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

电阻器、电感器和电容器的电压-电流关系可以通过相量表示法从时域转换到相量域或频域。
在时域中，欧姆定律提供了流经电阻的电流与其两端电压之间的关系。
同样，在相量表示中，电压与电流同相，并遵循欧姆定律。
对于电感器，电流的变化率决定了其两端的电压。正弦函数被转换为其极坐标形式的相量。
通过比较电流和电压相量，电流滞后于电压90度。
利用欧拉公式，可得到相量域中的电流-电压关系。
同理，在给电容器充电时，电压的变化率决定了流过它的电流，而正弦函数可用于以极坐标形式获得其相量。
相量表示表明，电流超前电压90度，通过代入电压的时间导数，可得到电流与电压相量之间的关系。

电路元件的相量关系

Phasor Relationships for Circuit Elements

相量表示是一种强大的工具，能够将电阻器、电感器和电容器的电压-电流关系从时域转换到频域。这种转换简化了对交流 (AC) 电路所进行的分析。 在时域中，欧姆定律提供了流经电阻器的电流与电阻器两端电压之间的基本关系： <img alt="Equation1" src="/files/ftp_upload/15107/15107_PT_Equation_1.svg" style="text-align: center; height: 12px;"> 其中 V 是电压，I 是电流，R 是电阻。在相量的表示中，这种关系也是成立的，电压和电流相量是同相的并且遵循欧姆定律。 对于电感器，其两端的电压与流过其电流之间的关系是由电流的变化率所给出的。表示这种关系的正弦函数可以转换为极坐标格式的相量。在比较电感器中的电流和电压相量时，可以观察到电流会滞后电压90度。利用复分析中的基本公式——欧拉恒等式，可以得出相量域中的电流-电压关系。 类似地，当对电容器进行充电时，通过电容器的电流是由电容器两端的电压所产生的变化率来进行决定的。同样，表示这种关系的正弦函数可以转换为其极坐标形式的相量。对于电容器来说，相量表明了电流会超前电压90度。电容器中电流和电压相量之间的关系可以通过对电压的时间进行求导来得出。

电阻器、电感器和电容器的电压-电流关系可以从时域变换到相量域或频域……

phasor-relationships-for-circuit-elements

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

AC Circuit Analysis

交流电路分析

KEY TERMS AND CONCEPTS

关键术语与概念

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.

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

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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.

electrical engineering

AC Circuit Phasors: Resistor, Inductor, Capacitor

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