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    Discerning Electrical Voltage

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    Find and plot Vo(t), if io=10e^-200t
    Assume v(o- bar on top of o)= +400 volts

    See the attachment for the diagram.

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    Solution Preview

    Use the Laplace Transform method.
    Kirchoff's voltage law gives:
    vo(s) - i(s)*[sL + 1/sC ] = Vo (s)

    Now, vo(s) = 400/s
    i(t) = 10*e^(-200t) ==> i(s) = 10/(s+200)

    So, Vo(s) = 400/s - [10/(s+200)]*[ (1+s^2LC)/(sC)

    Use the partial fraction ...

    Solution Summary

    This answer gives the electrical voltage through using the diagram, properties of exponential decay functions, and electrical circuits. The Laplace Transform method especially was helpful in determining voltage during different times.