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Electrical Theory
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Benjamin Franklin and Electricity  SOURCE
The Direction Assigned to Electric Currents
 The choice of which type of electricity is
called "positive" and which "negative" was made
around 1750 by Ben Franklin, early American scientist and man of many
talents (the stamp on the left commemorates his role as first US
postmasterand colonial postmaster before that). Franklin studied
static electricity, produced by rubbing glass, amber, sulfur etc. with
fur or dry cloth. Among his many discoveries was proof that lightning
was a discharge of electricity, by the foolhardy experiment of flying
a kite in a thunderstorm. The kite string produced large sparks but
luckily no lightning, which could have killed Franklin.

Franklin knew of two types of electric charge,
depending on the material one rubbed. He thought that one kind signified
a little excess of the "electric fluid" over the usual amount,
and he called that "positive" electricity (marked by +), while
the other kind was "negative" (marked ), signifying a slight
deficiency. It is not known whether he tossed a coin before deciding to
call the kind produced by rubbing glass "positive" and the
other "resinous" type "negative" (rather than the
other way around), but he might just as well have.
Later, when electric batteries were discovered,
scientists naturally assigned the direction of the flow of current to be
from (+) to (). A century after that electrons were discovered and it
was suddenly realized that in metal wires the electrons were the ones
that carried the current, moving in exactly the opposite direction.
Also, it was an excess of electrons which produced a negative electric
charge. However, it was much too late to change Franklin's naming
convention

A Simple Experiment
Ben Franklin's kite experiment observed atmospheric
electricity, of which lightning is just the most extreme form. The
electric charge originates in thunderheads (cumulonimbus clouds) by a
process is described in the last part of this
file. In thunderstorms and below them the electrification is strong and
lightning occurs, but it spreads over large areas, though at distant
points it gets weak.
A simple experiment for observing this
electricity was described on a weblist by Larry Cartwright,
retired physics teacher in Michigan:
"If you like experimenting with everyday
stuff (what the heck would you be doing teaching physics if you didn't
like experimenting, right?), find a building with ungrounded aluminum
siding and connect a small neon lamp between the siding and a grounded
pipe or rod. The lamp flashes whenever the siding reaches a certain
potential w/respect to ground. (Faster flashing = higher
electrification) You might get some surprises about the kinds of
weather that produce substantial charges on the building's surface. A
few years back, a person was killed at a park near here by a freak
lightning strike on a practically clear and sunny summer day. You can get the little NE2 lamps at
electronics parts suppliers such as Radio Shack, at a hardware store
(getting harder and harder to find traditional hardware stores), and
in the tools/hardware department of any wellequipped discount Mart or
home building supplies center. Multimegohm resistors can be used to
decrease the sensitivity of the lamp if you wish. By the way, definitely do not put yourself
between the siding and the ground on a cumulonimbus kind of day!"

Futher reading:
Another great name in electricity  SOURCE
(1787  1854)
Born in Erlangen, Germany, his later work as a physicist resulted in the
1827 discovery of the mathematical law of electriccurrent called "Ohm's
Law." The ohm, a unit of electrical resistance, is equal to that of a
conductor in which a current of one ampere is produced by a potential of one
volt across its terminals.


One of the great electricians of the past.  SOURCE
(1856  1943)
A SerbianAmerican physicist and electrical engineer who invented
fluorescent lighting, the Tesla induction motor, the Tesla coil, and developed
the alternating current (AC) electrical supply system. Nikola Tesla was born on
July 10, 1856 in Smiljan, Lika, which was then part ofÊ the AustroHungarian
Empire; the area now known as the Republic of Croatia. His father, Milutin
Tesla, was a Serbian Orthodox Priest and his mother, Djuka Mandic, was an
inventor of household appliances. He emigrated to the U.S. in 1884.
In 1885 George Westinghouse, head of the Westinghouse Electric Company,
bought the patent rights to Tesla's system of dynamos, transformers and motors.
Westinghouse used Tesla's alternating current system to light the World's
Columbian Exposition of 1893 in Chicago. The Tesla coil, invented in 1891, is
still used in radio and television sets and other electronic equipment. Tesla is
considered one of the outstanding intellects who paved the way for many of the
technological developments of modern times. A rock group from Sacramento,
California, named themselves after this scientist, calling themselves TESLA.




