Name: ac circuit phasors: resistor, inductor, capacitor
Uploaded: 2024-04-11T12:48:48.000Z
Duration: 1 min 16 s
Channel: JoVE

抵抗器、インダクタ、コンデンサの電圧-電流関係は、フェーザ表現を使用して時間領域からフェーザ領域または周波数領域に変換できます。
時間領域では、オームの法則は、抵抗器を流れる電流と抵抗器を横切る電圧との関係を提供します。
同様に、フェーザ表現では、電圧と電流は同相であり、オームの法則に従います。
インダクタの場合、電流の変化率によってインダクタの両端の電圧が得られます。正弦波関数は、極性形式でそのフェーザに変換されます。
電流フェーザと電圧フェーザを比較すると、電流は電圧より90度遅れます。
オイラー恒等式を使用して、フェーザ領域の電流と電圧の関係が得られます。
同様に、コンデンサを充電する場合、電圧の変化率によってコンデンサを通過する電流が決まり、正弦波関数を使用して極性のフェーザが得られます。
フェーザの表現は、電流が電圧を90度リードすることを示しており、電流と電圧フェーザの関係は、電圧の時間微分を代入することで取得できます。

回路要素のフェーザー関係

Phasor Relationships for Circuit Elements

フェーザー表現は、抵抗、インダクタ、およびコンデンサの電圧と電流の関係を時間領域から周波数領域に変換するために使用される強力なツールです。 この変換により、交流 (AC) 回路の解析が簡素化されます。

時間領域では、オームの法則により、抵抗器を流れる電流とその両端の電圧の間の基本的な関係が得られます。

<img alt="Equation1" src="/files/ftp_upload/15107/15107_PT_Equation_1.svg" style="text-align: center; height: 12px;">

ここで、V は電圧、I は電流、R は抵抗です。 フェーザー表現でもこの関係は当てはまり、電圧フェーザーと電流フェーザーは同相であり、オームの法則に従います。

インダクタの場合、その両端の電圧とそこを流れる電流との関係は、電流の変化率によって与えられます。 この関係を表す正弦関数は、極形式のフェーザーに変換できます。 インダクタの電流フェーザーと電圧フェーザーを比較すると、電流が電圧より 90 度遅れていることがわかります。 複素解析の基本公フェーザーを用すると、フェーザーの領域の電流と電圧の関係を取得できます。

同様に、コンデンサを充電する場合、コンデンサを流れる電流はコンデンサにかかる電圧の変化率によって決まります。 繰り返しますが、この関係を表す正弦関数は、極形式のフェーザーに変換できます。 コンデンサの場合、フェーザー表現は、電流が電圧より 90 度進んでいることを示します。 コンデンサの電流フェーザー電圧フェーザーの関係は、フェーザー間微分を使用して取得できます。

抵抗器、インダクタ、コンデンサの電圧-電流関係は、時間領域からフェーザ領域または周波数領域に変換できます。

phasor-relationships-for-circuit-elements

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

AC Circuit Analysis

交流回路解析

KEY TERMS AND CONCEPTS

主要用語と概念

ac circuit phasors: resistor, inductor, capacitor

AC circuit phasors help show how voltage and current behave for resistors, inductors, and capacitors. Phasor representation moves these relationships from the time domain to the frequency domain, which makes AC circuit analysis easier.

For a resistor, Ohm's law still applies. The voltage across the resistor and the current through it stay in phase, so their phasors point in the same direction.

An inductor works differently because its voltage depends on the rate of change of current. The sinusoidal form of this relationship can be written as a phasor in polar form. When the voltage and current phasors are compared, the current lags the voltage by 90 degrees. Euler's identity is used to obtain the current-voltage relationship in the phasor domain.

A capacitor also depends on change, but here the current depends on the rate of change of voltage across it. Its sinusoidal form can also be converted into a phasor in polar form. For a capacitor, the current leads the voltage by 90 degrees. The time derivative of the voltage is used to derive the current-voltage relationship for the phasor form.

AC Circuit Phasors: Resistor, Inductor, Capacitor

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phasor relationships for circuit elements

AC circuit phasors help show how voltage and current behave for resistors, inductors, and capacitors. Phasor representation moves these relationships from the time domain to the frequency domain, which makes AC circuit analysis easier. For a resistor, Ohm's law still applies. The voltage across the resistor and the current through it stay in phase, so their phasors point in the same direction. An inductor works differently because its voltage depends on the rate of change of current. The...

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AC Circuit Rules with Phasor Diagrams

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AC Circuit Response: Impedance and Admittance

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Series and Parallel Impedance Rules

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key terms and concepts

Learn how phasors describe AC circuit behavior in resistors, inductors, and capacitors, including in-phase signals and 90-degree lead or lag.

AC Circuit Phasors: Resistor, Inductor, Capacitor | 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

AC Circuit Phasors: Resistor, Inductor, Capacitor

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