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

Das Spannungs-Strom-Verhältnis für die Widerstände, Induktivitäten und Kondensatoren kann mit Hilfe der Phasordarstellung vom Zeitbereich in den Phasor- oder Frequenzbereich transformiert werden.
Im Zeitbereich stellt das Ohmsche Gesetz eine Beziehung zwischen dem Strom, der durch einen Widerstand fließt, und der Spannung über ihn her.
In ähnlicher Weise sind bei der Phasordarstellung die Spannung und der Strom phasengleich und folgen dem Ohmschen Gesetz.
Bei einer Induktivität gibt die Änderungsrate des Stroms die Spannung an. Die sinusförmige Funktion wird in ihren Phasor im polaren Format umgewandelt.
Vergleicht man die Strom- und Spannungsphasoren, so hinkt der Strom der Spannung um 90 Grad hinterher.
Unter Verwendung der Eulerschen Identität wird die Strom-Spannungs-Beziehung im Phasorbereich erhalten.
In ähnlicher Weise bestimmt beim Laden eines Kondensators die Änderungsrate der Spannung den Strom, der durch ihn fließt, und die Sinusfunktion wird verwendet, um seinen Phasor in polarer Form zu erhalten.
Die Phasordarstellungen geben an, dass der Strom die Spannung um 90 Grad leitet, und die Beziehung zwischen Strom- und Spannungsphasoren kann durch Einsetzen der Zeitableitung der Spannung erhalten werden.

zeigerbeziehungen für schaltkreiselemente

Die Zeigerdarstellung ist ein leistungsstarkes Werkzeug zur Transformation der Spannungs-Strom-Beziehung für Widerstände, Induktivitäten und Kondensatoren vom Zeitbereich in den Frequenzbereich. Diese Transformation vereinfacht die Analyse von Wechselstromkreisen. Im Zeitbereich stellt das Ohmsche Gesetz eine grundlegende Beziehung zwischen dem durch einen Widerstand fließenden Strom und der daran anliegenden Spannung bereit: <img alt="Equation1" src="/files/ftp_upload/15107/15107_PT_Equation_1.svg" style="text-align: center; height: 12px;"> Dabei ist V die Spannung, I der Strom und R der Widerstand. Auch in der Zeigerdarstellung gilt dieser Zusammenhang, wobei die Spannungs- und Stromzeiger in Phase sind und dem Ohmschen Gesetz folgen. Bei einer Induktivität ist die Beziehung zwischen der an ihr anliegenden Spannung und dem durch sie fließenden Strom durch die Stromänderungsrate gegeben. Die Sinusfunktion, die diese Beziehung darstellt, kann im Polarformat in ihren Zeiger umgewandelt werden. Beim Vergleich der Strom- und Spannungszeiger einer Induktivität kann beobachtet werden, dass der Strom der Spannung um 90 Grad nacheilt. Mithilfe der Eulerschen Identität, einer grundlegenden Formel in der komplexen Analyse, kann die Strom-Spannungs-Beziehung im Zeigerbereich ermittelt werden. Ebenso wird beim Laden eines Kondensators der durch ihn fließende Strom durch die Änderungsrate der an ihm anliegenden Spannung bestimmt. Auch hier kann die Sinusfunktion, die diese Beziehung darstellt, in ihren Zeiger in Polarform umgewandelt werden. Im Fall eines Kondensators zeigen die Zeigerdarstellungen an, dass der Strom der Spannung um 90 Grad vorauseilt. Die Beziehung zwischen den Strom- und Spannungszeigern eines Kondensators kann mithilfe der zeitlichen Ableitung der Spannung ermittelt werden.

Zeigerbeziehungen für Schaltkreiselemente

Das Spannungs-Strom-Verhältnis für die Widerstände, Induktivitäten und Kondensatoren kann vom Zeitbereich in den Phasen- oder Frequenzbereich transformiert werden ...

phasor-relationships-for-circuit-elements

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

AC Circuit Analysis

Analyse von Wechselstromschaltungen

KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

Phasor Relationships for Circuit Elements

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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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 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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