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## Measurement of AC Waveforms

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:
Figure below

*Peak voltage of a waveform.*

Another way is to measure the total height between opposite peaks. This is
known as the *peak-to-peak* (P-P) value of an AC waveform: Figure below

*Peak-to-peak voltage of a 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: Figure below

*A square wave produces a greater heating effect than the same peak voltage
triangle wave.*

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: Figure below

*The average value of a sinewave is zero.*

This, of course, will be true for any waveform having equal-area 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: Figure below

*Waveform seen by AC "average responding" meter.*

Polarity-insensitive mechanical meter movements (meters designed to respond equally to the positive and negative half-cycles 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, polarity-sensitive 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, motor-powered metal blade to cut wood. But while the bandsaw uses a continuous motion of the blade to cut, the jigsaw uses a back-and-forth motion. The comparison of alternating current (AC) to direct current (DC) may be likened to the comparison of these two saw types: Figure below

*Bandsaw-jigsaw analogy of DC vs AC.*

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 back-and-forth 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 sine-wave motion, while another
with a triangle-wave 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 side-by-side, 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 back-and-forth blade motion; to relate the wood-cutting 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:Figure below

*An RMS voltage produces the same heating effect as a the same DC
voltage*

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 peak-to-peak 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 high-voltage 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 peak-to-peak 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 cathode-ray-tube 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 mis-calibrated, 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 "True-RMS" 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, Peak-to-Peak, Average (practical, not algebraic), and RMS measurements to one another: Figure below

*Conversion factors for common waveforms.*

In addition to RMS, average, peak (crest), and peak-to-peak 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 RMS value divided by
its average value. Square-shaped 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 an RMS value of 0.707 (the reciprocal of the square root of 2)
and a form factor of 1.11 (0.707/0.636). Triangle- and sawtooth-shaped waveforms
have RMS values of 0.577 (the reciprocal of square root of 3) and form factors
of 1.15 (0.577/0.5).

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: Figure below

*Arbitrary waveforms have no simple conversions.*

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 sine-wave 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 sine-wave 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: 0.707/0.636: 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 sine-wave voltage or current will not indicate true RMS when reading a non-sinusoidal wave. Bear in mind that this limitation applies only to simple, analog AC meters not employing "True-RMS" 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, peak-to-peak, 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.*Peak-to-peak*amplitude is the total height of an AC waveform as measured from maximum positive to maximum negative peaks on a graph. Often abbreviated as "P-P".*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 equal-area 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 RMS 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.

Published under the terms and conditions of the Design Science License Disclaimer

## 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*: Figure below

*Graph of AC voltage over time (the 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 as in Table below.

*Trigonometric "sine" function.*

Angle (^{o}) |
sin(angle) | wave | Angle (^{o}) |
sin(angle) | wave |
---|---|---|---|---|---|

0 | 0.0000 | zero | 180 | 0.0000 | zero |

15 | 0.2588 | + | 195 | -0.2588 | - |

30 | 0.5000 | + | 210 | -0.5000 | - |

45 | 0.7071 | + | 225 | -0.7071 | - |

60 | 0.8660 | + | 240 | -0.8660 | - |

75 | 0.9659 | + | 255 | -0.9659 | - |

90 | 1.0000 | +peak | 270 | -1.0000 | -peak |

105 | 0.9659 | + | 285 | -0.9659 | - |

120 | 0.8660 | + | 300 | -0.8660 | - |

135 | 0.7071 | + | 315 | -0.7071 | - |

150 | 0.5000 | + | 330 | -0.5000 | - |

165 | 0.2588 | + | 345 | 0.2588 | - |

180 | 0.0000 | zero | 360 | 0.0000 | zero |

The reason why an electromechanical alternator outputs sine-wave 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 two-pole alternator
shaft as it rotates: Figure below

*Alternator voltage as function of shaft position (time).*

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 back-and-forth
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
power-line frequency is 60 Hz, meaning that the AC voltage oscillates at a rate
of 60 complete back-and-forth 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 self-explanatory 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 100-count ("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*, Figure below,
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 special-purpose oscilloscope expressly
designed for medical use. General-purpose 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.

*Time period of sinewave is shown on oscilloscope.*

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*. Low-pitch notes
such as those produced by a tuba or bassoon consist of air molecule vibrations
that are relatively slow (low frequency). High-pitch 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). Figure below
is a table showing the actual frequencies for a range of common musical notes.

*The frequency in Hertz (Hz) is shown for various 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:
Figure below

*An octave is shown on a musical keyboard.*

As you can see, one octave is equal to *seven* white keys' worth of
distance on a piano keyboard. The familiar musical mnemonic
(doe-ray-mee-fah-so-lah-tee) -- 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 in figure below

*Some common waveshapes (waveforms).*

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 real-life 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 *non-sinusoidal*. 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)

Published under the terms and conditions of the Design Science License Disclaimer

## Basic AC Theory

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 electro-mechanical 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): Figure below

*Direct vs alternating current*

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*: Figure below

*Alternator operation*

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: Figure below

*DC generator operation*

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 spark-producing 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*: Figure below

*Transformer "transforms" AC voltage and current.*

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: Figure below

*Speed multiplication gear train steps torque down and speed up. Step-down
transformer steps voltage down and current up.*

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: Figure below

*Speed reduction gear train steps torque up and speed down. Step-up
transformer steps voltage up and current down.*

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 in figure below. When transmitting electrical power over long distances, it is far more efficient to do so with stepped-up voltages and stepped-down currents (smaller-diameter wire with less resistive power losses), then step the voltage back down and the current back up for industry, business, or consumer use use.

*Transformers enable efficient long distance high voltage transmission of
electric energy.*

Transformer technology has made long-range electric power distribution practical. Without the ability to efficiently step voltage up and down, it would be cost-prohibitive to construct power systems for anything but close-range (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
high-voltage spark plug power from a low-voltage 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 mutually-inductive 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)

Published under the terms and conditions of the Design Science License Disclaimer