Name: ac waveform basics and phase
Uploaded: 2024-04-11T12:48:48.000Z
Duration: 1 min 18 s
Channel: JoVE

K12 Standards

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

High School

Physical Science

waves-and-their-applications-in-technologies-for-information-transfer

Waves and Their Applications in Technologies for Information Transfer

HS-PS4-2

Sinusoidal Sources

Prąd stały odnosi się do prądu jednokierunkowego, podczas gdy prąd przemienny odnosi się do prądu, który okresowo zmienia swój kierunek.
Prądy przemienne mają kluczowe znaczenie dla przesyłu i dystrybucji energii elektrycznej.
Zasilacze w domach wykorzystują źródła sinusoidalne do dostarczania energii elektrycznej. Źródła te generują napięcie, które zmienia się sinusoidalnie w czasie.
Matematycznie jest reprezentowany przez funkcję harmoniczną, znaną jako sinusoida, która jest zdefiniowana przez jej amplitudę, częstotliwość kątową i fazę.
Zmienność funkcji powtarza się co T sekund, a czas trwania jednego pełnego cyklu nazywany jest okresem. Jest to związane z częstotliwością kątową.
Liczba cykli na sekundę to częstotliwość.
Rozważmy dwie sinusoidy o tej samej częstotliwości. Jeśli sinusoida osiąga swoje maksima i minima wcześniej niż inna, to pierwsza sinusoida prowadzi drugą.
Mówi się wtedy, że dwie sinusoidy są poza fazą, a przesunięcie między nimi jest znane jako różnica faz.
Jeśli dwie sinusoidy osiągną jednocześnie swoje maksima i minima, są w fazie, a więc mają zerową różnicę faz.

Źródła sinusoidalne

Prąd stały (DC) odnosi się do prądu elektrycznego, który płynie w jednym kierunku, zachowując stałą polaryzację. Jest to przeciwieństwo prądu przemiennego (AC), który okresowo zmienia swój kierunek i wielkość. Prąd przemienny stanowi podstawę nowoczesnych systemów przesyłu i dystrybucji energii elektrycznej ze względu na jego wydajne możliwości transmisji na duże odległości.

W domach zasilacze wykorzystują źródła sinusoidalne do dostarczania energii elektrycznej. Źródła te wytwarzają napięcie, które zmienia się sinusoidalnie w czasie. Innymi słowy, napięcie oscyluje pomiędzy wartością maksymalną i minimalną w sposób gładki, przypominający falę.

Matematycznie tę zmianę reprezentuje funkcja harmoniczna znana jako sinusoida. Sinusoidę definiują trzy podstawowe parametry: jej amplituda (wartość szczytowa), częstotliwość kątowa (szybkość, z jaką oscyluje) i faza (jej położenie względem punktu odniesienia).

Przebieg sinusoidalny powtarza swój wzór co T sekund, gdzie T określa się jako okres funkcji. Okres jest odwrotnie proporcjonalny do częstotliwości kątowej i reprezentuje czas trwania jednego pełnego cyklu przebiegu.

Z drugiej strony częstotliwość sinusoidy definiuje się jako liczbę cykli występujących na sekundę. Jest to odwrotność okresu i zwykle jest mierzona w hercach (Hz).

Aby zrozumieć pojęcie fazy, rozważmy dwie sinusoidy o tej samej częstotliwości. Jeśli jedna sinusoida osiąga swoje maksima i minima wcześniej niż druga, wówczas mówi się, że pierwsza sinusoida „wyprzedza” drugą. W tym przypadku dwie sinusoidy są przesunięte w fazie, a przesunięcie między nimi nazywa się różnicą faz.

Z drugiej strony, jeśli dwie sinusoidy osiągają swoje maksima i minima jednocześnie, uważa się, że są w fazie. Oznacza to, że ich różnica faz wynosi zero.

Zrozumienie tych podstawowych pojęć związanych z prądem przemiennym ma kluczowe znaczenie dla różnych zastosowań, od projektowania obwodów elektronicznych po analizę systemów zasilania. Zasady prądu przemiennego stanowią podstawę wielu technologii w naszym codziennym życiu, w tym urządzeń gospodarstwa domowego, systemów telekomunikacyjnych i urządzeń do wytwarzania energii.

