Download Chapter 36. AC Circuits

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.
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Chapter 36. AC Circuits
Topics:
• AC Sources and Phasors
• Capacitor Circuits
• RC Filter Circuits
• Inductor Circuits
• The Series RLC Circuit
• Power in AC Circuits
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Chapter 36. Reading Quizzes
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The analysis of AC circuits uses
a rotating vector called a
A.
B.
C.
D.
E.
rotor.
wiggler.
phasor.
motor.
variator.
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The analysis of AC circuits uses
a rotating vector called a
A.
B.
C.
D.
E.
rotor.
wiggler.
phasor.
motor.
variator.
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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.
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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.
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In a series RLC circuit,
what quantity is maximum
at resonance?
A.
B.
C.
D.
The voltage
The current
The impedance
The phase
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In a series RLC circuit,
what quantity is maximum
at resonance?
A.
B.
C.
D.
The voltage
The current
The impedance
The phase
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Chapter 36. Basic Content and Examples
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AC Sources and Phasors
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AC Sources and Phasors
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AC Circuits
In an AC resistor
circuit, Ohm’s
law applies to
both the
instantaneous
and peak
currents and
voltages.
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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.
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EXAMPLE 36.1 Finding resistor voltages
QUESTION:
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EXAMPLE 36.1 Finding resistor voltages
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EXAMPLE 36.1 Finding resistor voltages
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EXAMPLE 36.1 Finding resistor voltages
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EXAMPLE 36.1 Finding resistor voltages
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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°.
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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.
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EXAMPLE 36.3 Capacitor current
QUESTION:
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EXAMPLE 36.3 Capacitor current
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EXAMPLE 36.3 Capacitor current
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EXAMPLE 36.3 Capacitor current
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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°.
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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.
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EXAMPLE 36.5 Current and voltage of an
inductor
QUESTION:
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EXAMPLE 36.5 Current and voltage of an
inductor
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EXAMPLE 36.5 Current and voltage of an
inductor
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EXAMPLE 36.5 Current and voltage of an
inductor
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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:
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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
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EXAMPLE 36.7 Lighting a bulb
QUESTION:
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EXAMPLE 36.7 Lighting a bulb
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EXAMPLE 36.7 Lighting a bulb
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EXAMPLE 36.7 Lighting a bulb
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EXAMPLE 36.7 Lighting a bulb
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Chapter 36. Summary Slides
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Important Concepts
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Important Concepts
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Key Skills
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Key Skills
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Applications
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Applications
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Chapter 36. Clicker Questions
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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.
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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.
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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.
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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.
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What is the capacitive reactance
of “no capacitor,” just a
continuous wire?
A. 0
B. ∞
C. Undefined
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What is the capacitive reactance
of “no capacitor,” just a
continuous wire?
A. 0
B. ∞
C. Undefined
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Rank in order, from largest to smallest, the cross-over
frequencies
of these four circuits.
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Rank in order, from largest to smallest, the cross-over
frequencies
of these four circuits.
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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
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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
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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
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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
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