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Notes to teachers and students:

Phasors! For those who understand them, they are of incomparable value for the study of elementary and advanced topics. For those who misunderstand them, they are a constant source of confusion and are of no apparent use. So, let's understand them.

The conceptual leap from the complex number e j θ to the phasor e j ( ω t + θ ) comes in "Phasor Representation of Signals" . Take as long as necessary to understand every geometrical and algebraic nuance. Write the MATLAB program in "Exercise 6" to fix the key ideas once and for all. Then use phasors to study beating between tones, multiphase power, and Lissajous figures in "Beating between Tones" through "Lissajous Figures" . We usually conduct a classroom demonstration of beating between tones usingtwo phase-locked sources, an oscilloscope, and a speaker. We also demonstrate Lissajous figures with this hardware.

"Sinusoidal Steady State and the Series RLC Circuit" and Light Scattering by a Slit" on sinusoidal steady state and light scattering are too demanding for freshmen but are right on target for sophomores. Thesesections may be covered in a sophomore course (or a supplement to a sophomore course) or skipped in a freshman course without consequence.

In the numerical experiment in "Numerical Experiment (Interference Patterns)" , students compute and plot interference patterns for two sinusoids that are out of phase.


In engineering and applied science, three test signals form the basis for our study of electrical and mechanical systems. The impulse is an idealized signal that models very short excitations (like current pulses, hammer blows, pile drives, and light flashes). The step is an idealized signal that models excitations that are switched on and stay on (like current in a relay that closes or a transistor that switches). The sinusoid is an idealized signal that models excitations that oscillate with a regular frequency (like AC power, AM radio, pure musical tones, and harmonic vibrations). All three signals are used in the laboratory to design and analyze electrical and mechanical circuits, control systems, radio antennas, and the like. The sinusoidal signal is particularly important because it may be used to determine the frequency selectivity of a circuit (like a superheterodyne radio receiver) to excitations of different frequencies. For this reason, every manufacturer of electronics test equipment builds sinusoidal oscillators that may be swept through many octaves of Orequency. (Hewlett-Packard was started in 1940 with the famous HP audio oscillator.)

In this chapter we use what we have learned about complex numbers and the function e j θ to develop a phasor calculus for representing and ma- nipulating sinusoids. This calculus operates very much like the calculus wedeveloped in "Complex Numbers" and "The Functions e x and e " for manipulating complex numbers. We ap- ply our calculus to the study of beating phenomena, multiphase power, series RLC circuits, and light scattering by a slit.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
How can I make nanorobot?
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
how can I make nanorobot?
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
Leah Reply
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Source:  OpenStax, A first course in electrical and computer engineering. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col10685/1.2
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