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The switch in the circuit in Fig. P12.30 has been open for a long time. At / = 0, the switch closes. a) Derive the integrodifferential equation that governs the behavior of the voltage v, for t 2 0. b) Show that Vac/RC g2 + (1/RC)s + (1/LC)' V.(s) = c) Show that Vae/ RLC s[s² + (1/RC)s + (1/LC)]' Figure P12.30 R + V de

The switch in the circuit in Fig. P12.30 has been open for a long time. At / = 0, the switch closes. a) Derive the integrodifferential equation that governs the behavior of the voltage v, for t 2 0. b) Show that Vac/RC g2 + (1/RC)s + (1/LC)' V.(s) = c) Show that Vae/ RLC s[s² + (1/RC)s + (1/LC)]' Figure P12.30 R + V de

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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The switch in the circuit in Fig. P12.30 has been open for a long time. At i = 0, the switch closes. a) Derive the integrodifferential equation that governs the behavior of the voltage v, for t 2 0. b) Show that Vac/RC V.(s) g2 + (1/RC)s + (1/LC)' c) Show that Vác/ RLC s[s² + (1/RC)s + (1/LC)]' 1,(8) Figure P12.30 R 1 = 0 V ac
Transcribed Image Text:The switch in the circuit in Fig. P12.30 has been open for a long time. At i = 0, the switch closes. a) Derive the integrodifferential equation that governs the behavior of the voltage v, for t 2 0. b) Show that Vac/RC V.(s) g2 + (1/RC)s + (1/LC)' c) Show that Vác/ RLC s[s² + (1/RC)s + (1/LC)]' 1,(8) Figure P12.30 R 1 = 0 V ac
Expert Solution
Step 1

Apply KCL at node connecting the resistor,  inductor and capacitor .

Using Laplace transform find S domain representation capacitor voltage. 

Current through inductor = (Voltage across inductor)/SL.

 

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