Prąd stały odnosi się do prądu jednokierunkowego, podczas gdy prąd przemienny odnosi się do prądu, który okresowo zmienia swój kierunek.
Przemienny...

Education

JoVE Core

Electrical Engineering

Elektrotechnika

Unit 1

Jednostka 1

AC Circuit Analysis

Analiza obwodów prądu przemiennego

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

ac waveform basics and phase

Alternating current, or AC, changes direction and magnitude over time, unlike direct current, or DC, which flows in one direction with constant polarity. AC is the main form of electricity used for modern power transmission and distribution because it can travel long distances efficiently. In homes, power supplies use sinusoidal sources to deliver electricity.

A sinusoidal source creates a voltage that rises and falls in a smooth wave-like pattern. This waveform is called a sinusoid, which is a harmonic function. The shape of the wave is described by three key parts: amplitude, angular frequency, and phase. Amplitude is the peak value. Angular frequency tells how fast the wave oscillates. Phase shows the wave’s position compared with a reference point.

A sinusoid repeats after a time called the period, or T. The period is the time for one complete cycle of the waveform. It is inversely related to angular frequency. Frequency is the number of cycles per second, and it is the reciprocal of the period. Frequency is measured in Hertz, or Hz.

Phase helps compare two sinusoids with the same frequency. If one wave reaches its maxima and minima earlier than the other, it leads the second wave. The waves are then out of phase, and the shift between them is called the phase difference. If both waves reach their maxima and minima at the same time, they are in phase. In that case, the phase difference is zero.

Understanding AC, sinusoidal sources, and phase is important in many settings. These ideas are used in electronic circuit design and in power system analysis. They also support technologies that shape daily life, including household appliances, telecommunications systems, and power generation facilities.

AC Waveform Basics and Phase

sinusoidal sources

Alternating current, or AC, changes direction and magnitude over time, unlike direct current, or DC, which flows in one direction with constant polarity. AC is the main form of electricity used for modern power transmission and distribution because it can travel long distances efficiently. In homes, power supplies use sinusoidal sources to deliver electricity. A sinusoidal source creates a voltage that rises and falls in a smooth wave-like pattern. This waveform is called a sinusoid, which is...

graphical and analytic representation of sinusoids

graphical-and-analytic-representation-of-sinusoids

Measuring Sinusoid Phase on an Oscilloscope

Measuring sinusoid phase on an oscilloscope helps compare two sinusoidal voltages with the same amplitude and period. An oscilloscope is an instrument used to display and analyze waveforms. The process starts by reading the peak-to-peak value, which is twice the amplitude of the sinusoid. This shows the maximum voltage swing of the waveform. Next, the period and angular frequency are measured. The period is the time for one complete cycle. Angular frequency, often written as omega, is the rate...

phasors

Phasors for AC Circuit Analysis

Phasors are a mathematical tool for analyzing alternating current, or AC, circuits. They represent sinusoids with complex numbers. The phasor magnitude matches the sinusoid amplitude, and the phasor angle shows the phase measured from the positive x-axis. Phasors make AC circuit analysis simpler by removing time from the current and voltage expressions. That lets an AC circuit be treated like its equivalent direct current, or DC, form for calculations. Phasors can also be written in...

phasor arithmetics

Phasor Rules for AC Circuit Analysis

Phasor rules make AC circuit analysis easier by linking sinusoids to their matching phasors. A phasor is a complex-number form of a sinusoidal signal. This connection helps explain how alternating current changes with time. Differentiation and integration work in both the time domain and the phasor domain. If you take the derivative of a sinusoid in time, its phasor is multiplied by jω, where j is the imaginary unit and ω is the angular frequency. If you integrate a sinusoid in time, its...

phasor relationships for circuit elements

phasor-relationships-for-circuit-elements

AC Circuit Phasors: Resistor, Inductor, Capacitor

AC circuit phasors help show how voltage and current behave for resistors, inductors, and capacitors. Phasor representation moves these relationships from the time domain to the frequency domain, which makes AC circuit analysis easier. For a resistor, Ohm's law still applies. The voltage across the resistor and the current through it stay in phase, so their phasors point in the same direction. An inductor works differently because its voltage depends on the rate of change of current. The...

