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RC Circuit Test Question

  1. Apr 8, 2008 #1
    1. The problem statement, all variables and given/known data
    Okay, I don't EXACTLY remember the problem statement or the circuit diagram, but I believe I can give enough information to do the problem. On this past quiz, I got 75/100, where there are 4 parts: 2 short answer, 1 part multiple choice, 1 part group test. I got 25 on MC, the group, and 24 on one of the short answer. This RC circuit question I got 1/25! I haven't gotten it back yet, but I thought I knew what I was doing.
    There was a one-loop (obviously series) RC circuit, with, in order from first to last going counter-clockwise from the right side of the loop, an ideal battery, a switch, a capacitor, a resistor, another capacitor, then another resistor. Basically it went
    (A)__R2___C2_(B)_R1__C1__ \__
    l************************l
    l************************+
    l************************V
    l************************-
    l___________________________l
    (Please ignored the asterisks, it was only a method applied to keep the spacing of the rectangle of the loop there in the post.)
    Then it asked to calculate the potential and current at time=0 at (A) and (B), then at t=infinity.


    2. Relevant equations
    Kirchoff's Loop Rule: sum of voltages is 0
    differential equation with charge term and time derivative of charge


    3. The attempt at a solution
    Current at t=0 is 0A for both (A) and (B) because, I forgot to put it down in the statement, but it said the capacitors are initially uncharged. I also said that the potential at both are equal to the battery's voltage, but now that I think about it, that doesn't sound plausible since there is no current. At t=infinity, I used Kirchoff's Loop Rule to solve for the current I
    0=V-Q/C1-IR1-Q/C2-IR2 ---> I(t)=e^(-t/((R1+R2)C(eq)))
    since the current should be everywhere the same on a series circuit. Then, for the potentials, I used Kirchoff's Loop Rule, but for (B) I took out the last two terms since the current "hasn't hit them" to drop the potential. I added the last two terms and solved for (B). Is this incorrect? I seem to be doubting myself now that I only got 1/25, which is like no partial credit. I filled the entire page with work. I also remember when calculating C(eq), I forgot to take 1/C(eq) after using 1/C(eq)=1/C1+1/C2. But that was used throughout the problem, so wouldn't that be double jeopardy to keep charging for that? I'm not sure, I need help please.
     
    Last edited: Apr 8, 2008
  2. jcsd
  3. Apr 8, 2008 #2
    When a long time has passed, the capacitors are fully charged. How could current flow through C1 if it's fully charged?
     
  4. Apr 8, 2008 #3
    I may be wrong but I dont think its best to apply Kirchoff's Loop Rules all too heavily when it comes to RC circuitry. The thing about his method is that it applies to steady state circuits (not so much to dynamic circuits)...although the net voltage = 0V around the circuit seems right. The thing about RC circuits is that there is a current at first, but since capacitors are technically open ends in a circuit, charge simply accumulates on the capacitor plates producing an electric field across the capacitors and, as a result, a voltage. Once the voltage of the capacitors sums up to the voltage of the battery, at that point there is no more effective current along the circuit. The current at t = 0 at point A should be some value greater than 0 and at point B it should technically equal point A. The voltage from A to B could be given as a sum of the voltages across the capacitors and the voltage drop across the resistors; if the net voltage across a circuit is 0V, then the voltage between points A and B at t = 0 should be the voltage of the battery. As t approaches infinite, the voltage across the capacitors should sum up to the voltage across the battery, so it should technically remain constant.
     
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