A short course in alternating current electrical theory  SOURCE
BASIC AC THEORY
What is alternating current (AC)?
Most students of electricity begin their study with what is known as direct
current (DC), which is electricity flowing in a constant direction, and/or
possessing a voltage with constant polarity. DC is the kind of electricity made
by a battery (with definite positive and negative terminals), or the kind of
charge generated by rubbing certain types of materials against each other.
As useful and as easy to understand as DC is, it is not the only
"kind" of electricity in use. Certain sources of electricity (most
notably, rotary electromechanical generators) naturally produce voltages
alternating in polarity, reversing positive and negative over time. Either as a
voltage switching polarity or as a current switching direction back and forth,
this "kind" of electricity is known as Alternating Current (AC):
Whereas the familiar battery symbol is used as a generic symbol for any DC
voltage source, the circle with the wavy line inside is the generic symbol for
any AC voltage source.
One might wonder why anyone would bother with such a thing as AC. It is true
that in some cases AC holds no practical advantage over DC. In applications
where electricity is used to dissipate energy in the form of heat, the polarity
or direction of current is irrelevant, so long as there is enough voltage and
current to the load to produce the desired heat (power dissipation). However,
with AC it is possible to build electric generators, motors and power
distribution systems that are far more efficient than DC, and so we find AC used
predominately across the world in high power applications. To explain the
details of why this is so, a bit of background knowledge about AC is necessary.
If a machine is constructed to rotate a magnetic field around a set of
stationary wire coils with the turning of a shaft, AC voltage will be produced
across the wire coils as that shaft is rotated, in accordance with Faraday's Law
of electromagnetic induction. This is the basic operating principle of an AC
generator, also known as an alternator:
Notice how the polarity of the voltage across the wire coils reverses as the
opposite poles of the rotating magnet pass by. Connected to a load, this
reversing voltage polarity will create a reversing current direction in the
circuit. The faster the alternator's shaft is turned, the faster the magnet will
spin, resulting in an alternating voltage and current that switches directions
more often in a given amount of time.
While DC generators work on the same general principle of electromagnetic
induction, their construction is not as simple as their AC counterparts. With a
DC generator, the coil of wire is mounted in the shaft where the magnet is on
the AC alternator, and electrical connections are made to this spinning coil via
stationary carbon "brushes" contacting copper strips on the rotating
shaft. All this is necessary to switch the coil's changing output polarity to
the external circuit so the external circuit sees a constant polarity:
The generator shown above will produce two pulses of voltage per revolution
of the shaft, both pulses in the same direction (polarity). In order for a DC
generator to produce constant voltage, rather than brief pulses of
voltage once every 1/2 revolution, there are multiple sets of coils making
intermittent contact with the brushes. The diagram shown above is a bit more
simplified than what you would see in real life.
The problems involved with making and breaking electrical contact with a
moving coil should be obvious (sparking and heat), especially if the shaft of
the generator is revolving at high speed. If the atmosphere surrounding the
machine contains flammable or explosive vapors, the practical problems of
sparkproducing brush contacts are even greater. An AC generator (alternator)
does not require brushes and commutators to work, and so is immune to these
problems experienced by DC generators.
The benefits of AC over DC with regard to generator design is also reflected
in electric motors. While DC motors require the use of brushes to make
electrical contact with moving coils of wire, AC motors do not. In fact, AC and
DC motor designs are very similar to their generator counterparts (identical for
the sake of this tutorial), the AC motor being dependent upon the reversing
magnetic field produced by alternating current through its stationary coils of
wire to rotate the rotating magnet around on its shaft, and the DC motor being
dependent on the brush contacts making and breaking connections to reverse
current through the rotating coil every 1/2 rotation (180 degrees).
So we know that AC generators and AC motors tend to be simpler than DC
generators and DC motors. This relative simplicity translates into greater
reliability and lower cost of manufacture. But what else is AC good for? Surely
there must be more to it than design details of generators and motors! Indeed
there is. There is an effect of electromagnetism known as mutual induction,
whereby two or more coils of wire placed so that the changing magnetic field
created by one induces a voltage in the other. If we have two mutually inductive
coils and we energize one coil with AC, we will create an AC voltage in the
other coil. When used as such, this device is known as a transformer:
The fundamental significance of a transformer is its ability to step voltage
up or down from the powered coil to the unpowered coil. The AC voltage induced
in the unpowered ("secondary") coil is equal to the AC voltage across
the powered ("primary") coil multiplied by the ratio of secondary coil
turns to primary coil turns. If the secondary coil is powering a load, the
current through the secondary coil is just the opposite: primary coil current
multiplied by the ratio of primary to secondary turns. This relationship has a
very close mechanical analogy, using torque and speed to represent voltage and
current, respectively:
If the winding ratio is reversed so that the primary coil has less turns
than the secondary coil, the transformer "steps up" the voltage from
the source level to a higher level at the load:
The transformer's ability to step AC voltage up or down with ease gives AC
an advantage unmatched by DC in the realm of power distribution. When
transmitting electrical power over long distances, it is far more efficient to
do so with steppedup voltages and steppeddown currents (smallerdiameter wire
with less resistive power losses), then step the voltage back down and the
current back up for industry, business, or consumer use use.
Transformer technology has made longrange electric power distribution
practical. Without the ability to efficiently step voltage up and down, it would
be costprohibitive to construct power systems for anything but closerange
(within a few miles at most) use.
As useful as transformers are, they only work with AC, not DC. Because the
phenomenon of mutual inductance relies on changing magnetic fields, and
direct current (DC) can only produce steady magnetic fields, transformers simply
will not work with direct current. Of course, direct current may be interrupted
(pulsed) through the primary winding of a transformer to create a changing
magnetic field (as is done in automotive ignition systems to produce
highvoltage spark plug power from a lowvoltage DC battery), but pulsed DC is
not that different from AC. Perhaps more than any other reason, this is why AC
finds such widespread application in power systems.

REVIEW:


DC stands for "Direct Current," meaning voltage or current
that maintains constant polarity or direction, respectively, over time.


AC stands for "Alternating Current," meaning voltage or
current that changes polarity or direction, respectively, over time.


AC electromechanical generators, known as alternators, are of
simpler construction than DC electromechanical generators.


AC and DC motor design follows respective generator design principles
very closely.


A transformer is a pair of mutuallyinductive coils used to
convey AC power from one coil to the other. Often, the number of turns in
each coil is set to create a voltage increase or decrease from the powered
(primary) coil to the unpowered (secondary) coil.


