Name: capacitors in series and parallel
Uploaded: 2024-04-11T12:48:39.000Z
Duration: 1 min 19 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.6

IPC.6.A

Equivalent Capacitance

Рассмотрим сложную цепь конденсаторов с тремя группами конденсаторов, соединенных параллельно, и эти группы затем соединяются последовательно друг с другом. Определите эквивалентную емкость между выводами этой сложной схемы.
Чтобы решить эту проблему, сначала анализируется группа в нижней части цепи, состоящая из четырех конденсаторов, соединенных параллельно. Сумма их емкостей дает эквивалентную емкость, представленную одним конденсатором C3.
Далее рассматривается средняя группа, имеющая по три конденсатора параллельно. Опять же, сложение их емкостей дает эквивалентную емкость C2.
Наконец, рассмотрим верхнюю группу, которая имеет два параллельных конденсатора. Эквивалентная емкость вычисляется и представляется с помощью одного конденсатора, C1.
Теперь сложная схема была упрощена до трех конденсаторов, соединенных последовательно.
Чтобы определить эквивалентную емкость для этой комбинации последовательностей, берется сумма обратных значений каждой емкости, в результате чего получается обратная эквивалентная емкость.
При перестановке членов получается эквивалентная емкость всей цепи между выводами.

Эквивалентная электроемкость

Изучение резистивных схем демонстрирует, что использование последовательно-параллельной комбинации служит эффективной стратегией упрощения схем. Конденсаторы могут быть расположены в цепи одним из двух способов: последовательно или параллельно. Способ подключения этих конденсаторов к батарее будет влиять как на падение потенциала на каждом отдельном конденсаторе, так и на величину заряда, который может хранить каждый конденсатор. Это определяется конкретным типом соединения. Чтобы упростить этот сценарий, комбинацию конденсаторов можно заменить одним эквивалентным конденсатором. Этот эквивалентный конденсатор способен хранить такое же количество заряда, что и исходная комбинация, при воздействии той же разности потенциалов.

При параллельном соединении N конденсаторов все они имеют одинаковое напряжение. Эквивалентная емкость для такой конфигурации определяется выражением

<img alt="Equation1" src="/files/ftp_upload/15087/15087_PT_Equation_1.svg" style="text-align: center; height: 14px;" />

Важно отметить, что эквивалентная емкость N конденсаторов, соединенных параллельно, равна сумме их индивидуальных емкостей.

Обращаясь к сценарию, когда N конденсаторов соединены последовательно, можно заметить, что через все конденсаторы протекает один и тот же ток i и, следовательно, один и тот же заряд. Эквивалентная емкость этой установки может быть представлена как

<img alt="Equation2" src="/files/ftp_upload/15087/15087_PT_Equation_2.svg" style="text-align: center; height: 32px;" />

В отличие от параллельной конфигурации, эквивалентная емкость последовательно соединенных конденсаторов рассчитывается как обратное суммы обратных величин индивидуальной емкости каждого конденсатора.

Рассмотрим сложную цепь конденсаторов с тремя группами конденсаторов, соединенных параллельно, и эти группы затем соединяются последовательно друг с другом. ...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Energy Storage Elements

Элементы хранения энергии

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

capacitors in series and parallel

Capacitors in series and parallel can be simplified by replacing the group with one equivalent capacitor. This equivalent capacitor stores the same charge as the original network when the same potential difference is applied. The idea helps make complex capacitor circuits easier to analyze.

In a parallel connection, capacitors share the same voltage across each branch. The equivalent capacitance of N capacitors in parallel is the sum of their individual capacitances. This type of connection increases the total ability of the circuit to store charge.

In a series connection, the same current flows through each capacitor, and the same charge passes through them. The equivalent capacitance for N capacitors in series is found from the reciprocal of the sum of the reciprocals of each capacitance. This result is different from the parallel case and gives a smaller effective capacitance.

Capacitors in Series and Parallel

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Learn how capacitors behave in series and parallel, and how to find equivalent capacitance by adding capacitances in parallel or using reciprocals in series.

Capacitors in Series and Parallel | JoVE K12

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Capacitors in Series and Parallel

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