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Homework Help: Wrong value for the voltage across a capacitor

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  1. Oct 13, 2018 #1
    1. The problem statement, all variables and given/known data
    The current through a 100 microfarad is i(t) = 50 sin(120*pi*t) mA
    Calculate the voltage across it at t = 1 ms. Consider zero initial voltage.
    2. Relevant equations
    v(t) = (1/c) integral of i(t) from t = 0 to t = t

    3. The attempt at a solution
    Am getting v(t) = - 1.326 ( cos(120*pi*t) - 1 ) V
    which gives v(1*10^-3) = -2.87 * 10^(-5) V
    But book is saying the voltage should be 93.14 mV

    Can any confirm if book answer is correct?
    I did the problem like 100 times, and still same value. I considered that given current in mA so I multiplied by 10^-3, and considered the 10^-6 from micro farad. integral of sin(120*p*t) is -cos(120*pi*t) / (120*pi)
    I have no idea where is my mistake.
     
  2. jcsd
  3. Oct 13, 2018 #2

    Charles Link

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    Homework Helper
    Gold Member

    The book's answer is correct, but so is most of your calculations. When you computed ## \cos(.377) ## , did you use radians or degrees? You need to use radians. ## \\ ##Edit: And yes, I tried the arithmetic with degrees, and I got very close to your (incorrect) answer, but I get +2.87 E-5, with a "+" sign.
     
    Last edited: Oct 13, 2018
  4. Oct 13, 2018 #3
    So i substitute pi with 180.
    And yes you are correct, while calculating final answer i forget to include the "-" sign
    I have negative sign in my v(t), and there will (cos(something) - 1) which will give minus for sure as maximum value for cosine is 1, with the negative in v(t), answer must be positive
    Thanks!
     
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