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

Соотношение напряжение-ток для резисторов, индукторов и конденсаторов может быть преобразовано из временной области в векторную или частотную область с помощью векторного представления.
Во временной области закон Ома обеспечивает связь между током, протекающим через резистор, и напряжением на нем.
Точно так же в векторном представлении напряжение и ток находятся в фазе и подчиняются закону Ома.
Для катушки индуктивности скорость изменения тока дает напряжение на ней. Синусоидальная функция преобразуется в свой вектор в полярном формате.
Сравнивая векторы тока и напряжения, можно сказать, что ток отстает от напряжения на 90 градусов.
Используя тождество Эйлера, получена зависимость ток-напряжение в векторной области.
Точно так же при зарядке конденсатора скорость изменения напряжения определяет проходящий через него ток, а синусоидальная функция используется для получения его вектора в полярном виде.
Векторные представления указывают на то, что ток опережает напряжение на 90 градусов, а соотношение между векторами тока и напряжения может быть получено путем подстановки производной напряжения по времени.

Фазорные связи для элементов схемы

Phasor Relationships for Circuit Elements

Фазорное представление — это мощный инструмент, используемый для преобразования зависимости напряжение-ток для резисторов, катушек индуктивности и конденсаторов из временной области в частотную область. Это преобразование упрощает анализ цепей переменного тока (AC).

Во временной области закон Ома обеспечивает фундаментальную связь между током, протекающим через резистор, и напряжением на нем:

<img alt="Equation1" src="/files/ftp_upload/15107/15107_PT_Equation_1.svg" style="text-align: center; height: 12px;" />

где V — напряжение, I — ток, а R — сопротивление. В векторном представлении это соотношение также справедливо: фазоры напряжения и тока находятся в фазе и подчиняются закону Ома.

Для катушки индуктивности соотношение между напряжением на ней и током, протекающим через нее, определяется скоростью изменения тока. Синусоидальная функция, представляющая это соотношение, может быть преобразована её фазор в полярном формате. При сравнении фазоров тока и напряжения для индуктора можно заметить, что ток отстает от напряжения на 90 градусов. Используя тождество Эйлера, фундаментальную формулу комплексного анализа, можно получить зависимость ток-напряжение в фазорном домене.

Аналогично, при зарядке конденсатора ток, проходящий через него, определяется скоростью изменения напряжения на нем. Опять же, синусоидальную функцию, представляющую эту зависимость, можно преобразовать в ее фазор в полярной форме. В случае конденсатора фазорные представления показывают, что ток опережает напряжение на 90 градусов. Взаимосвязь между фазорами тока и напряжения для конденсатора можно получить, используя производную напряжения по времени.

Соотношение напряжение-ток для резисторов, индукторов и конденсаторов может быть преобразовано из временной области в векторную или частотную область...

phasor-relationships-for-circuit-elements

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

AC Circuit Analysis

Анализ цепей переменного тока

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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.

AC Circuit Phasors: Resistor, Inductor, Capacitor

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phasor relationships for circuit elements

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...

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Series and Parallel Impedance Rules

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key terms and concepts

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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