Chapter 6 – Inductance, Capacitance, and Mutual...

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Chapter 6 – Inductance, Capacitance, and Mutual Inductance ►Objectives:

1. Know and be able to use the equations for voltage, current, power, and energy in an inductor; understand how an inductor behaves in the presence of constant current, and the requirement that the current be continuous in an inductor.

2. Know and be able to use the equations for voltage, current, power, and energy in a capacitor; understand how a capacitor behaves in the presence of constant current, and the requirement that the voltage be continuous in a capacitor.

3. Be able to combine inductors with initial conditions in series and in parallel to form a single equivalent inductor with an initial condition; be able to combine capacitors with initial conditions in series and in parallel to form a single equivalent capacitor with an initial condition.

4. Understand the basic concept of mutual inductance and be able to write mesh-current equations for a circuit containing magnetically coupled coils using the dot convention correctly.

►Overview: This chapter describes the behavior of inductors and capacitors, including the differential equation that relates voltage and current, and the integral equation that relates voltage and current and includes the initial condition, the power equation, and the energy equation. Emphasis is placed on the behavior of inductors and capacitors in the presence of a constant source and the requirement that neither the current in an inductor nor the voltage drop across a capacitor change instantaneously. The purpose of the many plots in this chapter is to give students a visual means to depict the relationships among voltage, current, power, and energy for both inductors and capacitors. Section 6.3 discusses combining inductors in series and in parallel, taking into account that the inductors to be combined may have non-zero initial currents. This section also discusses combining capacitors in series and in parallel, taking into account that the capacitors to be combined may have non-zero initial voltages. The first three sections of the chapter are prerequisites for the material that follows, particularly Chapters 7 and 8. The final two sections introduce the concept of mutual inductance, with an emphasis on writing the describing differential equations using the dot convention. Determining the dot markings on real mutually coupled coils is discussed briefly, and the concept of the coupling coefficient is presented. This introduction to mutual inductance is a prerequisite only for the linear and ideal transformer material in Chapter 9, and example in Chapter 13, and the occasional chapter problem in other chapters. Therefore, mutual inductance can be omitted without loss of continuity.

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