# CHAPTER 7

*Energy Storage Elements*

**IN THIS CHAPTER**

**7.1** Introduction

**7.2** Capacitors

**7.3** Energy Storage in a Capacitor

**7.4** Series and Parallel Capacitors

**7.5** Inductors

**7.6** Energy Storage in an Inductor

**7.7** Series and Parallel Inductors

**7.8** Initial Conditions of Switched Circuits

**7.9** Operational Amplifier Circuits and Linear Differential Equations

**7.10** Using MATLAB to Plot Capacitor or Inductor Voltage and Current

**7.11** How Can We Check … ?

**7.12 DESIGN EXAMPLE**—Integrator and Switch

**7.13** Summary

Problems

Design Problems

## 7.1 *Introduction*

This chapter introduces two more circuit elements, the capacitor and the inductor. The constitutive equations for the devices involve either integration or differentiation. Consequently:

- Electric circuits that contain capacitors and/or inductors are represented by differential equations. Circuits that do not contain capacitors or inductors are represented by algebraic equations. We say that circuits containing capacitors and/or inductors are
**dynamic** circuits, whereas circuits that do not contain capacitors or inductors are **static**. circuits.
- Circuits that contain capacitors and/or inductors are able to store energy.
- Circuits that contain capacitors and/or inductors have memory. The voltages and currents at a particular time depend not only on other voltages at currents at that same instant of time but also on previous values of those currents and voltages. ...