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Homework Help: Capacitor energy

  1. Nov 6, 2017 #1
    1. The problem statement, all variables and given/known data

    The initial voltage on the 0.5 microF capacitor shown in the figure is -20 V. the capacitor current has the waveform shown in the figure. https://i.imgur.com/P8jwI7s.jpg?1

    How much energy is stored in the capacitor at t = 870 micro seconds.

    2. Relevant equations

    v(t) = 1/c * integral from t to t0 i dtao + v(t0) EDIT: "integral from t to t0" is a definite integral with t on the top and t0 on the bottom
    w(t) = 1/2cv^2

    3. The attempt at a solution

    got v(t) = 50*e^-2000t + 30

    after plugging into w(t) tested the following answers:

    https://imgur.com/3P8ipf4
     
    Last edited: Nov 6, 2017
  2. jcsd
  3. Nov 6, 2017 #2

    haruspex

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    Your integral calculated the change in voltage (except, you have a sign error) How does that relate to the change in energy?
     
  4. Nov 6, 2017 #3
    "from t to t0" is admittedly ambiguous but i mean that t is on the top of the definite integral and t0 is on the bottom. voltage relates to energy by the equation w(t) = 1/2cv^2. i plugged in my equation for v(t) and the time as 870 microseconds. please let me know what else is unclear/wrong. thank you for your reply.
     
  5. Nov 6, 2017 #4

    haruspex

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    What does that give for t=0?
    But that's different from change in voltage and change in energy.
     
  6. Nov 6, 2017 #5
    "what does that give for t=0?"

    80 volts. what are you implying?

    "but that's different from change in voltage and change in energy"

    what are you implying? the expressions for v(t) and w(t) i have provided are the capacitor voltage and energy stored in a capacitor, respectively, at a particular instance for a time. i dont think the answer is w(870 microseconds) - w(0 seconds). please let me know if i am wrong. thank you for your reply.
     
  7. Nov 6, 2017 #6

    haruspex

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    But:
    Yes, you're right, I misread the question.
     
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