This document discusses sinusoidal waves and their characteristics. It defines key terms like period, frequency, amplitude, phase angle, and explains how to calculate these values. Period is the time for one full cycle, frequency is the number of cycles per second. Amplitude refers to the maximum voltage or current values. Phase angle describes the shift between two sinusoidal waves with the same frequency. A lagging signal has a negative phase angle compared to the reference, while a leading signal has a positive phase angle.
A synchronous motor is electrically identical with an alternator or AC generator.
A given alternator ( or synchronous machine) can be used as a motor, when driven electrically.
Some characteristic features of a synchronous motor are as follows:
1. It runs either at synchronous speed or not at all i.e. while running it maintains a constant speed. The only way to change its speed is to vary the supply frequency (because NS=120f/P).
2. It is not inherently self-starting. It has to be run up to synchronous (or near synchronous) speed by some means, before it can be synchronized to the supply.
3. It is capable of being operated under a wide range of power factors, both lagging and leading. Hence, it can be used for power correction purposes, in addition to supplying torque to drive loads.
This ppt describes about,
introduction of fuses, construction, Important terms, advantages and disadvantages, desirable characteristics of fuse element, Current time characteristics, Fuse types - Low voltages fuses and High voltage fuses, Semi enclosed rewirable fuse, HRC cartridge fuses - parts, operation, pros and cons, High voltage fuses and its types, selection of fuses, discrimination
Alternating current (AC), is an electric current in which the flow of electric charge periodically reverses direction, whereas in direct current (DC, also dc), the flow of electric charge is only in one direction.
A synchronous motor is electrically identical with an alternator or AC generator.
A given alternator ( or synchronous machine) can be used as a motor, when driven electrically.
Some characteristic features of a synchronous motor are as follows:
1. It runs either at synchronous speed or not at all i.e. while running it maintains a constant speed. The only way to change its speed is to vary the supply frequency (because NS=120f/P).
2. It is not inherently self-starting. It has to be run up to synchronous (or near synchronous) speed by some means, before it can be synchronized to the supply.
3. It is capable of being operated under a wide range of power factors, both lagging and leading. Hence, it can be used for power correction purposes, in addition to supplying torque to drive loads.
This ppt describes about,
introduction of fuses, construction, Important terms, advantages and disadvantages, desirable characteristics of fuse element, Current time characteristics, Fuse types - Low voltages fuses and High voltage fuses, Semi enclosed rewirable fuse, HRC cartridge fuses - parts, operation, pros and cons, High voltage fuses and its types, selection of fuses, discrimination
Alternating current (AC), is an electric current in which the flow of electric charge periodically reverses direction, whereas in direct current (DC, also dc), the flow of electric charge is only in one direction.
Ekeeda Provides Online Electronics Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree. Visit us: https://ekeeda.com/streamdetails/stream/Electronics-Engineering
Distribution System Voltage Drop and Power Loss CalculationAmeen San
Distribution System Voltage Drop and Power Loss
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Comparison of Overhead Versus Underground System
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A frequency meter is an instrument that displays the frequency of a periodic electrical signal. Various types of frequency meters are used. Many are instruments of the deflection type, ordinarily used for measuring low frequencies but capable of being used for frequencies as high as 900 Hz.
Ekeeda Provides Online Electronics Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree. Visit us: https://ekeeda.com/streamdetails/stream/Electronics-Engineering
Distribution System Voltage Drop and Power Loss CalculationAmeen San
Distribution System Voltage Drop and Power Loss
Calculation
Comparison of Overhead Versus Underground System
Power Loss Calculation,Voltage Drop Calculation
A frequency meter is an instrument that displays the frequency of a periodic electrical signal. Various types of frequency meters are used. Many are instruments of the deflection type, ordinarily used for measuring low frequencies but capable of being used for frequencies as high as 900 Hz.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
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Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
2. Objective of Lecture
Discuss the characteristics of a sinusoidal wave.
Define the mathematical relationship between the
period, frequency, and angular frequency of a sine
wave.
Explain how to define the amplitude of a sine wave.
Describe what a phase angle is and the difference
between lagging and leading signals.
3. Characteristics of a Sine Wave
The length of time it takes to complete one cycle or conversely
the number of cycles that occur in one second.
Period
Frequency
Angular Frequency
The maximum and minimum voltage or current swing
Amplitude
Peak-to-peak amplitude
Value of the root mean square (RMS)
Average value of a sine wave
DC offset
Comparison between two sine waves
Phase angle
Lagging and leading signals
4.
