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LC circuit: finding the time interval between maximum potential and maximum current

  1. Mar 20, 2012 #1
    1. The problem statement, all variables and given/known data
    The total energy stored in an LC circuit is 2J. The inductance is 10^-2 H and the capacitance is 100 μF. What is the time interval between a maximum current through the inductor and a maximum potential difference in the capacitor?


    2. Relevant equations
    T = 2∏/ω
    ω = √(1/LC)


    3. The attempt at a solution

    I understand how the two above equations can be used to find T. However, in the answer key I have, it requires you to take the T you get and divide by 4 to find the time. I don't understand where this step comes in.

    Also, is it possible to solve this question using the equation that tells us the charge on a capacitor (q = QV - e^(-t/RC)). I initially tried setting this up to find t when q = 0 and t when q = Q. However, is this not possible because we do know know and cannot find R? Or is there some other reason why using this equation won't work? Thanks!
     
    Last edited: Mar 20, 2012
  2. jcsd
  3. Mar 20, 2012 #2

    ehild

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    Re: LC circuit: finding the time interval between maximum potential and maximum curre

    It is a resonant LC circuit,without resistance. A similar equation you wrote (q = QV - e^(t/RC), which is not correct at all) would hold for a capacitor and resistor.
    The current in the LC circuit changes with time as Imax sin (ωt), the voltage is U=±Umax cos(ωt) across any of the inductor and capacitor. The power stored in a capacitor is 1/2 CU2, the same in the inductor is 1/2 L I2. Plot U2 and I2 vs time. How many times during a period you get a maximum of either U2 or I2?

    ehild
     
    Last edited: Mar 20, 2012
  4. Mar 20, 2012 #3
    Re: LC circuit: finding the time interval between maximum potential and maximum curre

    Oh, I see, thanks. Can you explain why we have to divide by 4 as the final step?
     
  5. Mar 20, 2012 #4

    ehild

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    Re: LC circuit: finding the time interval between maximum potential and maximum curre

    I edited my previous post, read it.

    ehild
     
  6. Mar 20, 2012 #5
    Re: LC circuit: finding the time interval between maximum potential and maximum curre

    Sorry, but this particular subject material is largely over my head. I can't really follow what you suggest I do. Is there another way to look at it? Alternatively, is it always true that one period includes 4 cycles, such that you always divide the period by 4 to find the time it takes to go from greatest charge on the capacitor to largest current? Sorry if I'm being annoying!
     
  7. Mar 21, 2012 #6

    ehild

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    Re: LC circuit: finding the time interval between maximum potential and maximum curre

    Why don't you plot U(t) and I(t)? When the current is maximum, the potential difference is zero, as U=LdI/dt. It will be maximum after pi//2 phase difference.

    ehild
     

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