Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Chapter 36. AC Circuits Today, a “grid” of AC electrical distribution systems spans the United States and other countries. Any device that plugs into an electric outlet uses an AC circuit. In this chapter, you will learn some of the basic techniques for analyzing AC circuits. Chapter Goal: To understand and apply basic techniques of AC circuit analysis.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Topics: AC Sources and Phasors Capacitor Circuits (Capacitive Reactance) RC Filter Circuits Inductor Circuits (Inductive Reactance) The Series RLC Circuit Chapter 36. AC Circuits

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley AC Sources and Phasors

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley AC Sources and Phasors

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley AC Circuits In an AC resistor circuit, Ohm’s law applies to both the instantaneous and peak currents and voltages.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley AC Circuits The resistor voltage v R is given by where V R is the peak or maximum voltage. The current through the resistor is where I R = V R /R is the peak current.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley

The AC current to and from a capacitor leads the capacitor voltage by π/2 rad, or 90°. Equivalent Ohm’s Law

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Capacitor Circuits The instantaneous voltage across a single capacitor in a basic capacitor circuit is equal to the instantaneous emf: Where V C is the maximum voltage across the capacitor, also equal to the maximum emf. The instantaneous current in the circuit is The AC current to and from a capacitor leads the capacitor voltage by π/2 rad, or 90°.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Capacitive Reactance The capacitive reactance X C is defined as The units of reactance, like those of resistance, are ohms. Reactance relates the peak voltage V C and current I C : NOTE: Reactance differs from resistance in that it does not relate the instantaneous capacitor voltage and current because they are out of phase. That is, v C ≠ i C X C.

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Equivalent Ohm’s Law

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Inductor Circuits The instantaneous voltage across a single inductor in a basic inductive circuit is equal to the instantaneous emf: Where V L is the maximum voltage across the inductor, also equal to the maximum emf. The instantaneous inductor current is The AC current through an inductor lags the inductor voltage by π/2 rad, or 90°.

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Inductive Reactance The inductive reactance X L is defined as Reactance relates the peak voltage V L and current I L : NOTE: Reactance differs from resistance in that it does not relate the instantaneous inductor voltage and current because they are out of phase. That is, v L ≠ i L X L.

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For ω->0, (X C >>R),V R ->0, V C ->ε o /X C ; like shorted resistor For ω-> , (X C ε o /X C, V C ->0 ; like shorted capacitor For ω=1/RC (R=X C ), V R =V C =(1/  2)(ε o /R) =(1/  2)(ε o /X C ) Define cross-over frequency ω c =1/RC

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