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Electric Current as a function of time

  1. Mar 19, 2012 #1
    1. The problem statement, all variables and given/known data
    8. An electric current in a conductor varies with time according to the expression
    I(t) = 100 sin (120*pi*t), where I is in amperes and t is in seconds. What is the total charge passing a given point in the conductor from t = 0 to t = 1/240 s?




    2. Relevant equations




    3. The attempt at a solution
    I have attempted to substitute the values of t into the equation and use the difference, but I do not feel that was the correct way. Next, I attempted to perform a definite integral, but I get 0 for both numbers.
     
  2. jcsd
  3. Mar 19, 2012 #2

    tiny-tim

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    welcome to pf!

    hi jmuduke! welcome to pf! :smile:
    yes, I = dQ/dt, so Q = ∫ I dt

    it's only over 90°, so you shouldn't get 0 for both limits :confused:

    show us what you did :smile:
     
  4. Mar 19, 2012 #3
    Thanks for the reply Tim!

    I calculated the integral and got -(5 cos(120*pi*t))/6*pi

    Originally, my calculator was set in radians, so that could have been why I got 0 for both limits. I changed it to degrees and got -0.265 for both limits then, but that result in the definite integral being 0, correct?
     
  5. Mar 20, 2012 #4

    tiny-tim

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    hi jmuduke! :smile:

    (just got up :zzz:)
    yes, cos(0) = 1, so that's correct for the t = 0 limit :smile:

    but for t = 1/240, cos(120πt) = cos(π/2) = cos90° = 0 :wink:
     
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