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

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

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

33.2 Resistors in an AC Circuit

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.

The rms current is

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

Example 33.1 What Is the rms Current?

33.3 Inductors in an AC Circuit

we define ωL as the inductive reactance:

so

the instantaneous voltage across the inductor is

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.

33.4 Capacitors in an AC Circuit

The voltage across the capacitor:

The instantaneous current in thecircuit:

The maximum current

capacitive reactance

the instantaneous voltage across the capacitor

Example 33.3 A Purely Capacitive AC Circuit

ω=2 πf =377 s-1

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

The phase angle ϕ between the current and the voltage isimpedance

Example 33.5 Analyzing a Series RLC Circuit

The instantaneous voltages across the three elements as

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

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

Example 33.6 Average Power in an RLC Series Circuit

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

33.7 Resonance in a Series RLC Circuit

Example 33.7 A Resonating Series RLC Circuit