summary important concepts key skills applications

advertisement
SUMMARY
The goal of Chapter 35 has been to understand and apply basic techniques of AC circuit analysis.
IMPORTANT CONCEPTS
Basic circuit elements
AC circuits are driven by an emf
Element
i and v
Resistance/
reactance
I and V
Power
Resistor
Capacitor
Inductor
In phase
i leads v by 90°
i lags v by 90°
R is fixed
XC 5 1/vC
XL 5 vL
V 5 IR
V 5 IXL
V 5 IXC
Vrms Irms
0
0
E 5 E0 cos vt
that oscillates with angular frequency v 5 2pf.
Phasors can be used
to represent the
oscillating emf,
current, and voltage.
The length
of the
phasor is
the peak
value E0.
E0
For many purposes, especially calculating power, the root-mean-square (rms)
quantities
vt
Vrms 5 V/ !2
E
The horizontal projection
is the instantaneous value E.
Irms 5 I/ !2
Erms 5 E/ !2
are equivalent to the corresponding DC quantities.
KEY SKILLS
Phasor diagrams
Kirchhoff’s laws
VR
• Start with a phasor (v or i)
common to two or more
circuit elements.
Loop law The sum of the potential differences
around a loop is zero.
E0
I
vt
• The sum of instantaneous
quantities is vector addition.
• Use the Pythagorean theorem
to relate peak quantities.
Junction law The sum of currents entering a
junction equals the sum leaving the junction.
VC
Instantaneous and peak quantities
For an RC circuit, shown here,
vR 1 vC 5 E
Instantaneous quantities v and i generally obey
different relationships than peak quantities V and I.
VR2 1 VC2 5 E02
APPLICATIONS
Series RLC circuits
RC filter circuits
R
VC 5 E0 XC /"R2 1 XC2
C
E
R
I 5 E0/Z where Z is the impedance
VC
VC S E0 as v S 0
E
L
Z 5 "R2 1 (XL 2 XC )2
VR 5 IR
A low-pass filter transmits low frequencies and blocks high
frequencies.
C
VR 5 E0 R/"R2 1 XC2
E
R
VR
VR S E0 as v S `
A high-pass filter transmits high frequencies and blocks low
frequencies.
Copyright ©2004 Pearson Education, Inc., publishing as Addison Wesley
VL 5 IXL
VC 5 IXC
C
When v 5 v0 5 1/ !LC (the resonance frequency), the
current in the circuit is a maximum Imax 5 E0/R.
In general, the current i lags behind E by the phase angle
f 5 tan21 ( (XL 2 XC )/R).
The power supplied by the emf is Psource 5 IrmsErms cos f,
where cos f is called the power factor.
The power lost in a resistor is PR 5 IrmsVrms 5 (Irms )2 R.
Download