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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 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.

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 ...

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