Name: ac circuit phasors: resistor, inductor, capacitor
Uploaded: 2024-04-11T12:48:48.000Z
Duration: 1 min 16 s
Channel: JoVE

Zależność napięcie-prąd dla rezystorów, cewek indukcyjnych i kondensatorów można przekształcić z dziedziny czasu na dziedzinę wskazową lub częstotliwości za pomocą reprezentacji wskazówki.
W dziedzinie czasu prawo Ohma zapewnia zależność między prądem przepływającym przez rezystor a napięciem na nim.
Podobnie, w reprezentacji wskazowej, napięcie i prąd są w fazie i są zgodne z prawem Ohma.
W przypadku cewki indukcyjnej szybkość zmiany prądu daje napięcie na niej. Funkcja sinusoidalna jest przekształcana w jej fazor w formacie biegunowym.
Porównując fazory prądu i napięcia, prąd opóźnia napięcie o 90 stopni.
Korzystając z tożsamości Eulera, uzyskuje się zależność prąd-napięcie w dziedzinie wskazówki.
Podobnie podczas ładowania kondensatora szybkość zmiany napięcia określa przepływający przez niego prąd, a funkcja sinusoidalna służy do uzyskania jego wskazówki w postaci biegunowej.
Reprezentacje wskazówkowe wskazują, że prąd prowadzi napięcie o 90 stopni, a zależność między wskazówkami prądu i napięcia można uzyskać przez podstawienie pochodnej czasowej napięcia.

relacje fazorowe dla elementów obwodu

Reprezentacja fazorowa to potężne narzędzie służące do przekształcania zależności napięcie-prąd dla rezystorów, cewek indukcyjnych i kondensatorów z dziedziny czasu na dziedzinę częstotliwości. Transformacja ta upraszcza analizę obwodów prądu przemiennego (AC).

W dziedzinie czasu prawo Ohma zapewnia podstawową zależność pomiędzy prądem płynącym przez rezystor a napięciem na nim:

<img alt="Equation1" src="/files/ftp_upload/15107/15107_PT_Equation_1.svg" style="text-align: center; height: 12px;" />

gdzie V to napięcie, I to prąd, a R to rezystancja. W reprezentacji fazorowej ta zależność również jest prawdziwa, a fazory napięcia i prądu są w fazie i są zgodne z prawem Ohma.

W przypadku cewki indukcyjnej związek między napięciem na niej a przepływającym przez nią prądem jest określony przez szybkość zmian prądu. Funkcję sinusoidalną reprezentującą tę zależność można przekształcić na jej fazor w formacie biegunowym. Porównując fazory prądu i napięcia dla cewki indukcyjnej, można zaobserwować, że prąd jest opóźniony w stosunku do napięcia o 90 stopni. Korzystając z tożsamości czterech kwadratów Eulera, podstawowego wzoru w analizie złożonej, można otrzymać zależność prądu od napięcia w dziedzinie fazorów.

Podobnie podczas ładowania kondensatora przepływający przez niego prąd zależy od szybkości zmian napięcia na nim. Ponownie funkcję sinusoidalną reprezentującą tę zależność można przekształcić na jej fazor w postaci biegunowej. W przypadku kondensatora reprezentacje fazorowe e wskazują, że prąd wyprzedza napięcie o 90 stopni. Zależność między fazorami prądu i napięcia kondensatora można obliczyć, korzystając z pochodnej napięcia po czasie.

Relacje fazorowe dla elementów obwodu

Zależność napięcie-prąd dla rezystorów, cewek indukcyjnych i kondensatorów może zostać przekształcona z dziedziny czasu na dziedzinę wskazów lub częstotliwości ...

phasor-relationships-for-circuit-elements

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

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 sinusoidal form of this relationship can be written as a phasor in polar form. When the voltage and current phasors are compared, the current lags the voltage by 90 degrees. Euler's identity is used to obtain the current-voltage relationship in the phasor domain.

A capacitor also depends on change, but here the current depends on the rate of change of voltage across it. Its sinusoidal form can also be converted into a phasor in polar form. For a capacitor, the current leads the voltage by 90 degrees. The time derivative of the voltage is used to derive the current-voltage relationship for the phasor form.

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phasor relationships for circuit elements

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Learn how phasors describe AC circuit behavior in resistors, inductors, and capacitors, including in-phase signals and 90-degree lead or lag.

AC Circuit Phasors: Resistor, Inductor, Capacitor | 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

AC Circuit Phasors: Resistor, Inductor, Capacitor

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