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Energy waveform

  1. Nov 19, 2011 #1
    From the given waveform (of current), sketch the energy from t = 0 to t = 2T. Given: R = 10 Ohms, i = 10 Amps
    mhxeh4.jpg

    I'm having trouble with this even though it's probably really easy.
    I know WR = ∫Ri2(t) dt
    so for one period, for example, I have
    ∫10(102) dt with limits of integration from 0 to T/2
    = 1000 t / t goes from 0 to T/2
    = 500T
    i believe this is a line with slope 500 going from 0 to T/2..but i'm not sure what i do for the other values of t
    when i graph it should I just graph 1000t and plug in values for t?
     
  2. jcsd
  3. Nov 20, 2011 #2

    rude man

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    Energy = time integral of power.

    So you're doing just fine up to T/2.

    Question to you: given the above, what should the curve look like between T2 and T?

    And when the second pulse starts, until 3T/2?
    And from 3T/2 to 2T?
     
  4. Nov 20, 2011 #3
    i would assume it just repeats, and from T/2 to T it would be zero and again from 5T/2 to 3T. but would it be somewhat like a sawtooth wave?
     
  5. Nov 20, 2011 #4

    rude man

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    Why would it be zero from T/2 to T? Where did the energy go?

    BTW the problem doesn't ask you to go beyond 2T so I wouldn't.
     
  6. Nov 20, 2011 #5

    NascentOxygen

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    When I is zero then additional energy dissipated as heat in the resistor would be zero. Note: additional energy during T/2 -> T is zero.
     
  7. Nov 21, 2011 #6
    why additional? what other energy is there? or where does it come from?
    i only know of energy being equal to ∫p dt = ∫ Ri2(t) dt, and isn't p 0 from T/2 to T?
     
  8. Nov 21, 2011 #7

    rude man

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    Magnifik -please - for the last time - the energy you built up from 0 to T/2 has not disasppeared, so your graph just HAS to show it!!! Energy cannot be created or destroyed!!!

    Yes - P is zero, but E is not, it's what it was at t = T/2 -.
     
  9. Nov 21, 2011 #8

    NascentOxygen

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    It's a resistor, so we are not talking about some vague concept or interplay of various energy forms. We are talking HEAT. Total heat energy. It's a graph that keeps increasing (never dropping) because it is a plot summing total heat energy since time t=0.
     
  10. Nov 21, 2011 #9
    i'm still confused as to what the graph would look like.
    is the total energy delivered over one period 500T? ... i think i just understood why T/2 to T is not 0 with that question
     
    Last edited: Nov 21, 2011
  11. Nov 21, 2011 #10

    rude man

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    Let me try an analogy. You have a 100W light bulb. You turn it on for 1/2 hour and then turn it off for the next half hour.

    Now graph what the watt-hour meter reads during the 1 hour time period.
     
  12. Nov 21, 2011 #11
    It would be 50 watt-hour for the hour long time period. then the next hour would be 50 again so total would be 100, etc., etc.
    if i plotted it over time, it would be a line with positive slope, yes?
     
  13. Nov 21, 2011 #12

    rude man

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    I asked for just the 1 hour interval.

    No, it would read 100t watt-hours during the first 30 minutes and 50 watt-hrs after that until 1 hr. t is in hours.
     
  14. Nov 21, 2011 #13
    Woops, misread your question. I thought you meant it was already on for 30 minutes and then off for the next 30 minutes so the power was like a pulse train.

    I thought for energy
    It's a graph that keeps increasing (never dropping) because it is a plot summing total heat energy since time t=0.
     
    Last edited: Nov 21, 2011
  15. Nov 21, 2011 #14

    rude man

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    Now you're cooking with gas - or whatever your electric utility burns! :-)
     
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