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RC Circuit , Calculate Time Constant

  1. Mar 11, 2012 #1
    1. The problem statement, all variables and given/known data


    Given this diagram:
    eafme9.png

    Picture mirror: http://i.minus.com/1331507225/3XjEXOAlTaoJBoBuQFoJiQ/itFBvAiitDZQc.png

    With S1 switch closed and S2 switch left open, I am trying to find the time constant

    2. Relevant equations

    I know τ = RC for a basic circuit, but how would you calculate it for a complex circuit? Is R the equivalent resistance to the battery?

    Q=VC
    V=IR

    i = dq/dt
    dq/dt + Q/τ - emf / R = 0



    3. The attempt at a solution

    I start with junction rule and loop rule

    I1 = I2 + I3
    -emf + I1R1 + Q/C + I2R2 = 0
    =emf + I1R1 + I3R3 + I3R4 = 0

    At this point the teacher says I2 = dq/dt and we need to get rid of I1 so we can put something next to the C in Q/C.

    I use I1 = I2+I3 in junction rule and put it into loop rule #2, getting:

    -emf + (I2 + I3)R1 + I3R3 + I3R4 = 0
    I2R1 + I3(R1+R3+R4) = emf
    I3 = (emf - I2R1) / (R1+R3+R3)

    Then I put I3 in for the I1 eq.

    I1 = I2 + (emf - I2R1) / (R1+R3+R3)

    At this point it's so messy and confusing I think I am doing it all wrong.

    The baseline she is giving us is that

    dq/dt + Q/[foo] - emf/[bar] = 0

    where [foo] would be the time constant. In a simple circuit she gives [foo] = RC and [bar] = R
     
    Last edited: Mar 11, 2012
  2. jcsd
  3. Mar 11, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    I do not see any diagram...


    ehild
     
  4. Mar 11, 2012 #3
    Weird, it's possible minus.com isn't showing up for you. I will upload it
     
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