Name: phasors for ac circuit analysis
Uploaded: 2024-04-11T12:48:48.000Z
Duration: 1 min 12 s
Channel: JoVE

Os fasores são representações complexas dos sinusóides onde a magnitude do fasor é igual à amplitude e o ângulo é igual à fase medida a partir do eixo x positivo.
Eles simplificam a análise de circuitos CA, eliminando a dependência do tempo da corrente e da tensão, transformando o circuito em sua forma CC equivalente.
Os fasores podem ser representados em formas retangulares, polares ou exponenciais usando a identidade de Euler.
Para obter o fasor de um senóide na forma seno, primeiro converta-o em forma de cosseno e depois expresse-o como a parte real do número complexo.
O fasor deste sinusóide é igual à parte independente do tempo do número complexo.
Por outro lado, o sinusóide de um determinado fasor é obtido multiplicando o fasor pelo fator tempo e tomando sua parte real.
Os fasores podem ser representados como vetores rotativos ou sinores no sentido anti-horário em um plano complexo com uma frequência angular constante, e os diagramas que os descrevem são conhecidos como diagramas fasoriais.
A projeção dos sinores rotativos no eixo real representa os sinusóides.

fasores

Os fasores são uma ferramenta matemática poderosa usada para analisar circuitos de corrente alternada (AC). Eles fornecem uma representação de números complexos de senoides, com a magnitude do fasor igualando a amplitude da senoide e o ângulo do fasor representando a fase medida a partir do eixo x positivo.

Um dos benefícios significativos do uso de fasores é que eles simplificam a análise de circuitos AC, eliminando a dependência temporal da corrente e da tensão. Essa transformação permite que um circuito AC seja analisado como se fosse sua forma equivalente de corrente contínua (DC), tornando os cálculos mais simples.

Os fasores podem ser representados de diferentes formas - retangular, polar ou exponencial - usando a identidade de Euler, uma fórmula fundamental em análise complexa que estabelece uma relação profunda entre funções trigonométricas e exponenciais.

Para obter o fasor de uma senoide na forma senoidal, deve-se primeiro convertê-lo na forma cosseno e depois expressá-lo como a parte real de um número complexo. O fasor desta senoide é igual à parte independente do tempo deste número complexo. Por outro lado, a senoide de um determinado fasor pode ser obtida multiplicando o fasor por um fator de tempo e calculando sua parte real.

Em um contexto gráfico, os fasores podem ser visualizados como vetores rotativos, ou 'sinores', girando no sentido anti-horário em um plano complexo com uma frequência angular constante. Os diagramas que representam esses sinores rotativos são conhecidos como diagramas fasoriais.

Um conceito chave para a compreensão do diagrama fasorial é que a projeção dos sinores rotativos no eixo real representa as senoides. Isto significa que a posição horizontal do sinor em qualquer momento corresponde ao valor instantâneo da função sinusoidal que representa.

Fasores

Fasores são representações complexas dos sinusóides onde a magnitude do fasor é igual à amplitude e o ângulo é igual à fase medida a partir de ...

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

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 rectangular, polar, or exponential form.

Euler’s identity links trigonometric functions and exponential functions, and it helps convert between these phasor forms. To find the phasor of a sinusoid in sine form, the signal is first written in cosine form. It is then expressed as the real part of a complex number, and the phasor is the time-independent part of that number.

A sinusoid can also be recovered from a phasor. The phasor is multiplied by a time factor, and then the real part is taken. In a graph, phasors appear as rotating vectors, or sinors, on the complex plane.

These rotating sinors move counterclockwise with constant angular frequency. The diagrams that show them are called phasor diagrams. The projection of a sinor onto the real axis gives the sinusoid, so the horizontal position at any moment shows the instantaneous value of the wave.

Phasors for AC Circuit Analysis

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phasors

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...

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key terms and concepts

Learn how phasors represent AC sinusoids, simplify circuit analysis, and appear as rotating vectors on the complex plane in phasor diagrams.

Phasors for AC Circuit Analysis | 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

Phasors for AC Circuit Analysis

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