Secondary voltage = Primary voltage (secondary turns / primary turns)


Secondary current = Primary current (primary turns / secondary turns)

AC waveforms
When an alternator produces AC voltage, the voltage switches polarity over
time, but does so in a very particular manner. When graphed over time, the
"wave" traced by this voltage of alternating polarity from an
alternator takes on a distinct shape, known as a sine wave:
In the voltage plot from an electromechanical alternator, the change from
one polarity to the other is a smooth one, the voltage level changing most
rapidly at the zero ("crossover") point and most slowly at its peak.
If we were to graph the trigonometric function of "sine" over a
horizontal range of 0 to 360 degrees, we would find the exact same pattern:
Angle
Sine(angle)
in degrees
0 ............... 0.0000 
zero
15 ...............
0.2588
30 ...............
0.5000
45 ...............
0.7071
60 ...............
0.8660
75 ...............
0.9659
90 ............... 1.0000  positive
peak
105 ..............
0.9659
120 ..............
0.8660
135 ..............
0.7071
150 ..............
0.5000
165 ..............
0.2588
180 .............. 0.0000 
zero
195 ..............
0.2588
210 ..............
0.5000
225 ..............
0.7071
240 ..............
0.8660
255 ..............
0.9659
270 .............. 1.0000  negative
peak
285 ..............
0.9659
300 ..............
0.8660
315 ..............
0.7071
330 ..............
0.5000
345 ..............
0.2588
360 .............. 0.0000 
zero
The reason why an electromechanical alternator outputs sinewave AC is due
to the physics of its operation. The voltage produced by the stationary coils by
the motion of the rotating magnet is proportional to the rate at which the
magnetic flux is changing perpendicular to the coils (Faraday's Law of
Electromagnetic Induction). That rate is greatest when the magnet poles are
closest to the coils, and least when the magnet poles are furthest away from the
coils. Mathematically, the rate of magnetic flux change due to a rotating magnet
follows that of a sine function, so the voltage produced by the coils follows
that same function.
If we were to follow the changing voltage produced by a coil in an
alternator from any point on the sine wave graph to that point when the wave
shape begins to repeat itself, we would have marked exactly one cycle of
that wave. This is most easily shown by spanning the distance between identical
peaks, but may be measured between any corresponding points on the graph. The
degree marks on the horizontal axis of the graph represent the domain of the
trigonometric sine function, and also the angular position of our simple
twopole alternator shaft as it rotates:
Since the horizontal axis of this graph can mark the passage of time as well
as shaft position in degrees, the dimension marked for one cycle is often
measured in a unit of time, most often seconds or fractions of a second. When
expressed as a measurement, this is often called the period of a wave.
The period of a wave in degrees is always 360, but the amount of time one
period occupies depends on the rate voltage oscillates back and forth.
A more popular measure for describing the alternating rate of an AC voltage
or current wave than period is the rate of that backandforth
oscillation. This is called frequency. The modern unit for frequency is
the Hertz (abbreviated Hz), which represents the number of wave cycles completed
during one second of time. In the United States of America, the standard
powerline frequency is 60 Hz, meaning that the AC voltage oscillates at a rate
of 60 complete backandforth cycles every second. In Europe, where the power
system frequency is 50 Hz, the AC voltage only completes 50 cycles every second.
A radio station transmitter broadcasting at a frequency of 100 MHz generates an
AC voltage oscillating at a rate of 100 million cycles every second.
Prior to the canonization of the Hertz unit, frequency was simply expressed
as "cycles per second." Older meters and electronic equipment often
bore frequency units of "CPS" (Cycles Per Second) instead of Hz. Many
people believe the change from selfexplanatory units like CPS to Hertz
constitutes a step backward in clarity. A similar change occurred when the unit
of "Celsius" replaced that of "Centigrade" for metric
temperature measurement. The name Centigrade was based on a 100count ("Centi")
scale ("grade") representing the melting and boiling points of H_{2}O,
respectively. The name Celsius, on the other hand, gives no hint as to the
unit's origin or meaning.
Period and frequency are mathematical reciprocals of one another. That is to
say, if a wave has a period of 10 seconds, its frequency will be 0.1 Hz, or 1/10
of a cycle per second:
An instrument called an oscilloscope is used to display a changing
voltage over time on a graphical screen. You may be familiar with the appearance
of an ECG or EKG (electrocardiograph) machine, used by physicians
to graph the oscillations of a patient's heart over time. The ECG is a
specialpurpose oscilloscope expressly designed for medical use. Generalpurpose
oscilloscopes have the ability to display voltage from virtually any voltage
source, plotted as a graph with time as the independent variable. The
relationship between period and frequency is very useful to know when displaying
an AC voltage or current waveform on an oscilloscope screen. By measuring the
period of the wave on the horizontal axis of the oscilloscope screen and
reciprocating that time value (in seconds), you can determine the frequency in
Hertz.
Voltage and current are by no means the only physical variables subject to
variation over time. Much more common to our everyday experience is sound,
which is nothing more than the alternating compression and decompression
(pressure waves) of air molecules, interpreted by our ears as a physical
sensation. Because alternating current is a wave phenomenon, it shares many of
the properties of other wave phenomena, like sound. For this reason, sound
(especially structured music) provides an excellent analogy for relating AC
concepts.
In musical terms, frequency is equivalent to pitch. Lowpitch notes
such as those produced by a tuba or bassoon consist of air molecule vibrations
that are relatively slow (low frequency). Highpitch notes such as those
produced by a flute or whistle consist of the same type of vibrations in the
air, only vibrating at a much faster rate (higher frequency). Here is a table
showing the actual frequencies for a range of common musical notes:
Astute observers will notice that all notes on the table bearing the same
letter designation are related by a frequency ratio of 2:1. For example, the
first frequency shown (designated with the letter "A") is 220 Hz. The
next highest "A" note has a frequency of 440 Hz  exactly twice as
many sound wave cycles per second. The same 2:1 ratio holds true for the first A
sharp (233.08 Hz) and the next A sharp (466.16 Hz), and for all note pairs found
in the table.
Audibly, two notes whose frequencies are exactly double each other sound
remarkably similar. This similarity in sound is musically recognized, the
shortest span on a musical scale separating such note pairs being called an octave.
Following this rule, the next highest "A" note (one octave above 440
Hz) will be 880 Hz, the next lowest "A" (one octave below 220 Hz) will
be 110 Hz. A view of a piano keyboard helps to put this scale into perspective:
As you can see, one octave is equal to eight white keys' worth of
distance on a piano keyboard. The familiar musical mnemonic (doeraymeefahsolahteedoe)
 yes, the same pattern immortalized in the whimsical Rodgers and Hammerstein
song sung in The Sound of Music  covers one octave from C to C.
While electromechanical alternators and many other physical phenomena
naturally produce sine waves, this is not the only kind of alternating wave in
existence. Other "waveforms" of AC are commonly produced within
electronic circuitry. Here are but a few sample waveforms and their common
designations:
These waveforms are by no means the only kinds of waveforms in existence.
They're simply a few that are common enough to have been given distinct names.
Even in circuits that are supposed to manifest "pure" sine, square,
triangle, or sawtooth voltage/current waveforms, the reallife result is often a
distorted version of the intended waveshape. Some waveforms are so complex that
they defy classification as a particular "type" (including waveforms
associated with many kinds of musical instruments). Generally speaking, any
waveshape bearing close resemblance to a perfect sine wave is termed sinusoidal,
anything different being labeled as nonsinusoidal. Being that the
waveform of an AC voltage or current is crucial to its impact in a circuit, we
need to be aware of the fact that AC waves come in a variety of shapes.

