The switch in the circuit in Fig. P12.28 has been in position a for a long time. At the

Chapter 12, Problem 12.28

(choose chapter or problem)

The switch in the circuit in Fig. P12.28 has been in position a for a long time. At t = 0, the switch moves instantaneously to position b.

a) Derive the integrodifferential equation that governs the behavior of the current \(i_{o}\) for \(t \geq 0^{+}\).

b) Show that

\(I_{o}(s)=\frac{I_{\mathrm{dc}}[s+(1 / R C)]}{\left[s^{2}+(1 / R C) s+(1 / L C)\right]}\).

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