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AC circuit and standing wave questions

  1. Dec 4, 2013 #1
    1. The problem statement, all variables and given/known data

    1. A 5.0 H inductor is connected to a 120 V rms, 60 Hz ac power supply. Periodically, the energy stored in the inductor reaches a maximum value. What is this maximum value?

    A) 0.010 J B) 0.020 J C) 0.40 J D) 0.80 J E) 10.0 J

    2. A standing wave on a string is represented by the equation y = A sin (kx) cos (ωt). The distance between consecutive nodes is:

    A) ∏/k B) ∏/ω C) 2∏/k D) k/∏ E) ω/∏


    3. The attempt at a solution
    These were two questions from an exam I had today and I wanted to check to see if my thinking was correct? For the first question, I put C.

    I first found the period, 1/f, and got 1/60 = .0167 sec.

    Next, I divided the 120 V rms by 5 H and got an answer of 24 V/H. Finally, I multiplied the frequency into this value and got an answer of 0.40 J. Was this correct?

    For number 2, I rationalized that a node corresponds to half of a wavelength, which is equivalent to pi. And I know that k is equal the number of wave peaks in a wave. Therefore, out of the choices possible, I thought that A made the most sense. If anyone could confirm whether or not that is correct, I would appreciate it.
     
  2. jcsd
  3. Dec 5, 2013 #2

    NascentOxygen

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    Staff: Mentor

    Hi Violagirl. It sounds like you evaluated the expression V/(f L) ?

    That looks suspiciously close to V/(2 Pi f L) which would be the formula for current. You also need a formula relating energy in an inductor to current in it.

    I don't follow that reasoning about k. Take another look at this. First, sketch what the outline (envelope) of the standing wave looks like.
     
  4. Dec 5, 2013 #3
    Thanks for clarifying number 1, it makes more sense now.

    For 2, well I know from the equation that k = 2pi/λ. For a standing wave, λ corresponds to 1/2L. And I know it's half a wavelength, it should be equivalent to pi. I guess from there though, I wasn't sure how to understand number 2...
     
  5. Dec 5, 2013 #4

    NascentOxygen

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    Staff: Mentor

    Do we? You're talking about the term sin (kx) ?

    We know it has a node where kx = 0
     
  6. Dec 5, 2013 #5
    Oooh, true. I guess I was thinking of it in general terms like 0, pi, 2pi, etc. And I guess from a standing wave, since we see one full peak from a standing wave, that I thought that k would correspond to pi since we see it travel from 0 to pi in the distance of a peak. This question was definitely tricky for me to think about.
     
  7. Dec 5, 2013 #6

    NascentOxygen

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    I think you mean the product kx would correspond to Pi, 2Pi, 3Pi, etc., don't you?
     
  8. Dec 5, 2013 #7
    Yes, that is true, kx is what would correspond to pi, 2pi, etc.
     
  9. Dec 6, 2013 #8

    NascentOxygen

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    Staff: Mentor

    So what is your answer for (2)?
     
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