REVIEW:


AC produced by an electromechanical alternator follows the graphical
shape of a sine wave.


One cycle of a wave is one complete evolution of its shape until
the point that it is ready to repeat itself.


The period of a wave is the amount of time it takes to complete
one cycle.


Frequency is the number of complete cycles that a wave completes
in a given amount of time. Usually measured in Hertz (Hz), 1 Hz being equal
to one complete wave cycle per second.


Frequency = 1/(period in seconds)

Measurements of AC magnitude
So far we know that AC voltage alternates in polarity and AC current
alternates in direction. We also know that AC can alternate in a variety of
different ways, and by tracing the alternation over time we can plot it as a
"waveform." We can measure the rate of alternation by measuring the
time it takes for a wave to evolve before it repeats itself (the
"period"), and express this as cycles per unit time, or
"frequency." In music, frequency is the same as pitch, which is
the essential property distinguishing one note from another.
However, we encounter a measurement problem if we try to express how large
or small an AC quantity is. With DC, where quantities of voltage and current are
generally stable, we have little trouble expressing how much voltage or current
we have in any part of a circuit. But how do you grant a single measurement of
magnitude to something that is constantly changing?
One way to express the intensity, or magnitude (also called the amplitude),
of an AC quantity is to measure its peak height on a waveform graph. This is
known as the peak or crest value of an AC waveform:
Another way is to measure the total height between opposite peaks. This is
known as the peaktopeak (PP) value of an AC waveform:
Unfortunately, either one of these expressions of waveform amplitude can be
misleading when comparing two different types of waves. For example, a square
wave peaking at 10 volts is obviously a greater amount of voltage for a greater
amount of time than a triangle wave peaking at 10 volts. The effects of these
two AC voltages powering a load would be quite different:
One way of expressing the amplitude of different waveshapes in a more
equivalent fashion is to mathematically average the values of all the points on
a waveform's graph to a single, aggregate number. This amplitude measure is
known simply as the average value of the waveform. If we average all the
points on the waveform algebraically (that is, to consider their sign,
either positive or negative), the average value for most waveforms is
technically zero, because all the positive points cancel out all the negative
points over a full cycle:
This, of course, will be true for any waveform having equalarea portions
above and below the "zero" line of a plot. However, as a practical
measure of a waveform's aggregate value, "average" is usually defined
as the mathematical mean of all the points' absolute values over a cycle.
In other words, we calculate the practical average value of the waveform by
considering all points on the wave as positive quantities, as if the waveform
looked like this:
Polarityinsensitive mechanical meter movements (meters designed to respond
equally to the positive and negative halfcycles of an alternating voltage or
current) register in proportion to the waveform's (practical) average value,
because the inertia of the pointer against the tension of the spring naturally
averages the force produced by the varying voltage/current values over time.
Conversely, polaritysensitive meter movements vibrate uselessly if exposed to
AC voltage or current, their needles oscillating rapidly about the zero mark,
indicating the true (algebraic) average value of zero for a symmetrical
waveform. When the "average" value of a waveform is referenced in this
text, it will be assumed that the "practical" definition of average is
intended unless otherwise specified.
Another method of deriving an aggregate value for waveform amplitude is
based on the waveform's ability to do useful work when applied to a load
resistance. Unfortunately, an AC measurement based on work performed by a
waveform is not the same as that waveform's "average" value, because
the power dissipated by a given load (work performed per unit time) is
not directly proportional to the magnitude of either the voltage or current
impressed upon it. Rather, power is proportional to the square of the
voltage or current applied to a resistance (P = E^{2}/R, and P = I^{2}R).
Although the mathematics of such an amplitude measurement might not be
straightforward, the utility of it is.
Consider a bandsaw and a jigsaw, two pieces of modern woodworking equipment.
Both types of saws cut with a thin, toothed, motorpowered metal blade to cut
wood. But while the bandsaw uses a continuous motion of the blade to cut, the
jigsaw uses a backandforth motion. The comparison of alternating current (AC)
to direct current (DC) may be likened to the comparison of these two saw types:
The problem of trying to describe the changing quantities of AC voltage or
current in a single, aggregate measurement is also present in this saw analogy:
how might we express the speed of a jigsaw blade? A bandsaw blade moves with a
constant speed, similar to the way DC voltage pushes or DC current moves with a
constant magnitude. A jigsaw blade, on the other hand, moves back and forth, its
blade speed constantly changing. What is more, the backandforth motion of any
two jigsaws may not be of the same type, depending on the mechanical design of
the saws. One jigsaw might move its blade with a sinewave motion, while another
with a trianglewave motion. To rate a jigsaw based on its peak blade
speed would be quite misleading when comparing one jigsaw to another (or a
jigsaw with a bandsaw!). Despite the fact that these different saws move their
blades in different manners, they are equal in one respect: they all cut wood,
and a quantitative comparison of this common function can serve as a common
basis for which to rate blade speed.
Picture a jigsaw and bandsaw sidebyside, equipped with identical blades
(same tooth pitch, angle, etc.), equally capable of cutting the same thickness
of the same type of wood at the same rate. We might say that the two saws were