kirchoff's laws using phasors

AC Circuit Rules with Phasor Diagrams

AC circuit analysis uses Kirchhoff's voltage law and Kirchhoff's current law with phasors. In household wiring, AC power from a distribution panel is sent to appliances connected in parallel. These rules help describe how voltage and current behave in sinusoidal steady state. Kirchhoff's voltage law, or KVL, says that the sum of phasor voltages around a closed loop in an AC circuit is zero. The voltages can first be written in the time domain and then changed into phasor form. In phasor...

impedances and admittance

AC Circuit Response: Impedance and Admittance

AC circuit response changes with frequency, and impedance describes how resistors, inductors, and capacitors affect sinusoidal current flow. In phasor form, voltage and current are used to show this behavior in a clear way. Impedance is a key idea in AC circuit analysis because it measures opposition to current in an alternating circuit. These components behave differently in AC than in DC. In DC circuits, inductors act like short circuits and capacitors act like open circuits. In AC circuits,...

impedance combination

Series and Parallel Impedance Rules

Impedance in series and parallel circuits follows the same rules used for resistors. A string of Christmas lights is a simple example. Each bulb represents one impedance element. In a series connection, the current stays the same through every component. This series behavior matches Kirchhoff’s Voltage Law, or KVL. The total impedance in the circuit is the sum of the individual impedances. The source voltage is then divided among the components based on their values. This is the voltage...

node analysis for ac circuits

AC Circuit Node Method in an Angioplasty Model

AC circuit node analysis is used to study an angioplasty system with a catheter turbine. The system helps remove plaque deposits from coronary arteries. Its electrical model is similar to a dual-node RLC circuit driven by a current-controlled voltage source. The analysis begins by collecting the input source voltage, inductance, and capacitance values. These measurements are used to find the driving voltage for the catheter shaft. The circuit is then viewed in the frequency domain, where...

mesh analysis for ac circuits

Impedance Matching with Mesh Currents

Impedance matching in radio communication uses resistor, capacitor, and inductor circuits to help signals move efficiently between a transmitter and a receiver. The circuit must balance the input and output signals before the current in the capacitor can be found. This makes the problem a good example of AC circuit analysis for high school students. The first step is to identify the input voltage and the output signal. The angular frequency is then taken from the time-domain form of the input...

source transformation for ac circuits

AC Source Conversion in Circuit Analysis

AC source conversion is a circuit analysis method used in the frequency domain. It changes a voltage source in series with an impedance into a current source in parallel with the same impedance, or it converts a current source back into a voltage source. The source values must keep the correct relationship during each change. This method helps solve for an unknown voltage in a circuit that includes a current source and components such as resistors, capacitors, and inductors. Each of these...

th&#233venin equivalent circuits

Finding Voltage and Impedance in Circuit A

The household power distribution system can be simplified with Thevenin's theorem. In this system, distribution lines and transformers form the main network. Electrical appliances can be treated as load impedance, which makes the circuit easier to analyze. An AC circuit can be split into two parts, circuit A and circuit B, with a single pair of terminals between them. Circuit A can then be replaced by its Thevenin equivalent circuit. That equivalent has a voltage source in series with an...

norton equivalent circuits

Norton Current in AC Circuit Analysis

Norton’s theorem helps simplify complex AC circuits by replacing a two-terminal linear network with a smaller equivalent circuit. That equivalent circuit uses an impedance in parallel with a constant current source. The method lets students break one complicated circuit into two parts and analyze them more easily. To build the Norton equivalent, the source is replaced by its internal impedance. The result is the Norton impedance, which is the same as the Thévenin impedance. This parallel...

superposition theorem for ac circuits

Analyzing Mixed-Frequency Linear Circuits

Analyzing mixed-frequency linear circuits starts with the principle of superposition. In a linear circuit, the total output from several inputs is the sum of the outputs from each input acting alone. Here, the inputs are the voltages from independent voltage sources and the currents from independent current sources. When one source is kept active, every other independent source is set to zero. A 0-V voltage source becomes a short circuit, and a 0-A current source becomes an open circuit. This...

op amp ac circuits

Analyzing an Op Amp Audio Filter

An op amp audio filter shapes an amplified sound signal by strongly reducing the lower-frequency parts. In this circuit, the focus is on a basic filter setup used after an amplifier in an audio system. The filter uses an operational amplifier in an inverting arrangement with resistors R1 and R2 and a capacitor C1. The analysis starts with a known input signal and asks for the output signal. To solve it, the capacitor impedance is found first. That requires the angular frequency from the...

