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

直列および/または並列構成で接続されたインダクタは、同等の単一インダクタに簡略化できます。
インダクタに同じ電流が流れるインダクタを直列に接続するとします。
キルヒホッフの電圧則をループに適用し、インダクタ電圧の式を代入すると、結果の式は、これらの直列接続されたインダクタの等価インダクタンスが個々のインダクタンスの合計に等しいことを示します。
次に、インダクタの並列接続について考えてみて、各インダクタに同じ電圧がかかります。キルヒホッフの電流法則がループに適用され、インダクタ電流の式が代入されます。
等価インダクタを流れる初期電流は個々のインダクタ電流の合計であるため、個々のインダクタンスの逆数の合計は等価インダクタンスの逆数に等しくなります。
直列および並列のインダクタの組み合わせは、抵抗と同様のルールに従います。
直列インダクタと並列インダクタの両方を備えた回路を考えてみましょう。インダクタの並列組み合わせの等価インダクタンスを計算し、直列インダクタンスに加算して、合計等価インダクタンスを求めます。

直列および並列インダクタ

電気回路では、インダクタを受動素子のツールキットに統合するには、これらのコンポーネントが関与する直列および並列の複雑な組み合わせをナビゲートする必要があります。 実際の回路では複数のインダクタの構成が使用されることが多く、それらの等価インダクタンスを決定する方法を理解することが重要です。

それぞれが同じ電流を流す N 個のインダクターの直列接続の場合、キルヒホッフの電圧則を適用すると、重要な関係が明らかになります。 この式をインダクタ電圧に置き換えると、洞察力に富んだ結論が得られます。つまり、この直列配置の等価インダクタンスは、個々のインダクタンスの単純な合計です。 この現象は、抵抗器がどのように直列に結合されるかを反映しており、これらの受動素子間の基本的な類似性が強調されます。

<img alt="Equation1" src="/files/ftp_upload/15090/15090_Equation_1.svg" style="text-align: center; height: 16px;">

インダクタを並列接続する事で、それぞれに同じ電圧がかかります。 キルヒホッフの現行の法則を適用できます。 これは今後の重要な値につながります。等価インダクタンスの逆数は、個々のインダクタンスの逆数の合計に等しいということです。 この並列結合ルールは、並列の抵抗器の動作を反映しており、さまざまな受動素子を処理するための調和のとれたアプローチを示しています。

<img alt="Equation2" src="/files/ftp_upload/15090/15090_Equation_2.svg" style="text-align: center; height: 34px;">

実際には、回路には直列インダクタと並列インダクタが混在することがよくあります。 このようなシナリオに直面した場合、並列インダクタの等価インダクタンスが計算され、直列インダクタンスに加算されて、回路全体の等価インダクタンスが得られます。

直列および/または並列構成で接続されたインダクタは、同等の単一インダクタに簡略化できます。
インダクタの直列接続を考えてみましょう...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Energy Storage Elements

エネルギー貯蔵素子

KEY TERMS AND CONCEPTS

主要用語と概念

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

capacitors

Capacitor Charge and Discharge

Capacitors store electric energy and help control signals in devices like car radios. They work by holding charge on two parallel conducting plates with a dielectric, which is the insulating material between the plates. When a voltage source is connected, positive charge builds up on one plate and negative charge builds up on the other. This charge separation creates a potential difference, and it keeps increasing until it matches the source voltage. The electric field inside the capacitor...

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Capacitor Voltage and Charge Behavior

Capacitor voltage and charge behavior depend on how a parallel plate capacitor connects to a battery. When the battery is attached, a potential difference forms across the plates. That voltage determines how much electrical energy the capacitor can store. The voltage across a capacitor can be found by integrating the equation that links voltage and current. That relationship lets students predict the voltage at any moment during charging or discharging. It also shows why a capacitor keeps a...

series and parallel capacitors

Capacitance in Series and Parallel

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

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...

inductors

Inductors in Electric Circuits

Inductors are passive components used in electric circuits to store energy in a magnetic field. They are often made by coiling a wire around a magnetic core. This structure gives the component its inductive behavior and its ability to respond to changing current. When current flows through an inductor, the voltage across it is proportional to how quickly the current changes with time. This relationship is written using the passive sign convention, and the constant of proportionality is called...

energy stored in inductors

How Inductor Current Stores Magnetic Energy

An inductor stores energy in its magnetic field. That field is created by the current flowing through the coil. When the current stays steady, there is no measurable voltage across the inductor, so it behaves like a short circuit for direct current. The energy stored in an inductor is the total power delivered over time. It can be written as a function of inductance, L, and current, i, where the stored energy increases with the current in the coil. This relationship helps explain how much...

series and parallel inductors

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...

design example: automobile ignition system

design-example-automobile-ignition-system

Car Spark Coil Voltage Design Example

An automobile ignition system uses a spark plug and a spark coil to create the high voltage needed to ignite the fuel-air mixture in each cylinder. The spark plug has two electrodes with an air gap between them. When enough voltage appears across that gap, a spark forms and starts combustion. A 12-volt car battery does not create that spark by itself. The system uses an inductor, which is a component that resists rapid changes in current, to build a much larger voltage. In this ignition setup,...

key terms and concepts

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Resistors In Series

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Resistors In Parallel

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Combination Of Resistors

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Energy Stored in Capacitors

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By integrating the equation relating voltage and ...

Series and Parallel Capacitors

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Equivalent Capacitance

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Inductors

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Energy Stored in Inductors

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Design and construct series and parallel circuits that model real-world circuits such as in-home wiring, automobile wiring, and simple electrical devices to evaluate the transfer of electrical energy

Magnetism

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IPC.6.B

Energy

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IPC.6.C

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IPC.6.D

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IPC.6.E

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IPC.6.G

Science concepts. The student knows the impact of energy transfer and energy conservation in everyday life. The student is expected to:

Equivalent Inductance in Circuit Networks

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