Discerning Electrical Voltage
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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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.
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