equivalent or equal in their cutting capacity. Might this comparison be used to
assign a "bandsaw equivalent" blade speed to the jigsaw's
backandforth blade motion; to relate the woodcutting effectiveness of one to
the other? This is the general idea used to assign a "DC equivalent"
measurement to any AC voltage or current: whatever magnitude of DC voltage or
current would produce the same amount of heat energy dissipation through an
equal resistance:
In the two circuits above, we have the same amount of load resistance (2
Ω) dissipating the same amount of power in the form of heat (50 watts), one
powered by AC and the other by DC. Because the AC voltage source pictured above
is equivalent (in terms of power delivered to a load) to a 10 volt DC battery,
we would call this a "10 volt" AC source. More specifically, we would
denote its voltage value as being 10 volts RMS. The qualifier
"RMS" stands for Root Mean Square, the algorithm used to obtain
the DC equivalent value from points on a graph (essentially, the procedure
consists of squaring all the positive and negative points on a waveform graph,
averaging those squared values, then taking the square root of that average to
obtain the final answer). Sometimes the alternative terms equivalent or DC
equivalent are used instead of "RMS," but the quantity and
principle are both the same.
RMS amplitude measurement is the best way to relate AC quantities to DC
quantities, or other AC quantities of differing waveform shapes, when dealing
with measurements of electric power. For other considerations, peak or
peaktopeak measurements may be the best to employ. For instance, when
determining the proper size of wire (ampacity) to conduct electric power from a
source to a load, RMS current measurement is the best to use, because the
principal concern with current is overheating of the wire, which is a function
of power dissipation caused by current through the resistance of the wire.
However, when rating insulators for service in highvoltage AC applications,
peak voltage measurements are the most appropriate, because the principal
concern here is insulator "flashover" caused by brief spikes of
voltage, irrespective of time.
Peak and peaktopeak measurements are best performed with an oscilloscope,
which can capture the crests of the waveform with a high degree of accuracy due
to the fast action of the cathoderaytube in response to changes in voltage.
For RMS measurements, analog meter movements (D'Arsonval, Weston, iron vane,
electrodynamometer) will work so long as they have been calibrated in RMS
figures. Because the mechanical inertia and dampening effects of an
electromechanical meter movement makes the deflection of the needle naturally
proportional to the average value of the AC, not the true RMS value,
analog meters must be specifically calibrated (or miscalibrated, depending on
how you look at it) to indicate voltage or current in RMS units. The accuracy of
this calibration depends on an assumed waveshape, usually a sine wave.
Electronic meters specifically designed for RMS measurement are best for the
task. Some instrument manufacturers have designed ingenious methods for
determining the RMS value of any waveform. One such manufacturer produces
"TrueRMS" meters with a tiny resistive heating element powered by a
voltage proportional to that being measured. The heating effect of that
resistance element is measured thermally to give a true RMS value with no
mathematical calculations whatsoever, just the laws of physics in action in
fulfillment of the definition of RMS. The accuracy of this type of RMS
measurement is independent of waveshape.
For "pure" waveforms, simple conversion coefficients exist for
equating Peak, PeaktoPeak, Average (practical, not algebraic), and RMS
measurements to one another:
In addition to RMS, average, peak (crest), and peaktopeak measures of an
AC waveform, there are ratios expressing the proportionality between some of
these fundamental measurements. The crest factor of an AC waveform, for
instance, is the ratio of its peak (crest) value divided by its RMS value. The form
factor of an AC waveform is the ratio of its peak value divided by its
average value. Squareshaped waveforms always have crest and form factors equal
to 1, since the peak is the same as the RMS and average values. Sinusoidal
waveforms have crest factors of 1.414 (the square root of 2) and form factors of
1.571 (π/2). Triangle and sawtoothshaped waveforms have crest values of
1.732 (the square root of 3) and form factors of 2.
Bear in mind that the conversion constants shown here for peak, RMS, and
average amplitudes of sine waves, square waves, and triangle waves hold true
only for pure forms of these waveshapes. The RMS and average values of
distorted waveshapes are not related by the same ratios:
This is a very important concept to understand when using an analog meter
movement to measure AC voltage or current. An analog movement, calibrated to
indicate sinewave RMS amplitude, will only be accurate when measuring pure sine
waves. If the waveform of the voltage or current being measured is anything but
a pure sine wave, the indication given by the meter will not be the true RMS
value of the waveform, because the degree of needle deflection in an analog
meter movement is proportional to the average value of the waveform, not
the RMS. RMS meter calibration is obtained by "skewing" the span of
the meter so that it displays a small multiple of the average value, which will
be equal to be the RMS value for a particular waveshape and a particular
waveshape only.
Since the sinewave shape is most common in electrical measurements, it is
the waveshape assumed for analog meter calibration, and the small multiple used
in the calibration of the meter is 1.1107 (the form factor π/2 divided by
the crest factor 1.414: the ratio of RMS divided by average for a sinusoidal
waveform). Any waveshape other than a pure sine wave will have a different ratio
of RMS and average values, and thus a meter calibrated for sinewave voltage or
current will not indicate true RMS when reading a nonsinusoidal wave. Bear in
mind that this limitation applies only to simple, analog AC meters not employing
"TrueRMS" technology.

