chapter 33 alternating current circuits chapter outline 33.1 ac sources 33.2 resistors in an ac...

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Chapter 33 Chapter 33 Alternating Current Alternating Current Circuits Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors in an AC Circuit 33.5 The RLC Series Circuit 33.6 Power in an AC Circuit 33.7 Resonance in a Series RLC Circuit

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Page 1: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

Chapter 33Chapter 33Alternating Current Alternating Current CircuitsCircuits

CHAPTER OUTLINE33.1 AC Sources33.2 Resistors in an AC Circuit33.3 Inductors in an AC Circuit33.4 Capacitors in an AC Circuit33.5 The RLC Series Circuit33.6 Power in an AC Circuit33.7 Resonance in a Series RLC Circuit

Page 2: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

33.1 AC Sources

where ΔVmax is the maximum output voltage of the AC source, or the voltage amplitude.

The angular frequency of the AC voltage is

Page 3: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

33.2 Resistors in an AC Circuit

Page 4: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

The instantaneous voltage across the resistor is

for a sinusoidal applied voltage, the current in a resistor is always in phase with the voltage across the resistor.

Page 5: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

The rms current is

Page 6: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

The average power delivered to a resistor that carries an alternating current is

Page 7: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

Example 33.1 What Is the rms Current?

Page 8: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

33.3 Inductors in an AC Circuit

Page 9: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors
Page 10: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

we define ωL as the inductive reactance:

so

Page 11: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

the instantaneous voltage across the inductor is

Page 12: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

Example 33.2 A Purely Inductive AC Circuit

In a purely inductive AC circuit, L = 25.0 mH and the rms voltage is 150 V. Calculate the inductive reactance and rms current in the circuit if the frequency is 60.0 Hz.

Page 13: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

33.4 Capacitors in an AC Circuit

The voltage across the capacitor:

The instantaneous current in thecircuit:

Page 14: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

The maximum current

capacitive reactance

the instantaneous voltage across the capacitor

Page 15: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

Example 33.3 A Purely Capacitive AC Circuit

ω=2 πf =377 s-1

Page 16: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

The maximum voltage values across the elements:

the current at all points in a series AC circuit has the same amplitude and phase.

The instantaneous applied voltage is

33.5 The RLC Series Circuit

Page 17: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

The phase angle ϕ between the current and the voltage isimpedance

Page 18: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors
Page 19: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

Example 33.5 Analyzing a Series RLC Circuit

Page 20: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors
Page 21: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

The instantaneous voltages across the three elements as

Page 22: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

1- A 10-μF capacitor is plugged into a 110 V-rms 60-Hz voltage source, with anammeter in series. What is the rms value of the current through the capacitor?a. 0.202 A (rms)b. 0.415 A (rms)c. 0.626 A (rms)d. 0.838 A (rms)e. 0.066 A (rms)

2- If an R = 1-kΩ resistor, a C = 1-μF capacitor, and an L = 0.2-H inductor are connected in series with a V = 150 sin (377t) volts source, what is the maximum current delivered by the source?a. 0.007 Ab. 27 mAc. 54 mAd. 0.308 Ae. 0.34 A

Page 23: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

33.6 Power in an AC Circuit

The instantaneous power P

The average power delivered by the source is converted to internalenergy in the resistor

No power losses are associated with pure capacitors and pureinductors in an AC circuit

If

Page 24: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

Example 33.6 Average Power in an RLC Series Circuit

Calculate the average power delivered to the series RLCcircuit described in Example 33.5.

Page 25: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

33.7 Resonance in a Series RLC Circuit

Page 26: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors
Page 27: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors
Page 28: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors

Example 33.7 A Resonating Series RLC Circuit

Page 29: Chapter 33 Alternating Current Circuits CHAPTER OUTLINE 33.1 AC Sources 33.2 Resistors in an AC Circuit 33.3 Inductors in an AC Circuit 33.4 Capacitors