design example: capacitance multiplier circuit

design-example-capacitance-multiplier-circuit

Capacitance Multiplier Circuit for Larger Capacitance

A capacitance multiplier circuit creates a larger effective capacitance from a small physical capacitor. In integrated circuit technology, this approach is useful when a small capacitor is not enough. The circuit can multiply capacitance by as much as 1000, so a 10-pF capacitor can act like a 100-nF capacitor. The design uses two op-amps. The first op-amp works as a voltage follower, which helps isolate the generated capacitance from the loading caused by the second stage. The second op-amp...

key terms and concepts

Learn how AC sinusoidal sources work, including amplitude, frequency, period, and phase, plus why phase difference matters in power and circuits.

AC Waveform Basics and Phase | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Travelling Waves

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Equations of Wave Motion

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Graphing the Wave Function

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Kinetic and Potential Energy of a Wave

All forms of waves carry energy; this is directly visualized in nature. For instance, the waves of earthquakes are so intense that they can shake huge ...

Energy and Power of a Wave

The total energy associated with a wavelength is the sum of the potential energy and the kinetic energy. The average rate of energy transfer associated ...

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Modes of Standing Waves - I

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Modes of Standing Waves: II

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Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media. 

Clarification statement: Examples of data could include electromagnetic radiation traveling in a vacuum and glass, sound waves traveling through air and water, and seismic waves traveling through the earth. 

Assessment Boundary: Assessment is limited to algebraic relationships and describing those relationships qualitatively.

HS-PS4-1

Speed of Sound in Gases

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Reconstruction of Signal using Interpolation

Consider a continuous signal and its sampled counterpart with a sampling period T.
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Classification of Signals

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Evaluate questions about the advantages of using a digital transmission and storage of information. 

Clarification statement: Examples of advantages could include that digital information is stable because it can be stored reliably in computer memory, transferred easily, and copied and shared rapidly. Disadvantages could include issues of easy deletion, security, and theft.

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Dual Nature of Electromagnetic (EM) Radiation

Electromagnetic (EM) radiation consists of electric and magnetic field components oscillating in planes perpendicular to each other and mutually ...

Electromagnetic Waves in Matter

Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, ...

Electromagnetic Waves

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Generating Electromagnetic Radiations

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Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model, and that for some situations one model is more useful than the other. 

Clarification statement: Emphasis is on how the experimental evidence supports the claim and how a theory is generally modified in light of new evidence. Examples of a phenomenon could include resonance, interference, diffraction, and photoelectric effect. 

Assessment Boundary: Assessment does not include using quantum theory.

HS-PS4-3

The Electromagnetic Spectrum

The electromagnetic spectrum consists of all the types of electromagnetic radiation arranged according to their frequency and wavelength. Each of the ...

Biological Effects of Radiation

All radioactive nuclides emit high-energy particles or electromagnetic waves. When this radiation encounters living cells, it can cause heating, break ...

Evaluate the validity and reliability of claims in published materials of the effects that different frequencies of electromagnetic radiation have when absorbed by matter. 

Clarification statement: Emphasis is on the idea that photons associated with different frequencies of light have different energies, and the damage to living tissue from electromagnetic radiation depends on the energy of the radiation. Examples of published materials could include trade books, magazines, web resources, videos, and other passages that may reflect bias. 

Assessment Boundary: Assessment is limited to qualitative descriptions.

HS-PS4-4

Control Systems

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Electromagnetic Wave Equation

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Plane Electromagnetic Waves I

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of ...

Plane Electromagnetic Waves II

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Propagation Speed of Electromagnetic Waves

Electromagnetic waves are consistent with Ampere&#39;s law. Assuming there is no conduction current Ampere&#39;s law is given as:


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Intensity Of Electromagnetic Waves

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Standing Electromagnetic Waves

Electromagnetic waves can be reflected; the surface of a conductor or a dielectric can act as a reflector. As electric and magnetic fields obey the ...

Standing Waves in a Cavity

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Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy. 

Clarification statement: Examples could include solar cells capturing light and converting it to electricity; medical imaging; and communications technology. 

Assessment Boundary: Assessments are limited to qualitative information. Assessments do not include band theory.

HS-PS4-5

AC Waveform Basics and Phase

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