REVIEW:


The amplitude of an AC waveform is its height as depicted on a
graph over time. An amplitude measurement can take the form of peak,
peaktopeak, average, or RMS quantity.


Peak amplitude is the height of an AC waveform as measured from
the zero mark to the highest positive or lowest negative point on a graph.
Also known as the crest amplitude of a wave.


Peaktopeak amplitude is the total height of an AC waveform as
measured from maximum positive to maximum negative peaks on a graph. Often
abbreviated as "PP".


Average amplitude is the mathematical "mean" of all a
waveform's points over the period of one cycle. Technically, the average
amplitude of any waveform with equalarea portions above and below the
"zero" line on a graph is zero. However, as a practical measure of
amplitude, a waveform's average value is often calculated as the
mathematical mean of all the points' absolute values (taking all the
negative values and considering them as positive). For a sine wave, the
average value so calculated is approximately 0.637 of its peak value.


"RMS" stands for Root Mean Square, and is a way of
expressing an AC quantity of voltage or current in terms functionally
equivalent to DC. For example, 10 volts AC RMS is the amount of voltage that
would produce the same amount of heat dissipation across a resistor of given
value as a 10 volt DC power supply. Also known as the "equivalent"
or "DC equivalent" value of an AC voltage or current. For a sine
wave, the RMS value is approximately 0.707 of its peak value.


The crest factor of an AC waveform is the ratio of its peak
(crest) to its RMS value.


The form factor of an AC waveform is the ratio of its peak
(crest) value to its average value.


Analog, electromechanical meter movements respond proportionally to the average
value of an AC voltage or current. When RMS indication is desired, the
meter's calibration must be "skewed" accordingly. This means that
the accuracy of an electromechanical meter's RMS indication is dependent on
the purity of the waveform: whether it is the exact same waveshape as the
waveform used in calibrating.

Simple AC circuit calculations
Over the course of the next few chapters, you will learn that AC circuit
measurements and calculations can get very complicated due to the complex nature
of alternating current in circuits with inductance and capacitance. However,
with simple circuits involving nothing more than an AC power source and
resistance, the same laws and rules of DC apply simply and directly.
Series resistances still add, parallel resistances still diminish, and the
Laws of Kirchhoff and Ohm still hold true. Actually, as we will discover later
on, these rules and laws always hold true, it's just that we have to
express the quantities of voltage, current, and opposition to current in more
advanced mathematical forms. With purely resistive circuits, however, these
complexities of AC are of no practical consequence, and so we can treat the
numbers as though we were dealing with simple DC quantities.
Because all these mathematical relationships still hold true, we can make
use of our familiar "table" method of organizing circuit values just
as with DC:
One major caveat needs to be given here: all measurements of AC voltage and
current must be expressed in the same terms (peak, peaktopeak, average, or
RMS). If the source voltage is given in peak AC volts, then all currents and
voltages subsequently calculated are cast in terms of peak units. If the source
voltage is given in AC RMS volts, then all calculated currents and voltages are
cast in AC RMS units as well. This holds true for any calculation based
on Ohm's Laws, Kirchhoff's Laws, etc. Unless otherwise stated, all values of
voltage and current in AC circuits are generally assumed to be RMS rather than
peak, average, or peaktopeak. In some areas of electronics, peak measurements
are assumed, but in most applications (especially industrial electronics) the
assumption is RMS.

REVIEW:


All the old rules and laws of DC (Kirchhoff's Voltage and Current Laws,
Ohm's Law) still hold true for AC. However, with more complex circuits, we
may need to represent the AC quantities in more complex form. More on this
later, I promise!


The "table" method of organizing circuit values is still a
valid analysis tool for AC circuits.

