Answered: t = 0) V1 V2

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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Question

The circuit parameters in the circuit ishown are R=1600 Ω; L=200 mH; and C=200 nF. If ig(t)=6 mA, find v2(t)

Expert Solution

Step 1

When the switch is closed initially, write the expression for the voltage across the capacitor and the current through the inductor.

$\begin{array}{rcl} v_{1} (0^{-}) & = & 0 V \\ i_{L} (0^{-}) & = & 0 A \end{array}$

Step 2

When the switch is opened, calculate the current through the inductor using current division rule and Laplace transform.

$\begin{array}{rcl} I_{L} (s) & = & (\frac{\frac{1}{s C}}{\frac{1}{s C} + R + s L}) I_{g} (s) \\ = & (\frac{1}{L C s^{2} + R C s + 1}) (\frac{0.006}{s}) \\ = & (\frac{1}{(200 \times 10^{- 3}) (200 \times 10^{- 9}) s^{2} + (1600) (200 \times 10^{- 9}) s + 1}) (\frac{0.006}{s}) \\ = & \frac{0.006}{s (4 \times 10^{- 8} s^{2} + 3.2 \times 10^{- 4} + 1)} \\ = & \frac{150000}{s (s^{2} + 8000 s + 2.5 \times 10^{7})} \end{array}$

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