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underdamped parallel RLC circuit

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Problem 10.1 only.
See attached file for full problem description.

a) For the circuit shown above, make a plot in the complex plane that indicates the roots of the characteristic equation.
b) Determine whether the circuit is overdamped, underdamped, or critically-damped.
c) Suppose v(0) = 0 and i(0) = 12 mA. Calculate v(t) and i(t)

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An underdamped parallel RLC circuit is investigated. The solution is detailed and was rated '5/5' by the student who posted the question originally.

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Please see the attached file.

a) The voltage of the inductor is
The resistor, capacitor and the inductor are in parallel, the .
The current through the ...

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