AC phase
Things start to get complicated when we need to relate two or more AC
voltages or currents that are out of step with each other. By "out of
step," I mean that the two waveforms are not synchronized: that their peaks
and zero points do not match up at the same points in time. The following graph
illustrates an example of this:
The two waves shown above (A versus B) are of the same amplitude and
frequency, but they are out of step with each other. In technical terms, this is
called a phase shift. Earlier we saw how we could plot a "sine
wave" by calculating the trigonometric sine function for angles ranging
from 0 to 360 degrees, a full circle. The starting point of a sine wave was zero
amplitude at zero degrees, progressing to full positive amplitude at 90 degrees,
zero at 180 degrees, full negative at 270 degrees, and back to the starting
point of zero at 360 degrees. We can use this angle scale along the horizontal
axis of our waveform plot to express just how far out of step one wave is with
another:
The shift between these two waveforms is about 45 degrees, the "A"
wave being ahead of the "B" wave. A sampling of different phase shifts
is given in the following graphs to better illustrate this concept:
Because the waveforms in the above examples are at the same frequency, they
will be out of step by the same angular amount at every point in time. For this
reason, we can express phase shift for two or more waveforms of the same
frequency as a constant quantity for the entire wave, and not just an expression
of shift between any two particular points along the waves. That is, it is safe
to say something like, "voltage 'A' is 45 degrees out of phase with voltage
'B'." Whichever waveform is ahead in its evolution is said to be leading
and the one behind is said to be lagging.
Phase shift, like voltage, is always a measurement relative between two
things. There's really no such thing as a waveform with an absolute phase
measurement because there's no known universal reference for phase. Typically in
the analysis of AC circuits, the voltage waveform of the power supply is used as
a reference for phase, that voltage stated as "xxx volts at 0
degrees." Any other AC voltage or current in that circuit will have its
phase shift expressed in terms relative to that source voltage.
This is what makes AC circuit calculations more complicated than DC. When
applying Ohm's Law and Kirchhoff's Laws, quantities of AC voltage and current
must reflect phase shift as well as amplitude. Mathematical operations of
addition, subtraction, multiplication, and division must operate on these
quantities of phase shift as well as amplitude. Fortunately, there is a
mathematical system of quantities called complex numbers ideally suited
for this task of representing amplitude and phase.
Because the subject of complex numbers is so essential to the understanding
of AC circuits, the next chapter will be devoted to that subject alone.

REVIEW:


Phase shift is where two or more waveforms are out of step with
each other.


The amount of phase shift between two waves can be expressed in terms of
degrees, as defined by the degree units on the horizontal axis of the
waveform graph used in plotting the trigonometric sine function.


A leading waveform is defined as one waveform that is ahead of
another in its evolution. A lagging waveform is one that is behind
another. Example:




Calculations for AC circuit analysis must take into consideration both
amplitude and phase shift of voltage and current waveforms to be completely
accurate. This requires the use of a mathematical system called complex
numbers.

Principles of radio
One of the more fascinating applications of electricity is in the generation
of invisible ripples of energy called radio waves. The limited scope of
this lesson on alternating current does not permit full exploration of the
concept, some of the basic principles will be covered.
With Oersted's accidental discovery of electromagnetism, it was realized
that electricity and magnetism were related to each other. When an electric
current was passed through a conductor, a magnetic field was generated
perpendicular to the axis of flow. Likewise, if a conductor was exposed to a
change in magnetic flux perpendicular to the conductor, a voltage was produced
along the length of that conductor. So far, scientists knew that electricity and
magnetism always seemed to affect each other at right angles. However, a major
discovery lay hidden just beneath this seemingly simple concept of related
perpendicularity, and its unveiling was one of the pivotal moments in modern
science.
This breakthrough in physics is hard to overstate. The man responsible for
this conceptual revolution was the Scottish physicist James Clerk Maxwell
(18311879), who "unified" the study of electricity and magnetism in
four relatively tidy equations. In essence, what he discovered was that electric
and magnetic fields were intrinsically related to one another, with or
without the presence of a conductive path for electrons to flow. Stated more
formally, Maxwell's discovery was this:
A changing electric field produces a perpendicular magnetic field,
and
A changing magnetic field produces a perpendicular electric field.
All of this can take place in open space, the alternating electric and
magnetic fields supporting each other as they travel through space at the speed
of light. This dynamic structure of electric and magnetic fields propagating
through space is better known as an electromagnetic wave.
There are many kinds of natural radiative energy composed of electromagnetic
waves. Even light is electromagnetic in nature. So are Xrays and
"gamma" ray radiation. The only difference between these kinds of
electromagnetic radiation is the frequency of their oscillation (alternation of
the electric and magnetic fields back and forth in polarity). By using a source
of AC voltage and a special device called an antenna, we can create
electromagnetic waves (of a much lower frequency than that of light) with ease.
An antenna is nothing more than a device built to produce a dispersing
electric or magnetic field. Two fundamental types of antennae are the dipole
and the loop:
While the dipole looks like nothing more than an open circuit, and the loop
a short circuit, these pieces of wire are effective radiators of electromagnetic
fields when connected to AC sources of the proper frequency. The two open wires
of the dipole act as a sort of capacitor (two conductors separated by a
dielectric), with the electric field open to dispersal instead of being
concentrated between two closelyspaced plates. The closed wire path of the loop
antenna acts like an inductor with a large air core, again providing ample
opportunity for the field to disperse away from the antenna instead of being
concentrated and contained as in a normal inductor.
As the powered dipole radiates its changing electric field into space, a
changing magnetic field is produced at right angles, thus sustaining the
electric field further into space, and so on as the wave propagates at the speed
of light. As the powered loop antenna radiates its changing magnetic field into
space, a changing electric field is produced at right angles, with the same
endresult of a continuous electromagnetic wave sent away from the antenna.
Either antenna achieves the same basic task: the controlled production of an
electromagnetic field.
When attached to a source of highfrequency AC power, an antenna acts as a transmitting
device, converting AC voltage and current into electromagnetic wave energy.
Antennas also have the ability to intercept electromagnetic waves and convert
their energy into AC voltage and current. In this mode, an antenna acts as a receiving
device:
While there is much more that may be said about antenna technology,
this brief introduction is enough to give you the general idea of what's going
on (and perhaps enough information to provoke a few experiments).

