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How to find Qmax of a capacitor in parallel RC circuit?

  1. Feb 25, 2013 #1
    1. The problem statement, all variables and given/known data
    i tried using the usual Q=VC to answer this question for a multiloop RC circuit, "What is Q(∞), the charge on the capacitor after the switch has been closed for a very long time?" and my answer was wrong. clearly, i can't find Qmax because the resistors contribute to the voltage drop.
    i can't seep to wrap my head around finding the proper equations for finding Q using kirchoffs laws and end up having multiples unknowns. the image of the schematic is attached. any help? thnx.


    2. Relevant equations

    kirchoff's loop rule and junction rules
    I) I1=I2+I3
    II) -I2R2+Q/C+I3R3=0
    III) -I3R3-I4R4+V-I1R1=0


    3. The attempt at a solution
    based on a previous question, i was able to find I4= V ((Req for R2andR3)+R4+R1)
     

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    Last edited: Feb 25, 2013
  2. jcsd
  3. Feb 25, 2013 #2

    gneill

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    Suppose you were to remove the capacitor from the circuit. What voltage would be presented at the terminals where it was connected?
     
  4. Feb 25, 2013 #3
    removing the capacitor, it would be a regular combination circuit where V3=V2, R3 and R2 would have an equivalent Req= 1/((1/r2)+(1/r3)). but would the current be additive, or equivalent (based on kirchoff's rule i1=i2+i3) ?
    the potential would be same at both junctions.
     
  5. Feb 25, 2013 #4

    gneill

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    By remove I mean cut it out of the circuit and leave its connection points open. Like this:

    attachment.php?attachmentid=56100&stc=1&d=1361820134.gif
     

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  6. Feb 25, 2013 #5
    oh! then only one loop remains. that's what establishes one of the loop equations:
    -i3r3-i4r4+v-i1r1=0.
    here, we'd have known value for V and i4r4, but unknowns for i3 and i1
     
  7. Feb 25, 2013 #6

    gneill

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    If it's a single loop, and all the components are connected in series, what can you say about the current in all the components?
     
  8. Feb 25, 2013 #7
    same throughout. so the equation would simplify to :
    -I(R3+R4+R1)= -V
    the I would be the one i found for R4...?
     
  9. Feb 25, 2013 #8

    gneill

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    Perhaps. I never saw your work for finding that.

    So what's the potential at the output terminals?
     
  10. Feb 25, 2013 #9
    the answer i found for r4 was marked correct, therefore my confident guarantee of it :D.
    just to get clear on the terminology, would the output terminals be the junctions where i1 splits into i3 and i2, or the void created by removing the capacitor?
    i would presume the potential would be the same at either end.
     
  11. Feb 25, 2013 #10

    gneill

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    I intended the "void" as you call it, and as I drew it in the diagram that I provided in a post above. I'm looking for Vc as indicated.
     
  12. Feb 25, 2013 #11
    So maybe in wrong here, but then there are no unknowns?All the R values for the resistors and the V from the battery are given, and current for R4 I found was based on this question,"The switch has been open for a long time when at time t = 0, the switch is closed. What is I4(0), the magnitude of the current through the resistor R4 just after the switch is closed?"

    I'm lost now. What am I solving for?
     
  13. Feb 25, 2013 #12
    the answer i found for r4 was marked correct, therefore my confident guarantee of it :D.
    just to get clear on the terminology, would the output terminals be the junctions where i1 splits into i3 and i2, or the void created by removing the capacitor?
    i would presume the potential would be the same at either end.
     
  14. Feb 25, 2013 #13

    gneill

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    I have no idea what things you solved for before, or what the component values might be since you haven't posted them in this thread.

    I am approaching the problem that you stated in the first post of this thread: "What is Q(∞), the charge on the capacitor after the switch has been closed for a very long time?" So we are looking for Q(∞), right?

    So as far as I know, we are dealing with the problem symbolically (without numerical values to plug in), and the switch has been closed for a long time so that the circuit has reached a steady state with the capacitor charged to its maximum amount. To accomplish this, it would be expedient to find the steady-state potential across the capacitor. That is why the potential across the output terminals that I drew is important; that voltage will be the same as that across the capacitor at steady state.
     
  15. Feb 25, 2013 #14
    you're right. should i post the whole question with all the known values? it might be better approachable then
     
  16. Feb 25, 2013 #15
    so here is the question:

    A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 31 Ω, R3 = 108 Ω and R4 = 141 Ω. The capacitance is C = 44 μF and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.

    The switch has been open for a long time when at time t = 0, the switch is closed. What is I4(0), the magnitude of the current through the resistor R4 just after the switch is closed?
    What is Q(∞), the charge on the capacitor after the switch has been closed for a very long time?

    After the switch has been closed for a very long time, it is then opened. What is Q(topen), the charge on the capacitor at a time topen = 599 μs after the switch was opened?

    What is IC,max(closed), the current that flows through the capacitor whose magnitude is maximum during the time when the switch is closed? A positive value for the current is defined to be in the direction of the arrow shown.

    What is IC,max(open), the current that flows through the capacitor whose magnitude is maximum during the time when the switch is open? A positive value for the current is defined to be in the direction of the arrow shown.
     
  17. Feb 25, 2013 #16

    gneill

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    Okay, that makes things nice and clear :smile:

    Am I correct in assuming that we are working on this part:
     
  18. Feb 25, 2013 #17
    yes sir :D.
     
  19. Feb 25, 2013 #18

    gneill

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    Okay, so I come back to the question, what is the voltage across the open terminals where the capacitor would sit?
     
  20. Feb 25, 2013 #19
    using the equation we reached at before, -I(R3+R4+R1)= -V, i used the current for I4 from part 1 and multiplied it by the sum of the three resitors in the left loop and got 17.135 V .... :S which is greater than V(battery) !
     
  21. Feb 25, 2013 #20

    gneill

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    What's your current value? Remember, this is steady state when there's no current through R2 and the capacitor. This will not be the same current as when the capacitor is first starting to charge up.
     
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