about the current through the capacitor at t=0 i.e. just after the switch is closed?
     
  14. May 21, 2017 #13

    cnh1995

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    Ok. I think you do need to solve the equations for solving b and c because of presence of R1. The current through R1 is governed by both L and C values. My apologies.
    But you do not need them to know i1 and i2 at t=0.
     
  15. May 21, 2017 #14
    Question asks that,I need to know
     
  16. May 21, 2017 #15

    cnh1995

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    Yes. So what is the current through the capacitor at t=0?
    How does a capacitor behave when energized at t=0?
     
  17. May 21, 2017 #16

    ehild

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    The fourth equation is not needed. And di/dt should be di1/dt.
    So you have the system of equations
    ##i_3=i_1+i_2##
    ##ε-i_3R_3-i_1R_1-L(di_1/dt)=0##
    ##ε-i_3R_3-i_2R_2-Q/C=0##
    Substitute ##i_3=i_1+i_2## for i3. You might need the relation between Q and i2. Then you have a system of equations for two currents and their derivatives.
    The problem asks the initial values. You found that i1(0)=0. What about i2(0)? Answer @cnh1995's question.
     
    Last edited: May 22, 2017
  18. May 22, 2017 #17
    Zero ? At the begining there should be no current ? Seems wrong but also makes sense.
    I see well I find ##-i_2R_2=Q\C## but in any case at t=0,Q=0
     
  19. May 22, 2017 #18

    BvU

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    Yes but for t>0 you should get something else
     
  20. May 22, 2017 #19
    upload_2017-5-22_10-48-55.png
    Rest of the question.Well at ##t=∞## there would be no current on the capacitor brench.

    In the brench where inductor exist, there would be current.I can write an equation like, ##ε-iR_3-iR_1-L(di\dt)=0##.Do I need to solve this ? I couldnt directly see the answer.
    For (e) probably its ##εC##.
    For (f), I need to find that current passes through inductor,I know the equations and ıf my answer to e is true then I can find it easily.
     
  21. May 22, 2017 #20

    ehild

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    No, it is not true . You ignored i3, and it is not zero at t=0.
     
  22. May 22, 2017 #21

    BvU

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    Yes, no and Oh? :smile: What do you expect of the ##dI/dt## in the last term ?
    (e) No. draw the circuit a little differently: ##\varepsilon## on the left and all the R etc on the right
    (f) What you say is true...
     
    Last edited: May 22, 2017
  23. May 22, 2017 #22

    BvU

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    Shame on me o:). Wake up first and then check PF. Over to you, Ersbeth
     
  24. May 22, 2017 #23
    I didnt understand...I ll ask my proffesor I guess...
     
  25. May 22, 2017 #24

    ehild

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    Substitute I3=I1+I2 into your second and third equations. What do you get?
    Use that i1=0 and Q=0 at t=0 in the second equation. What is i2 at t=0?
    Knowing i2(0) and i1(0) you get d(i1)/dt from the first equation.
     
  26. May 22, 2017 #25
    I find ##i_2=2A## and ##di_1\dt=6A\s##
     
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