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Given voltage and current equations, find instantaneous Power

  1. Sep 5, 2009 #1
    1. The problem statement, all variables and given/known data
    The voltage across and current through a certain device are given by:
    v(t) = 5cos(4*pi*t)
    i(t) = .1cos(4*pi*t)

    Determine:
    (a) the instantaneous power p(t) at t= 0 and t = .25 seconds
    (b) the average power pav, defined as the average value of p(t) over a full time period of the cosine function (0 to .5 seconds)


    2. Relevant equations
    Power = Voltage * Current


    3. The attempt at a solution

    (a) I plugged 0 and .25 in for t into both of the equations, and multiplied the answers together. For both t = 0 and t = .25, I got .5 Watts for my answer. In the back of the book, it says for t = 0 it should be 0 watts, and for t=.25 s .5 watts. I got the answer correctly for t=.25s, but what am I missing for the beginning part? I have been going over this problem for a while now and I cannot figure it out for the life of me.

    (b) 1/(b-a) *integral (i(t)*v(t)) evaluated from a to b, a being 0 and b being .25 seconds. I'm pretty sure this is the right direction for this part.

    Thanks in advance for your time / help!
     
  2. jcsd
  3. Sep 6, 2009 #2

    Redbelly98

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    Staff Emeritus
    Science Advisor
    Homework Helper

    (a) I agree with your answer, the power is 0.5 W at t = 0 s. You might double-check that the expressions for v and i you used are correct, but it sounds like you've looked things over pretty carefully already.

    (b) Yes, that's exactly the way to do it. Integrate p over 1 period.
     
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