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

병렬로 연결된 세 그룹의 커패시터가 있는 복잡한 커패시터 네트워크를 생각해 보십시오. 이 그룹은 서로 직렬로 연결됩니다. 이 복잡한 회로의 단자 사이의 등가 커패시턴스를 결정하십시오.
이 문제를 해결하기 위해 병렬로 연결된 4개의 커패시터로 구성된 회로 하단의 그룹을 먼저 분석합니다. 커패시턴스의 합은 단일 커패시터 C3 로 표시되는 등가 커패시턴스를 제공합니다.
다음으로, 3 개의 커패시터를 병렬로 갖는 중간 그룹이 고려됩니다. 다시 말하지만, 커패시턴스를 더하면 동등한 커패시턴스 C2가 됩니다.
마지막으로, 두 개의 커패시터가 병렬로 있는 상위 그룹을 고려하십시오. 등가 커패시턴스는 하나의 커패시터 C1로 계산되고 표시됩니다.
이제 복잡한 회로는 직렬로 연결된 세 개의 커패시터로 단순화되었습니다.
이 직렬 조합에 대한 등가 커패시턴스를 결정하기 위해 각 커패시턴스의 역수의 합이 취해져 등가 커패시턴스의 역이 됩니다.
항을 재배열하면 단자 사이의 전체 회로의 등가 커패시턴스가 얻어집니다.

등가 용량

저항성 회로 연구를 통해 직렬-병렬 조합을 사용하는 것이 회로를 단순화하는 효과적인 전략이라는 것을 알 수 있습니다. 축전기는 직렬 구성 또는 병렬 구성의 두 가지 방법 중 하나로 회로 내에서 배열될 수 있습니다. 이러한 축전기가 배터리에 연결되는 방식은 각 개별 축전기의 전위 강하와 각 축전기가 저장할 수 있는 전하 크기에 영향을 미칩니다. 이는 특정 연결 유형에 따라 결정됩니다. 이 시나리오를 단순화하기 위해 축전기 조합을 단일 등가 축전기로 대체할 수 있습니다. 이 등가 축전기는 동일한 전위차가 가해질 때 원래 조합과 동일한 양의 전하를 저장할 수 있습니다.

N개의 축전기가 병렬로 연결되면 모두 동일한 전압을 공유합니다. 이러한 구성에 대한 등가 전기용량은 다음과 같이 주어집니다.

<img alt="Equation1" src="/files/ftp_upload/15087/15087_PT_Equation_1.svg" style="text-align: center; height: 14px;">

병렬로 연결된 N개의 축전기의 등가 전기용량은 개별 전기용량의 총계와 동일하다는 점에 유의하는 것이 중요합니다.

이제 N개의 축전기가 직렬로 상호 연결된 시나리오로 전환하면 동일한 전류 i, 결과적으로 동일한 전하가 모든 축전기를 통해 흐르는 것이 관찰됩니다. 이 설정의 등가 전기용량은 다음과 같이 표시됩니다.

<img alt="Equation2" src="/files/ftp_upload/15087/15087_PT_Equation_2.svg" style="text-align: center; height: 32px;">

병렬 구성과 달리 직렬로 연결된 축전기의 등가 전기용량은 각 축전기의 개별 전기용량의 역수 합의 역수로 계산됩니다.

병렬로 연결된 세 그룹의 커패시터가 있는 복잡한 커패시터 네트워크를 생각해 보십시오. 이 그룹은 서로 직렬로 연결됩니다. ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Energy Storage Elements

에너지 저장 소자

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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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Capacitors in series and parallel affect a circuit in different ways. These arrangements change the total capacitance, which is the circuit's overall ability to store charge. Knowing the difference helps explain how a circuit responds to signals. When capacitors are connected in series to a battery, the plate tied to the battery's positive terminal becomes positively charged. The plate connected to the negative terminal becomes negatively charged. The other plates develop equal and opposite...

equivalent capacitance

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...

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key terms and concepts

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

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Capacitors in Series and Parallel

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