Name: series and parallel impedance rules
Uploaded: 2024-04-11T12:48:49.000Z
Duration: 1 min 21 s
Channel: JoVE

Рассмотрим гирлянду рождественских огней, где каждая лампочка представляет собой импеданс. Такое последовательное расположение импедансов обеспечивает равномерный ток на каждом компоненте.
Применяя закон напряжения Кирхгофа, эквивалентный импеданс равен сумме отдельных импедансов, подобно резисторам, идущим последовательно.
Напряжение источника распределяется пропорционально между несколькими компонентами на основе их соответствующих импедансов, придерживаясь принципа деления напряжения.
При последовательном соединении неисправность одной лампы приводит к обрыву цепи, нарушая протекание тока.
Таким образом, рождественские гирлянды обычно подключаются в параллельной конфигурации, гарантируя постоянное напряжение на каждом компоненте.
Применение закона тока Кирхгофа к этой параллельной цепи показывает, что обратная величина эквивалентного импеданса равна сумме обратных импедансов отдельных импедансов, подобно резисторам, идущим параллельно.
Таким образом, эквивалентный допуск дается суммой отдельных допусков.
Исходный ток делится между компонентами обратно пропорционально их импедансам, демонстрируя принцип деления тока.
В этом случае каждый компонент прокладывает независимый путь к источнику питания, обеспечивая изолированное протекание тока.

Комбинация импедансов

Рассмотрим цепочку рождественских гирлянд, где каждая лампочка символизирует электрический импеданс, или комплексное электрическое сопротивление. В этой последовательной конфигурации поток электрического тока остается равномерным по всем компонентам. Такое поведение соответствует закону напряжений Кирхгофа (KVL), который утверждает, что общий импеданс в такой установке равен сумме отдельных импедансов — аналогично резисторам, включенным последовательно. Отсюда следует, что напряжение от источника питания распределяется пропорционально между этими компонентами, придерживаясь принципа деления напряжения.

<img alt="Equation1" src="/files/ftp_upload/15569/15569_PT_Equation_1.svg" style="text-align: center; height: 48px;" />

Однако недостаток этого последовательного соединения очевиден, когда одна лампочка выходит из строя, вызывая разрыв цепи, прерывающий течение тока. Рождественские гирлянды обычно располагаются параллельно, чтобы обеспечить непрерывное и стабильное электропитание. Эта установка гарантирует постоянное напряжение на каждой лампочке в соответствии с законом Кирхгофа (KCL), где обратная величина эквивалентного импеданса равна сумме обратных величин отдельных импедансов - аналогично резисторам, включенным параллельно. Отсюда следует, что эквивалентный адмиттанс представляет собой сумму отдельных адмиттансов.

В этом параллельном расположении ток источника делится обратно пропорционально в зависимости от импеданса отдельных лампочек, что иллюстрирует принцип деления тока. Примечательно, что каждая лампочка устанавливает независимый путь к источнику питания, обеспечивая изолированный и непрерывный ток.

<img alt="Equation2" src="/files/ftp_upload/15569/15569_PT_Equation_2.svg" style="text-align: center; height: 48px;" />

<img alt="Equation3" src="/files/ftp_upload/15569/15569_PT_Equation_3.svg" style="text-align: center; height: 40px;" />

Кроме того, в более сложных схемах с последовательными и параллельными импедансами преобразования «дельта- wye» и «wye -дельта» также могут использоваться для схем импеданса, предлагая ценные инструменты для анализа и проектирования схем. Эти преобразования облегчают переходы между различными конфигурациями импеданса, повышая универсальность схем, основанных на импедансе.

Рассмотрим гирлянду рождественских огней, где каждая лампочка представляет собой импеданс. Такое последовательное расположение импедансов обеспечивает равномерный ток по всему ...

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

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 division principle. One weak point of a series circuit is that one failed bulb can open the circuit and stop current flow.

Christmas lights are often wired in parallel to avoid that problem. In a parallel circuit, each bulb keeps its own path to the power source. The voltage across each bulb stays constant. This matches Kirchhoff’s Current Law, or KCL. For parallel impedance, the reciprocal of the equivalent impedance equals the sum of the reciprocals of the individual impedances.

The equivalent admittance is the sum of the individual admittances. Admittance is the inverse of impedance. In this setup, the source current splits according to the impedances of the branches. This is the current division principle. Because each bulb has an independent path, current can keep flowing even if one branch fails.

For circuits that mix series and parallel impedances, delta-to-wye and wye-to-delta transformations are useful. These methods let students convert one impedance network into another form. They make circuit analysis and design more flexible.

Series and Parallel Impedance Rules

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impedance combination

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Learn how impedance combines in series and parallel circuits, including KVL, KCL, voltage division, current division, and circuit transformations.

Series and Parallel Impedance Rules | 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

Series and Parallel Impedance Rules

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