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  1. #1
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    Math problem

    We have alternating current in the United Sates. This electric current alternates with a frequency of 60 cycles per second. Suppose that at time of t = 0.02 seconds, the current is at its maximum of l = 5 amperes. If the current varies sinusoidally over time, write and expression l(t) for the current as as function of time in t in seconds.

    Anybody? I need to show work too.
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  2. #2
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    Quote Originally Posted by Airjunkie View Post
    We have alternating current in the United Sates. This electric current alternates with a frequency of 60 cycles per second. Suppose that at time of t = 0.02 seconds, the current is at its maximum of l = 5 amperes. If the current varies sinusoidally over time, write and expression l(t) for the current as as function of time in t in seconds.

    Anybody? I need to show work too.
    I is a sinusoidal function so you can start with
    I(t) = I_0~sin( \omega t + \phi )

    We know that f = 60 Hz, so
    \omega = 2 \pi f = 120 \pi

    I(t) = I_0~sin( 120 \pi t + \phi )

    At t = 0.02 s the current is at its maximum, thus we know that
    120 \pi (0.02) + \phi = \frac{\pi}{2}

    \phi = 1.9\pi

    So
    I(t) = I_0~sin( 120 \pi t - 1.9 \pi )

    And finally, I_0 = 5~A, so
    I(t) = 5~sin( 120 \pi t - 1.9 \pi )

    -Dan
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