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.
Chapter 36. AC Circuits
Topics:
• AC Sources and Phasors
• Capacitor Circuits
• RC Filter Circuits
• Inductor Circuits
• The Series RLC Circuit
• Power in AC Circuits
AC Sources and Phasors
AC Sources and Phasors
AC Circuits
In an AC resistor
circuit, Ohm’s
law applies to
both the
instantaneous
and peak
currents and
voltages.
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.
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°.
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:
Ic 
Vc
Xc
or
Vc  IcXc
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.
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°.
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.
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:
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
Summary:
Important Concepts
Important Concepts
Applications
Applications
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
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
Consider the parallel RLC circuit
I  0
1  1


 C 
2
R  L

2