Parallel RLC Natural Response

Inside this lesson

Write the KCL equation for a source-free parallel RLC circuit and reduce it to a second-order homogeneous ODE
Derive the characteristic equation s² + (1/(RC))s + 1/(LC) = 0 and identify α = 1/(2RC) and ω0 = 1/√(LC)
Compute the characteristic roots for given component values, including the case of complex conjugate roots
Articulate the duality between the series and parallel RLC topologies: R ↔ 1/R in the α formula, while ω0 is unchanged

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Educational content covering topics typical of a first- and second-year electrical engineering curriculum. Not a substitute for accredited coursework, and not suitable for real circuit or system design without review by a licensed professional engineer.