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RC circuit switch

  1. Mar 19, 2014 #1

    Maylis

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    Gold Member

    1. The problem statement, all variables and given/known data
    2. The switch in the circuit below had been closed for a long time before it was opened at t = 0. Given that Vs = 10 V, R1 = 20 kΩ, R2 = 100 kΩ, C1 = 6 μF, and C2 = 12 μF, determine i(t) for t ≥ 0.


    2. Relevant equations



    3. The attempt at a solution
    For this problem, my initial thought is that the voltage must be the same across C1 and C2, since they are open, no current runs through R1 nor R2, so the voltage across both is 10 V. Then, I use the equation for the voltage as a function of time, and get the expression. I then take the derivative and multiply by the equivalent capacitance to get my expression.

    I got a negative answer, I'm not sure if this is right. It would mean the current is the opposite direction that I labeled. Would the current go from the larger capacitor to the smaller one?
     

    Attached Files:

  2. jcsd
  3. Mar 19, 2014 #2

    gneill

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    Staff: Mentor

    If the potentials on the capacitors are identical when the switch opens, what does that tell you about the current through R2?
     
  4. Mar 19, 2014 #3

    Maylis

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    Yes, the current is zero. Does that mean the current is zero at all times when the switch is turned off? I think my voltage expression is correct, so I just take the derivative to find the current expression.
     
  5. Mar 19, 2014 #4

    gneill

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    Yes, the current is zero. No potential difference across R2 means that no current will flow. If no current flows then the potentials on the capacitors cannot change over time... what does that tell you about i(t) ?
     
  6. Mar 19, 2014 #5

    Maylis

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    i(t) = 0 for all t?
     
  7. Mar 19, 2014 #6

    gneill

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    Yup. Well, for all t ≥ 0 that is.
     
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