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Capcitor transient problem

  1. Nov 1, 2012 #1
    1. The problem statement, all variables and given/known data
    Ok so I have attached the question im working on. Capacitor transient question.jpg
    Basically when I have the circuit before or after switching in steady state I believe the current will equal zero. However if this is the case, how do I determine what happens immediately after switching?

    2. Relevant equations
    i(t) = A + Be-t/tau
    tau = RC
    (capacitor in steady state becomes an open circuit)
    3. The attempt at a solution
    tau = 1000x1000x10-6 = 1
    i(0-) = 0 = A+B
    i(0+) = 0 = B
    therefore A = 0?
     
  2. jcsd
  3. Nov 1, 2012 #2

    berkeman

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    Staff: Mentor

    i(0+) is not zero. You have a fully charged capacitor connected to a resistor at that time. You have the correct overall equation:

    i(t) = A + Be-t/tau

    Now you just need to solve it given the initial condition of the charged capacitor which starts to discharge through the resistor after t=0...
     
  4. Nov 1, 2012 #3
    sorry that was meant to be i(∞) = 0 = B

    i(0+) is what I want to know how to work out.
     
  5. Nov 1, 2012 #4

    berkeman

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    That may be true, but it's not relevant to the solution really. What is i(0+)?

    Can you visualize what happens? Some initial current flows based on the initial voltage and the resistance, and that current decays according to the equation. And since you correctly calculated tau as 1 second, and they ask for something after 1 second, can you guess the answer?
     
  6. Nov 1, 2012 #5
    Ignore this post I did it before I saw your last one sorry
    Actually sorry I see where I went wrong that should be i(∞) = 0 = A
    But that will still give me A+B=0 initially thus giving B = 0??
     
  7. Nov 1, 2012 #6

    berkeman

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    No. What is the initial current? It's the initial cap voltage divided by the resistance, right? In fact, the current at any time is the cap voltage divided by the resistance, right?

    Use that and e0=____ (fill in the blank) to figure out the constants...
     
  8. Nov 1, 2012 #7
    Ok so the initial current immediately after switching will be 12mA?
    Therefore B will equal 12x10-3?
    Thus i(t) = 12x10-3e-t?
     
  9. Nov 1, 2012 #8

    berkeman

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    You left the time constant divider out of the exponent. Even though it is "1", you should still show something there to show that the units work. So you could put a 1s in the denominator of the exponential term, for example. Other than that, it looks good. What is the answer at 1 second?
     
  10. Nov 1, 2012 #9
    Ok, I'll remember that for next time.
    I got i(1) = 4.415mA
     
  11. Nov 1, 2012 #10

    berkeman

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    Staff: Mentor

    Good! And notice how after 1 second, the value has decayed to 1/e of its initial value. That's how those exponential decays work. :smile:
     
  12. Nov 1, 2012 #11
    Ahh ok thats actually really easy now that I see how it works. I never understood how the initial (0+) condition worked before.
    Thanks for all the help :)
     
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