Jennifer Lopez

Description

• fiche de synthèse - matière potentielle : birth

Numerology Chart Analysis for Jennifer Lopez by Hans Decoz for Lotus Tarot Birth data: Jennifer Lynn Lopez July 24, 1969

• great significance
• numerology chart analysis
• fine qualities
• personal criticisms
• title page
• title-page
• birth
• date of birth
• life
• data

Sujets

• Hancock
• Personal

Informations

• Publié par: choun
• Nombre de lectures: 27
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

44920_21_p693-725 1/12/05 8:33 AM Page 693
Arecibo, a large radio telescope in
Puerto Rico, gathers electromagnetic
radiation in the form of radio waves.
These long wavelengths pass through
obscuring dust clouds, allowing
astronomers to create images of the
core region of the Milky Way Galaxy,
which can't be observed in the visible
spectrum.
CHAPTER
21
OUTLINE
21.1 Resistors in an AC CircuitAlternating Current Circuits
21.2 Capacitors in an AC Circuit
21.3 Inductors in an AC Circuit
21.4 The RLC Series Circuitand Electromagnetic Waves
21.5 Power in an AC Circuit
21.6 Resonance in a Series
Every time we turn on a television set, a stereo system, or any of a multitude of other electric RLC Circuit
appliances, we call on alternating currents (AC) to provide the power to operate them. We 21.7 The Transformer
begin our study of AC circuits by examining the characteristics of a circuit containing a source 21.8 Maxwell’s Predictions
of emf and one other circuit element: a resistor, a capacitor, or an inductor. Then we examine
21.9 Hertz’s Confirmation of
what happens when these elements are connected in combination with each other. Our
Maxwell’s Predictions
discussion is limited to simple series configurations of the three kinds of elements.
21.10 Production ofWe conclude this chapter with a discussion of electromagnetic waves, which are
Electromagnetic Waves composed of fluctuating electric and magnetic fields. Electromagnetic waves in the form of
by an Antennavisible light enable us to view the world around us; infrared waves warm our environment;
22.11 Properties of radio-frequency waves carry our television and radio programs, as well as information about
Electromagnetic Wavesprocesses in the core of our galaxy. X-rays allow us to perceive structures hidden inside our
bodies, and study properties of distant, collapsed stars. Light is key to our understanding of 21.12 The Spectrum of
the universe.aves
21.13 The Doppler Effect for
Electromagnetic Waves21.1 RESISTORS IN AN AC CIRCUIT
An AC circuit consists of combinations of circuit elements and an AC generator or
an AC source, which provides the alternating current. We have seen that the
output of an AC generator is sinusoidal and varies with time according to
v V sin 2ft [21.1]max
where v is the instantaneous voltage, V is the maximum voltage of the AC gen-max
erator, and f is the frequency at which the voltage changes, measured in hertz (Hz).
(Compare Equations 20.7 and 20.8 with Equation 21.1.) We first consider a simple
693
© Bettmann/Corbis
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694 Chapter 21 Alternating Current Circuits and Electromagnetic Waves
∆vR circuit consisting of a resistor and an AC source (designated by the symbol
), as in Active Figure 21.1. The current and the voltage across the
R resistor are shown in Active Figure 21.2.
To explain the concept of alternating current, we begin by discussing the
current-versus-time curve in Active Figure 21.2. At point a on the curve, the cur-
rent has a maximum value in one direction, arbitrarily called the positive direc-
tion. Between points a and b, the current is decreasing in magnitude but is still in
v = V sin 2ftmax the positive direction. At point b, the current is momentarily zero; it then begins to
ACTIVE FIGURE 21.1 increase in the opposite (negative) direction between points b and c. At point c,
A series circuit consisting of a resistor the current has reached its maximum value in the negative direction.
R connected to an AC generator,
The current and voltage are in step with each other because they vary identi-designated by the symbol
cally with time. Because the current and the voltage reach their maximum values at
.
the same time, they are said to be in phase. Notice that the average value of the cur-
rent over one cycle is zero. This is because the current is maintained in one direction
(the positive direction) for the same amount of time and at the same magnitude as
Log into PhysicsNow at www.cp7e.com it is in the opposite direction (the negative direction). However, the direction of
and go to Active Figure 21.1, where the current has no effect on the behavior of the resistor in the circuit: the colli-
you can adjust the resistance, the
sions between electrons and the fixed atoms of the resistor result in an increase infrequency, and the maximum voltage
