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

직렬 및/또는 병렬 구성으로 연결된 인덕터는 동등한 단일 인덕터로 단순화할 수 있습니다.
동일한 전류가 흐르는 인덕터의 직렬 연결을 고려하십시오.
Kirchhoff의 전압 법칙이 루프에 적용되고 인덕터 전압에 대한 표현이 대체되면 결과 표현식은 이러한 직렬 연결 인덕터의 등가 인덕턴스가 개별 인덕턴스의 합과 같음을 나타냅니다.
다음으로, 각 인덕터에서 동일한 전압이 발생하는 인덕터의 병렬 연결을 고려하십시오. Kirchhoff의 현재 법칙이 루프에 적용되고 인덕터 전류에 대한 표현이 대체됩니다.
등가 인덕터를 통과하는 초기 전류는 개별 인덕터 전류의 합이기 때문에 개별 인덕턴스의 역수의 합은 등가 인덕턴스의 역수와 같습니다.
직렬 및 병렬로 인덕터의 조합은 저항기와 유사한 규칙을 따릅니다.
직렬 인덕터와 병렬 인덕터가 모두 있는 회로를 생각해 보십시오. 인덕터의 병렬 조합의 등가 인덕턴스를 계산하고 직렬 인덕턴스에 추가하여 총 등가 인덕턴스를 얻습니다.

직렬 및 병렬 유도자

전기 회로에서 유도자를 수동 소자의 툴킷에 통합하려면 이러한 구성 요소와 관련된 복잡한 직렬 및 병렬 조합을 탐색해야 합니다. 실제 회로에는 다중 유도자 구성이 포함되는 경우가 많으므로 등가 유도계수를 결정하는 방법을 이해하는 것이 중요합니다.

각각 동일한 전류를 전달하는 N 유도자의 직렬 연결에 대해 키르히호프의 전압 법칙을 적용하면 중요한 관계가 드러납니다. 유도자 전압에 대한 표현을 대체하면 통찰력 있는 결론을 얻을 수 있습니다. 이 직렬 배열의 등가 유도계수는 개별 유도계수의 간단한 합입니다. 이 현상은 저항기가 직렬로 결합하는 방식을 반영하여 이러한 수동 소자 간의 근본적인 유사성을 강조합니다.

<img alt="Equation1" src="/files/ftp_upload/15090/15090_Equation_1.svg" style="text-align: center; height: 16px;">

유도자의 병렬 연결에서 각각은 동일한 전압을 전달합니다. 키르히호프의 현행 법칙을 적용할 수 있습니다. 이는 중요한 계시로 이어집니다. 즉, 등가 유도계수의 역수는 개별 유도계수의 역수의 합과 같습니다. 이 병렬 조합 규칙은 저항기의 병렬 동작을 반영하여 다양한 수동 소자를 다루는 조화로운 접근 방식을 보여줍니다.

<img alt="Equation2" src="/files/ftp_upload/15090/15090_Equation_2.svg" style="text-align: center; height: 34px;">

실제로 회로에는 직렬 및 병렬 유도자가 혼합되어 있는 경우가 많습니다. 이러한 시나리오에 직면하면 병렬 유도자의 등가 유도계수를 계산하고 직렬 유도계수에 추가하여 회로의 전체 등가 유도계수를 얻습니다.

직렬 및/또는 병렬 구성으로 연결된 인덕터는 동등한 단일 인덕터로 단순화할 수 있습니다.
인덕터의 직렬 연결을 고려하십시오 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Energy Storage Elements

에너지 저장 소자

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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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Learn how series and parallel inductors combine in circuits. See how Kirchhoff's laws give the rules for equivalent inductance in mixed networks.

Equivalent Inductance in Circuit Networks | 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.

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Equivalent Inductance in Circuit Networks

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