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First order transient circuit

  1. Nov 15, 2015 #1
    1. The problem statement, all variables and given/known data
    Captura de pantalla 2015-11-15 a las 14.01.12.png

    It asks me to find io(t=0-), io(t=0+), and Vc(t=0-). C=100μF R= 2kΩ
    2. Relevant equations
    V=I*R, i(t)= i(∞)+[i(0+)-i(∞)]*e-t/τ, Vc(0-)=Vc(0+)

    3. The attempt at a solution

    I first tried to calculate Vc(0-) as it will be the same as Vc(0+), stating that at t=0- the capacitor acts as an open circuit because it's been fully charged (the switch has been off since -∞), and I think it's 24V but I'm not sure about that. I also calculated io(0-), which is 2A, but I couldn't go any further.

    Thank you guys.
     
  2. jcsd
  3. Nov 15, 2015 #2

    gneill

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    Staff: Mentor

    Can you show some details of your calculations for initial values of Vc and io?

    To me, 24 V looks too low and 2 A looks to large...
     
  4. Nov 15, 2015 #3
    You're right about the io, I believe it should be 36-12=io(2000+3*2000+2*2000) io=2x10-3 A. For the Vc I just did 36-12, but now that I think of it maybe it's 32, as the voltage drops 4V in the first resistance. I struggle a lot to calculate voltages when the capacitor is in the middle of the circuit.
     
  5. Nov 15, 2015 #4

    gneill

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    Staff: Mentor

    Those are better values :smile: You should always lay out the equations, particularly to confirm any "intuitive" results.
     
  6. Nov 15, 2015 #5
    Yeah you're right, thanks. I'm now trying to calculate io(0+) and io(∞). For io(0+) I replaced the capacitor for a voltage source of 32V (assuming the other calculations were right) and applying KVL I figured that the intensity should be 32/6000= 5,3x10-3. But i'm not sure how the capacitor acts when t=∞ /:
     
  7. Nov 15, 2015 #6

    gneill

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    Staff: Mentor

    At steady state, capacitor currents go to zero. Effectively they "look like" an open circuit to the rest of the circuit. So for t=∞ remove the capacitor and find the potential across the points where it was connected.

    Fig1.png
     
  8. Nov 15, 2015 #7
    Thank you very much @gneill, my teacher posted the solution and it turns out the second calculations I assumed (with your help) were right! :D Do you know any good books with this type of exercices so I can practice for my exam? Thank you again for your time.
     
  9. Nov 15, 2015 #8

    gneill

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    Staff: Mentor

    Well done.

    I don't know of any particular books, but a Google search on "first order circuits examples" will turn up lots of hits.
     
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