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Output Voltage, AC Source

  1. Nov 13, 2008 #1
    1. The problem statement, all variables and given/known data
    The rms output voltage of an AC source is 180 V, and the operating frequency is 90 Hz. Write the equation giving the output voltage as a function of time t. (Use t as necessary.)

    2. Relevant equations
    [tex](\Delta v) = (\Delta V_{max})sin\omega t[/tex]
    [tex]\Delta V_{max}= \sqrt{2}V_{max}[/tex]
    [tex]\omega = 2\pi f[/tex]


    3. The attempt at a solution

    I thought it was a simple solve for the values of omega, Vmax, and plug those into the first equation, but I am apparently wrong according to the website. I don't think I have messed up. The only other thing I can think of is that they want it in cosine instead of sine. I got the following answer:

    Voutput = 255sin(566t)
     
  2. jcsd
  3. Nov 14, 2008 #2
  4. Nov 14, 2008 #3

    LowlyPion

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    Homework Helper

    Vrms = Vp/√2

    Vt = Vp*sin(ωt) = √2*Vrms*sin(2*π*f*t) = 254.55*sin(565.48*t)

    That's the way I figure it.

    It's difficult to imagine that they would be picky about that small a rounding error.
     
  5. Nov 14, 2008 #4
    I meant that with my one equation...I meant that Vmax = sqrt(2)Vrms. And...I know it must be right, they are just being picky about how it's typed in, yet, I get the same answer you get. It shouldn't be cosine (thought it could be, but would require a phase angle). It also shouldn't be negative as far as I can tell. And, as my answer is within 1% of your answer, it shouldn't be picky about that either. I will just try one other thing and then email my teacher about it.
     
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