Circuit Analysis And Design 3E – Fawwaz Ulaby (1)

6-2.2 Discharging Mode If instead of starting out with an uncharged RLC circuit, we were to start with a fully charged capacitor, as depicted by the circuit in Fig. 6-4(c), and then discharge it by moving the SPDT switch from terminal 1 to terminal 2, the voltage υC(t) across the capacitor will decay from its initial value, Vs, to a final value of zero volts. The specific path between Vs and zero again depends on the value of α relative to that of ω0, as shown in Fig.

6-4(d). In fact, the three responses of the discharging RLC circuit are essentially mirror images of those for the charging-up circuit; the initial and final conditions of the circuit in Fig. 6-4(a) are the converse of those for the circuit in Fig. 6-4(c). The capacitor voltage of the charging-up circuit starts at zero and concludes at 24 V, in contrast to the discharging circuit that starts at 24 V and concludes at zero. Now let us consider an RLC circuit in which the capacitor has 12 V across it (due to some previous charging-up action), and then a switch is closed to connect the RLC segment to a (a) At t = 0− + _ t = 0 υC(0−) (b) After t = 0 υC decreases from 36 V to reach 24 V after a long time + _ (c) Long after closing the switch υC(∞) = 24 V i = 0 + _ Figure 6-6: Connecting a series RLC circuit with a charged-up capacitor to a source with lower voltage.

source with Vs = 24V, as shown in Fig. 6-5(a).After closing the switch(Fig.6-5(b)),thesituationissuchthatVs = 24Vexceeds the initial voltage of 12 V across the capacitor. Consequently, charge will flow to the capacitor to build up its voltage, and will continue to do so until the capacitor reaches the maximum possible voltage, namely Vs = 24 V. When it reaches that state, the current goes to zero (Fig.

6-5(c)). The scenario in Fig. 6-6 depicts a similar circuit, but one that starts with a capacitor whose initial voltage υC(0−) is 36 V, which is higher than that of Vs = 24V.

The University of Utah Copyright  2025 Fawwaz T. Ulaby, Michel M. Maharbiz, Cynthia M. Furse This book is published by Michigan Publishing under an agreement with the authors. It is made available free of charge in electronic form to any student or instructor interested in the subject matter. Published in the United States of America by Michigan Publishing. Manufactured in the United States of America ISBN 978-1-60785-922-2 (hardcover) ISBN 978-1-60785-923-9 (electronic) The free ECE Textbook initiative is sponsored by the ECE Department at the University of Michigan.

Toanacademic,writingabookisanendeavoroflove. We dedicate this book to Jean, Anissa, and Katie. Brief Contents Chapter 1 Circuit Terminology 1 Chapter 2 Resistive Circuits 50 Chapter 3 Analysis Techniques 115 Chapter 4 Operational Amplifiers 183 Chapter 5 RC and RL First-Order Circuits 248 Chapter 6 RLC Circuits 330 Chapter 7 ac Analysis 385 Chapter 8 ac Power 459 Chapter 9 Frequency Response of Circuits and Filters 500 Chapter 10 Three-Phase Circuits 566 Chapter 11 Magnetically Coupled Circuits 601 Chapter 12 Circuit Analysis by Laplace Transform 630 Chapter 13 Fourier Analysis Technique 674 Appendix A Symbols, Quantities, and Units 727 Appendix B Solving Simultaneous Equations 729 Appendix C Overview of Multisim 733 Appendix D Mathematical Formulas 736 Appendix E MATLAB® and MathScript® 738 Appendix F Answers to Selected Problems 743 Index 749 Contents Preface Chapter 1 Circuit Terminology 1 Overview 2 1-1 Historical Timeline 4 1-2 Units, Dimensions, and Notation 9 TB1 Micro- and Nanotechnology 10 1-3 Circuit Representation 15 1-4 Electric Charge and Current 20 1-5 Voltage and Power 25 TB2 Voltage: How Big Is Big?

This is a short excerpt from the opening of “” by Unknown, quoted for review and introduction purposes. All rights belong to the copyright holders.

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