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Math Help - RMS value

  1. #1
    Senior Member DivideBy0's Avatar
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    RMS value

    Can I take the RMS of DC and AC, or only AC? And why isn't it exactly equal to Peak/sqrt(2)? My teacher said there is a pretty big margin for error when calculating RMS, but he didn't state why.
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    Grand Panjandrum
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    Quote Originally Posted by DivideBy0 View Post
    Can I take the RMS of DC and AC, or only AC? And why isn't it exactly equal to Peak/sqrt(2)? My teacher said there is a pretty big margin for error when calculating RMS, but he didn't state why.
    RMS of DC is ~|V|, where V is the mean voltage.

    The relationship of RMS to peak depends on the waveform, so if you have
    a zero mean square wave with values +/- V, the RMS voltave is V, while
    for a pure sinusoid of peak voltage V it is V/sqrt(2), etc ..

    RonL
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by DivideBy0 View Post
    Can I take the RMS of DC and AC, or only AC? And why isn't it exactly equal to Peak/sqrt(2)? My teacher said there is a pretty big margin for error when calculating RMS, but he didn't state why.
    You CAN take an RMS value for a DC source. But since the current (potential, etc.) is constant for a DC source it makes no sense to talk about an RMS value for it. RMS stands for "Root-Mean-Square" which takes the average value of the square of the signal (mean), then takes the square root of that. If the signal is constant this gives you nothing new to work with.

    -Dan
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    Senior Member DivideBy0's Avatar
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    If you had a fully rectified AC wave, then you could take an RMS of the DC, couldn't you? Because it's still fluctuating up and down? And if you have a half-rectification, would the RMS be half that of fully rectified AC?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by DivideBy0 View Post
    If you had a fully rectified AC wave, then you could take an RMS of the DC, couldn't you? Because it's still fluctuating up and down? And if you have a half-rectification, would the RMS be half that of fully rectified AC?
    Of course you can. But as CaptainBlack stated, the RMS value is simply equal to the magnitude of the signal. ie if you are looking for the RMS voltage, it would simply be |V|, the absolute value of the voltage.

    If the signal were half-rectified, then the square of the signal appears as a constant value: V^2. So the average of this would still be V^2, and upon taking the square root we would get |V| again.

    -Dan
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  6. #6
    Senior Member DivideBy0's Avatar
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    Alrighty, thanks guys. I have the physics final exam tomorrow! XD
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    Grand Panjandrum
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    Quote Originally Posted by DivideBy0 View Post
    Alrighty, thanks guys. I have the physics final exam tomorrow! XD
    The RMS of a full wave rectified sinusoid is the same as that of the original
    sinusoid V/sqrt(2). Of half wave rectified its half of that of full wave rectified.

    RonL
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