of the circuit shown. The results can be the resistor’s temperature regardless of the direction of the current.
studied with the graph and phasor We can quantify this discussion by recalling that the rate at which electrical
diagram in Active Figure 21.2.
energy is dissipated in a resistor, the power , is
2 i R
where i is the instantaneous current in the resistor. Because the heating effect of a
current is proportional to the square of the current, it makes no difference whether
the sign associated with the current is positive or negative. However, the heatingi , ∆vR R
effect produced by an alternating current with a maximum value of I is not themax
same as that produced by a direct current of the same value. The reason is that theaI imax R
alternating current has this maximum value for only an instant of time during a
∆V ∆vmax R cycle. The important quantity in an AC circuit is a special kind of average value of
b current, called the rms current—the direct current that dissipates the samet
T amount of energy in a resistor that is dissipated by the actual alternating current.
To find the rms current, we first square the current, Then find its average value,
and finally take the square root of this average value. Hence, the rms current is the
c 2square root of the average (mean) of the square of the current. Because i varies as
1ACTIVE FIGURE 21.2 2 2 2 1sin 2ft, the average value of iis (Fig. I 21.3b). Therefore, the rms currentmax2 A plot of current and voltage across a
I is related to the maximum value of the alternating current I byresistor versus time. rms max
I maxI 0.707I [21.2]rms max
Log into PhysicsNow at www.cp7e.com √2
and go to Active Figure 21.2, where
you can adjust the resistance, the This equation says that an alternating current with a maximum value of 3 A pro-
frequency, and the maximum voltage duces the same heating effect in a resistor as a direct current of (3/√2) A. We can
of the circuit in Active Figure 21.1.
therefore say that the average power dissipated in a resistor that carries alternatingThe results can be studied with the
graph and phasor diagram in Active current I is
Figure 21.20.
2 I R.av rms
1 2 2The fact that (i ) I /2 can be shown as follows: The current in the circuit varies with time according to av max
2 2 2 2the expression i I sin 2ft, so i I sin 2ft. Therefore, we can find the average value of i by calculatingmax max
2 2 2the average value of sin 2ft. Note that a graph of cos 2ft versus time is identical to a graph of sin 2ft versus time,
2except that the points are shifted on the time axis. Thus, the time average of sin 2ft is equal to the time average of
2cos 2ft, taken over one or more cycles. That is,
2 2(sin 2ft) (cos 2ft)av av
2 2With this fact and the trigonometric identity sin cos 1, we get
2 2 2(sin 2ft) (cos 2ft) 2(sin 2ft) 1av av av
12(sin 2 ft) av 2
2 2 2 22 2When this result is substituted into the expression i I sin 2ft, we get (i ) I I /2, or max maxav rms
I I / 2, where I is the rms current.√ rmsrms max44920_21_p693-725 1/12/05 8:33 AM Page 695
21.1 Resistors in an AC Circuit 695
i Figure 21.3 (a) Plot of the current
in a resistor as a function of time.
Imax (b) Plot of the square of the current
in a resistor as a function of time.
t Notice that the gray shaded regions
under the curve and above the dashed
2line for I /2 have the same area max
as the gray shaded regions above the(a)
curve and below the dashed line
2for I /2. Thus, the average max
2 2 2i value of Iis .I /2max
2I max
2 1 2(i ) = Iav max2
t
(b)
Alternating voltages are also best discussed in terms of rms voltages, with a rela-
tionship identical to the preceding one,
Vmax
V 0.707 V [21.3] rms voltagerms max
√2
where V is the rms voltage and V is the maximum value of the alternatingrms max
voltage.
When we speak of measuring an AC voltage of 120 V from an electric outlet, we TABLE 21.1
really mean an rms voltage of 120 V. A quick calculation using Equation 21.3 shows Notation Used in This
that such an AC voltage actually has a peak value of about 170 V. In this chapter we Chapter
use rms values when discussing alternating currents and voltages. One reason is
Voltage Current
that AC ammeters and voltmeters are designed to read rms values. Further, if we
Instantaneous viuse rms values, many of the equations for alternating current will have the same
valueform as those used in the study of direct-current (DC) circuits. Table 21.1 summa-
Maximum V Imax maxrizes the notations used throughout the chapter.
valueConsider the series circuit in Figure 21.1, consisting of a resistor connected to
rms value V Irms rmsan AC generator. A resistor impedes the current in an AC circuit, just as it does in
a DC circuit. Ohm’s law is therefore valid for an AC circuit, and we have
V I R [21.4a]R,rms rms
The rms voltage across a resistor is equal to the rms current in the circuit times the
resi