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Prove rms voltage using integration

  1. Dec 27, 2009 #1
    1. The problem statement, all variables and given/known data

    ac voltage
    v=sinx



    2. Relevant equations

    how do you prove that rms voltage is 0.707v using integration

    3. The attempt at a solution
     
  2. jcsd
  3. Dec 27, 2009 #2
    The root-mean-square value of a function is the root of the average of the square of the function.
    The average of the square of a function f (x) over an interval is given by:
    [tex]\frac{\int_{t_{1}}^{t_{2}} (f (x))^{2} dx}{t_{2} - t_{1}}[/tex]​
    You can do the relevant integration yourself for f (x) = sin x (or any sinusoidal function for that matter)
     
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