Download Chapter 33 Alternating Current Circuits

6/10/2014
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 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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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
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33.2 Resistors in an AC Circuit
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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.
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The rms current is
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The average power delivered to a resistor that carries an
alternating current is
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Example 33.1 What Is the rms Current?
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33.3 Inductors in an AC Circuit
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we define ωL as the inductive
reactance:
so
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the instantaneous voltage across the inductor is
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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.
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33.4 Capacitors in an AC Circuit
The voltage across the capacitor:
The instantaneous current in the
circuit:
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The maximum current
capacitive reactance
the instantaneous voltage across the
capacitor
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Example 33.3 A Purely Capacitive AC Circuit
ω=2 πf =377 s-1
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33.5 The RLC Series Circuit
The instantaneous applied voltage is
the current at all points in a series AC circuit has the
same amplitude and phase.
The maximum voltage values across the
elements:
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impedance
The phase angle ϕ between the
current and the voltage is
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Example 33.5 Analyzing a Series RLC Circuit
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The instantaneous voltages across the three elements as
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1- A 10-μF capacitor is plugged into a 110 V-rms 60-Hz voltage source, with an
ammeter 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 A
b. 27 mA
c. 54 mA
d. 0.308 A
e. 0.34 A
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33.6 Power in an AC Circuit
No power losses are associated with pure capacitors and pure
inductors in an AC circuit
The instantaneous power P
The average power delivered by the source is converted to internal
energy in the resistor
If
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Example 33.6 Average Power in an RLC Series Circuit
Calculate the average power delivered to the series RLC
circuit described in Example 33.5.
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33.7 Resonance in a Series RLC Circuit
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Example 33.7 A Resonating Series RLC Circuit
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