REVIEW:


James Maxwell discovered that changing electric fields produce
perpendicular magnetic fields, and visaversa, even in empty space.


A twin set of electric and magnetic fields, oscillating at right angles
to each other and traveling at the speed of light, constitutes an electromagnetic
wave.


An antenna is a device made of wire, designed to radiate a
changing electric field or changing magnetic field when powered by a
highfrequency AC source, or intercept an electromagnetic field and convert
it to an AC voltage or current.


The dipole antenna consists of two pieces of wire (not touching),
primarily generating an electric field when energized, and secondarily
producing a magnetic field in space.


The loop antenna consists of a loop of wire, primarily generating
a magnetic field when energized, and secondarily producing an electric field
in space.

Application of electrical theory has followed this timeline  SOURCE
Year

Event

1752

After eons of superstitious imaginations about electricity, Ben
Franklin figured out that static electricity and lightning were the
same. His correct understanding of the nature of electricity paved the
way for the future.

1800

First electric battery.

1816

First energy utility in US founded.

1820

Relationship of electricity and magnetism confirmed.

1821

First electric motor (Faraday).

1826

Ohms Law (G.S. Ohm).

1831

Principles of electromagnetism, induction, generation and
transmission (Faraday).

1837

First industrial electric motors.

1839

First fuel cell.

1860's

Mathematical theory of electromagnetic fields published. Maxwell
created a new era of physics when he unified magnetism, electricity and
light. One of the most significant events, possibly the very most
significant event, of the 19th century was Maxwell's discovery of the
four laws of electrodynamics ("Maxwell's Equations"). This led
to electric power, radios, and television.

1878

Edison Electric Light Co. (US) and American Electric and
Illuminating (Canada) founded.

1879

First commercial power station opens in San Francisco, uses Brush
generator and arc lights.

1880

First power system isolated from Edison.

1882


Edison’s Pearl Street Station.


First hydroelectric station opens (Wisconsin)


1883

Transformer invented.

1884

Steam turbine invented.

1886

Stanley develops transformer and Alternating Current electric
system.

1897

Electron discovered.

1900

Highest voltage transmission line 60 Kilovolt.

1902

5Megawatt turbine for Fisk St. Station (Chicago).

1903


First successful gas turbine (France).


World’s first all turbine station (Chicago).


Shawinigan Water & Power installs world’s largest
generator (5,000 Watts) and world’s largest and highest voltage
line—136 Km and 50 Kilovolts (to Montreal).


Electric vacuum cleaner.


Electric washing machine.


1909

First pumped storage plant (Switzerland).

1911

Air conditioning.

1913

Electric refrigerator.

1920


First U.S. station to only burn pulverized coal.


Federal Power Commission (FPC).


1922

Connecticut Valley Power Exchange (CONVEX) starts, pioneering
interconnection between utilities.

1928


Construction of Boulder Dam begins.


Federal Trade Commission begins investigation of holding
companies.


1933

Tennessee Valley Authority (TVA) established.

1935


Public Utility Holding Company Act.


Federal Power Act.


Securities and Exchange Commission.


Bonneville Power Administration.


First night baseball game in major leagues.


1936


Highest steam temperature reaches 900 degrees Fahrenheit vs.
600 degrees Fahrenheit in early 1920s.


287 Kilovolt line runs 266 miles to Boulder (Hoover) Dam.


Rural Electrification Act.


1947

Transistor invented.

1953


First 345 Kilovolt transmission line.


First nuclear power station ordered.


1954


First high voltage direct current (HVDC) line (20
megawatts/1900 Kilovolts, 96 Km).


Atomic Energy Act of 1954 allows private ownership of nuclear
reactors.


1963

Clean Air Act.

1965

Northeast Blackout.

1968

North American Electric Reliability Council (NERC) formed.

1969

National Environmental Policy Act of 1969.

1970


Environmental Protection Agency (EPA) formed.


Water and Environmental Quality Act.


Clean Air Act of 1970.


1972

Clean Water Act of 1972.

1975

Brown’s Ferry nuclear accident.

1977


New York City blackout.


Department of Energy (DOE) formed.


1978


Public Utilities Regulatory Policies Act (PURPA) passed, ends
utility monopoly over generation.


Power Plant and Industrial Fuel Use Act limits use of natural
gas in electric generation (repealed 1987).


1979

Three Mile Island nuclear accident.

1980


First U.S. windfarm.


Pacific Northwest Electric Power Planning and Conservation
Act establishes regional regulation and planning.


1981

PURPA ruled unconstitutional by Federal judge.

1982

U.S. Supreme Court upholds legality of PURPA in FERC v.
Mississippi (456 US 742).

1984

Annapolis, N.S., tidal power plant—first of its kind in North
America (Canada).

1985

Citizens Power, first power marketer, goes into business.

1986

Chernobyl nuclear accident (USSR).

1990

Clean Air Act amendments mandate additional pollution controls.

1992

National Energy Policy Act.

1997


ISO New England begins operation (first ISO).


New England Electric sells power plants (first major plant
divestiture).


1998


California opens market and ISO.


Scottish Power (UK) to buy Pacificorp, first foreign takeover
of US utility. National (UK) Grid then announces purchase of New
England Electric System.


1999


Electricity marketed on Internet.


FERC issues Order 2000, promoting regional transmission.


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