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Math Help - Root Mean Square Value

  1. #1
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    Root Mean Square Value

    Question: show that the RMS value of current
    i = 4sin100 pi T is 2.828A
    NOTE: sin^2 theta = 1/2 (1-cos2theta)

    I have tryed to rearange the forumle inorder to work out T
    4sin 100=  i X pi T
    T=4sin 100 i X pi
    4sin 100 = 3.939 (2.828 X pi) = 34.99
    T=34 but i dont think thats right.
    can anyone help me.
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  2. #2
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    Quote Originally Posted by batman121 View Post
    Question: show that the RMS value of current
    i = 4sin100 pi T is 2.828A
    NOTE: sin^2 theta = 1/2 (1-cos2theta)

    I have tryed to rearange the forumle inorder to work out T
    4sin 100=  i X pi T
    T=4sin 100 i X pi
    4sin 100 = 3.939 (2.828 X pi) = 34.99
    T=34 but i dont think thats right.
    can anyone help me.
    The formula for a continuous function f(t) defined over the interval T_1 \le t \le T_2 is

    <br />
I_{\mathrm{rms}} = \sqrt {{1 \over {T_2-T_1}} {\int_{T_1}^{T_2} {[i(t)]}^2\, dt}}<br />
    <br />
I_{\mathrm{rms}} = \sqrt {{1 \over {T}} {\int_{0}^{T} {[4\sin 100\pi t]}^2\, dt}}

    I_{\mathrm{rms}} = \sqrt {{8 \over {T}} {\int_{0}^{T} (1 - \cos200\pi t)\, dt}} \\

    I_{\mathrm{rms}} = \sqrt {{8 \over {T}} T} \\

    I_{\mathrm{rms}} = \sqrt {8} A\\
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