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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 Chapter 36. AC Circuits Topics: • AC Sources and Phasors • Capacitor Circuits • RC Filter Circuits • Inductor Circuits • The Series RLC Circuit • Power in AC Circuits Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Chapter 36. Reading Quizzes Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The analysis of AC circuits uses a rotating vector called a A. B. C. D. E. rotor. wiggler. phasor. motor. variator. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The analysis of AC circuits uses a rotating vector called a A. B. C. D. E. rotor. wiggler. phasor. motor. variator. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley In a capacitor, the peak current and peak voltage are related by the A. B. C. D. capacitive resistance. capacitive reactance. capacitive impedance. capacitive inductance. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley In a capacitor, the peak current and peak voltage are related by the A. B. C. D. capacitive resistance. capacitive reactance. capacitive impedance. capacitive inductance. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley In a series RLC circuit, what quantity is maximum at resonance? A. B. C. D. The voltage The current The impedance The phase Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley In a series RLC circuit, what quantity is maximum at resonance? A. B. C. D. The voltage The current The impedance The phase Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Chapter 36. Basic Content and Examples 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 vR is given by where VR is the peak or maximum voltage. The current through the resistor is where IR = VR/R is the peak current. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.1 Finding resistor voltages QUESTION: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.1 Finding resistor voltages Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.1 Finding resistor voltages Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.1 Finding resistor voltages Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.1 Finding resistor voltages Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley 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 VC 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 XC is defined as The units of reactance, like those of resistance, are ohms. Reactance relates the peak voltage VC and current IC: 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, vC ≠ iCXC. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.3 Capacitor current QUESTION: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.3 Capacitor current Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.3 Capacitor current Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.3 Capacitor current Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley 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 VL 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 XL is defined as Reactance relates the peak voltage VL and current IL: 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, vL ≠ iLXL. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.5 Current and voltage of an inductor QUESTION: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.5 Current and voltage of an inductor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.5 Current and voltage of an inductor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.5 Current and voltage of an inductor Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The Series RLC Circuit The impedance Z of a series RLC circuit is defined as Impedance, like resistance and reactance, is measured in ohms. The circuit’s peak current is related to the source emf and the circuit impedance by Z is at a minimum, making I a maximum, when XL = XC, at the circuit’s resonance frequency: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Power in AC Circuits The root-mean-square current Irms is related to the peak current IR by Similarly, the root-mean-square voltage and emf are The average power supplied by the emf is Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.7 Lighting a bulb QUESTION: Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.7 Lighting a bulb Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.7 Lighting a bulb Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.7 Lighting a bulb Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley EXAMPLE 36.7 Lighting a bulb Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Chapter 36. Summary Slides Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Important Concepts Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Important Concepts Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Key Skills Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Key Skills Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Applications Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Applications Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Chapter 36. Clicker Questions Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The magnitude of the instantaneous value of the emf represented by this phasor is A. constant. B. increasing. C. decreasing. D. It’s not possible to tell without knowing t. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The magnitude of the instantaneous value of the emf represented by this phasor is A. constant. B. increasing. C. decreasing. D. It’s not possible to tell without knowing t. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The resistor whose voltage and current phasors are shown here has resistance R A. > 1 Ω. B. < 1 Ω. C. It’s not possible to tell. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The resistor whose voltage and current phasors are shown here has resistance R A. > 1 Ω. B. < 1 Ω. C. It’s not possible to tell. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley What is the capacitive reactance of “no capacitor,” just a continuous wire? A. 0 B. ∞ C. Undefined Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley What is the capacitive reactance of “no capacitor,” just a continuous wire? A. 0 B. ∞ C. Undefined Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Rank in order, from largest to smallest, the cross-over frequencies of these four circuits. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Rank in order, from largest to smallest, the cross-over frequencies of these four circuits. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley A series RLC circuit has VC = 5.0 V, VR = 7.0 V, and VL = 9.0 V. Is the frequency above, below or equal to the resonance frequency? A. Above the resonance frequency B. Below the resonance frequency C. Equal to the resonance frequency Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley A series RLC circuit has VC = 5.0 V, VR = 7.0 V, and VL = 9.0 V. Is the frequency above, below or equal to the resonance frequency? A. Above the resonance frequency B. Below the resonance frequency C. Equal to the resonance frequency Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The emf and the current in a series RLC circuit oscillate as shown. Which of the following would increase the rate at which energy is supplied to the circuit? A. Decrease ε0 B. Increase C C. Increase L D. Decrease L Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley The emf and the current in a series RLC circuit oscillate as shown. Which of the following would increase the rate at which energy is supplied to the circuit? A. Decrease ε0 B. Increase C C. Increase L D. Decrease L Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley