Name: equivalent inductance in circuit networks
Uploaded: 2024-04-11T12:48:39.000Z
Duration: 1 min 17 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.6

IPC.6.A

Series and Parallel Inductors

Катушки индуктивности, подключенные последовательно и/или параллельно, могут быть упрощены до эквивалентного одного индуктора.
Рассмотрим последовательное соединение индукторов с протекающим через них одинаковым током.
Когда закон напряжения Кирхгофа применяется к петле и подставляется выражение для напряжений индукторов, результирующее выражение указывает, что эквивалентная индуктивность этих последовательно соединенных индукторов равна сумме отдельных индуктивностей.
Далее рассмотрим параллельное подключение индукторов, при котором каждый индуктор испытывает одинаковое напряжение на своей поверхности. К петле применяется закон тока Кирхгофа, и подставляется выражение для тока индуктивности.
Поскольку начальный ток через эквивалентный индуктор является суммой токов отдельных индукторов, сумма обратных значений отдельных индуктивностей равна обратной величине эквивалентной индуктивности.
Комбинации индукторов последовательно и параллельно следуют тем же правилам, что и резисторы.
Рассмотрим схему с последовательными и параллельными катушками индуктивности. Эквивалентная индуктивность параллельной комбинации индукторов рассчитывается и прибавляется к последовательной индуктивности для получения полной эквивалентной индуктивности.

Последовательные и параллельные индукторы

В электрических цепях интеграция индукторов в набор пассивных элементов требует понимания особенностей последовательных и параллельных комбинаций с участием этих компонентов. Практические схемы часто имеют конфигурации из нескольких индукторов, и жизненно важно понимать, как определить их эквивалентную индуктивность.

Для последовательного соединения N индукторов, по каждому из которых протекает одинаковый ток, применение закона напряжений Кирхгофа обнаруживает критическую зависимость. Замена выражения для напряжения индуктора приводит к важному выводу: эквивалентная индуктивность этой последовательной схемы представляет собой простую сумму отдельных индуктивностей. Это явление отражает то, как резисторы соединяются в последовательность, подчеркивая фундаментальное сходство между этими пассивными элементами.

<img alt="Equation1" src="/files/ftp_upload/15090/15090_Equation_1.svg" style="text-align: center; height: 16px;" />

При параллельном соединении индукторов, на каждый приходится одинаковое напряжение; в таком случает можно применить закон токов Кирхгофа. Это приводит к важному выводу: обратная величина эквивалентной индуктивности равна сумме обратных величин отдельных индуктивностей. Это правило параллельного соединения отражает поведение параллельных резисторов, иллюстрируя элегантный подход к работе с различными пассивными элементами.

<img alt="Equation2" src="/files/ftp_upload/15090/15090_Equation_2.svg" style="text-align: center; height: 34px;" />

На практике схемы часто представляют собой смесь последовательных и параллельных индукторов. При работе с такими сценариями эквивалентная индуктивность параллельных индукторов рассчитывается и добавляется к последовательной индуктивности, чтобы получить общую эквивалентную индуктивность цепи.

Катушки индуктивности, подключенные последовательно и/или параллельно, могут быть упрощены до эквивалентного одного индуктора.
Рассмотрим последовательное подключение индукторов...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Energy Storage Elements

Элементы хранения энергии

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

equivalent inductance in circuit networks

Equivalent inductance in circuit networks helps simplify circuits with multiple inductors. When inductors are combined, the circuit can often be replaced by one inductor with the same effect on the current and voltage.

For inductors in series, the same current flows through each component. Applying Kirchhoff's voltage law shows that the total voltage is the sum of the inductor voltages. As a result, the equivalent inductance of a series group is the sum of the individual inductances. This is the same pattern used for resistors in series.

For inductors in parallel, each branch has the same voltage. Kirchhoff's current law gives the key relationship for this arrangement. The reciprocal of the equivalent inductance equals the sum of the reciprocals of the individual inductances. This matches the rule used for resistors in parallel.

Many practical circuits use a mix of series and parallel inductors. In those cases, the parallel inductors are first combined into one equivalent inductance. That result is then added to the inductance in series to find the total equivalent inductance of the circuit.

Equivalent Inductance in Circuit Networks

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Equivalent inductance in circuit networks helps simplify circuits with multiple inductors. When inductors are combined, the circuit can often be replaced by one inductor with the same effect on the current and voltage. For inductors in series, the same current flows through each component. Applying Kirchhoff's voltage law shows that the total voltage is the sum of the inductor voltages. As a result, the equivalent inductance of a series group is the sum of the individual inductances. This is...

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Equivalent Inductance in Circuit Networks

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