5. Time Period, T
mssttT 7.16
60
1
12
The time that it takes for a
sine wave to complete one full
cycle. This can be measured
by finding the times at which
the signal crosses zero (need
two zero crossings). The unit
usually used is seconds (s).
An alternative way to measure
the period is to determine the
time required for the sine
wave return to the same
maximum or minimum value.
t1 t2
6. Frequency, f
The number of cycles a sine wave will complete in one
second(fractions are okay). The unit is cycles/second
or Hertz (Hz).
The longer the period, the lower the frequency is.
The shorter the period, the higher the frequency is.
T
f
1
Hz
msT
f 60
7.16
11
7. Electric Utilities
Standardization on the frequency of the electricity
distribution systems didn’t occur until the mid-
1900’s.
The frequency of the ac voltage supplied by power
companies in the US is 60 Hz.
The frequency used in much of Europe and Asia is 50 Hz.
While some electronic circuits function properly when
connected to a power supply operating at either frequency,
some are designed for a specific frequency, which is one
reason why power adaptors are needed when you travel.
If you look at the label on the tablet ‘brick’, the frequency
of the ac signal is specified.
8. Angular frequency
Motors are used in the alternators in coal- and gas-
powered electric generation stations. One full rotation
of the motor shaft produces one complete cycle of the
ac electricity produced.
Position of the motor shaft is measured in radians (rad)
or degrees (o).
1 rad = 57.3o
2p rad = 360o
rad/s37760 Hzf
T
f
p
p
2
2
10. Instantaneous Value
Instantaneous value or amplitude is the magnitude of
the sinusoid at a point in time.
VssradVtvmst
VssradVtvst
tsradVtv
94.2)]01.0)(/377sin[(5)(10
0)]0)(/377sin[(5)(0
])/377sin[(5)(
11. Average Value
The average value of a
sinusoid signal is the
integral of the sine wave
over one full cycle. This
is always equal to zero.
If the average of an ac
signal is not zero, then
there is a dc component
known as a DC offset.
12. Root Mean Square (RMS)
Most equipment that measure the amplitude of a
sinusoidal signal displays the results as a root mean
square value. This is signified by the unit Vac or VRMS.
RMS voltage and current are used to calculate the average
power associated with the voltage or current signal in one
cycle.
T
RMS dttv
T
V
0
2
)(
1
RVP
VVV
RMSAve
ppRMS
2
707.0
2
2
13. Phase Angle
The phase angle is an angular measurement of the
position of one sinusoid signal with respect to a
reference.
The signal and reference must have the same frequency.
14. Calculation of Phase
Suppose there are three signals
One signal is the reference
I have chosen the reference to be the signal in blue on the
following slide
The phase of the other two signals will be calculated
with respect to the reference signal.
The period of each signal should be the same, which means
that all signals have the same frequency.
16. Example #1
Calculate the period, T, for the reference signal
This is the time for a full cycle to be completed.
T= 500 second for Signal 1
Calculate the difference in time between zero crossings
of
Signal 2 and Signal 1: Dt = 40 second – 0 seconds = 40 s
Signal 3 and Signal 1: Dt = 480 seconds – 0 seconds= 480 s
17. Example #1 (con’t)
The sinusoidal function that describes Signal 1, the
reference voltage, is
V(t) = 5V sin (t) where 2p/T = 12.6 mrad/s
To write the sinusoidal function that describes Signals
2 and 3, we need to address the fact that there is a shift
in the zero crossings
V(t) = A sin (t + f) where 2p/T
f 2p Dt/T in radians or f = 360o Dt/T
f is called the phase shift
18. Lagging and Leading
Don’t get fooled by the positions of the curves on the
graph!
Signal 2: V(t) = 5V sin [12.6 mrad/s)t – 28.8o]
f is -0.502 radians or -28.8 degrees
Signal 2 lags Signal 1 as it reaches zero at a later time than Signal 1
Signal 3: V(t) = 5V sin [12.6 mrad/s)t + 14.4o]
f is 0.251 radians or 14.4 degrees
Signal 3 leads Signal 1 as it reaches zero at an earlier time than
Signal 1
19. Formulas
)sin()( f tVtv p
where f is in degrees and the units
for are usually not included.
20. Summary
AC signals are sinusoidal functions.
The mathematical description of the sinusoid includes the peak
amplitude and the angular frequency and may include a phase
angle.
RMS values of a sinusoid are calculated using the
formula
Phase angle for a sinusoid is calculated with respect to
a reference.
A signal lags a reference when fsignal – freference < 0o.
It leads a reference when fsignal – freference > 0o.
T
f
p
p
2
2 )sin()( f tVtv p
T
RMS dttv
T
V
0
2
)(
1
pRMS VV 707.0