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

A relação tensão-corrente para os resistores, indutores e capacitores pode ser transformada do domínio do tempo para o fasor ou domínio da frequência usando representação fasorial.
No domínio do tempo, a lei de Ohm fornece uma relação entre a corrente que flui através de um resistor e a tensão através dele.
Da mesma forma, na representação fasor, a tensão e a corrente estão em fase e seguem a lei de Ohm.
Para um indutor, a taxa de variação da corrente fornece a tensão através dele. A função senoidal é convertida em seu fasor em formato polar.
Comparando os fasores de corrente e tensão, a corrente fica atrás da tensão em 90 graus.
Usando a identidade de Euler, a relação corrente-tensão no domínio fasorial é obtida.
Da mesma forma, ao carregar um capacitor, a taxa de variação de tensão determina a corrente que passa por ele, e a função senoidal é usada para obter seu fasor na forma polar.
As representações fasoriais indicam que a corrente conduz a tensão em 90 graus, e a relação entre os fasores de corrente e tensão pode ser obtida substituindo a derivada temporal da tensão.

relações fasoriais para elementos de circuito

A representação fasorial é uma ferramenta poderosa usada para transformar a relação tensão-corrente para resistores, indutores e capacitores do domínio do tempo para o domínio da frequência. Esta transformação simplifica a análise de circuitos de corrente alternada (AC).

No domínio do tempo, a lei de Ohm fornece uma relação fundamental entre a corrente que flui através de um resistor e a tensão através dele:

<img alt="Equation1" src="/files/ftp_upload/15107/15107_PT_Equation_1.svg" style="text-align: center; height: 12px;" />

onde V é a tensão, I é a corrente e R é a resistência. Na representação fasorial, esta relação também é verdadeira, com os fasores de tensão e corrente estando em fase e seguindo a lei de Ohm.

Para um indutor, a relação entre a tensão através dele e a corrente que flui através dele é dada pela taxa de variação da corrente. A função senoidal que representa esta relação pode ser convertida em seu fasor no formato polar. Ao comparar os fasores de corrente e tensão de um indutor, pode-se observar que a corrente está atrasada em relação à tensão em 90 graus. Utilizando a identidade de Euler, fórmula fundamental em análise complexa, pode-se obter a relação corrente-tensão no domínio fasorial.

Da mesma forma, ao carregar um capacitor, a corrente que passa por ele é determinada pela taxa de variação da tensão através dele. Novamente, a função senoidal que representa esta relação pode ser convertida em seu fasor na forma polar. No caso de um capacitor, as representações fasoriais indicam que a corrente está adiantada em 90 graus em relação à tensão. A relação entre os fasores de corrente e tensão de um capacitor pode ser obtida usando a derivada temporal da tensão.

Relações Fasoriais para Elementos de Circuito

A relação tensão-corrente para os resistores, indutores e capacitores pode ser transformada do domínio do tempo para o fasor ou domínio da frequência ...

phasor-relationships-for-circuit-elements

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

AC Circuit Analysis

Análise de Circuitos CA

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

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

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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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