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

La relazione tensione-corrente per i resistori, gli induttori e i condensatori può essere trasformata dal dominio del tempo al dominio del fasore o della frequenza utilizzando la rappresentazione dei fasori.
Nel dominio del tempo, la legge di Ohm fornisce una relazione tra la corrente che scorre attraverso un resistore e la tensione che lo attraversa.
Allo stesso modo, nella rappresentazione dei fasori, la tensione e la corrente sono in fase e seguono la legge di Ohm.
Per un induttore, la velocità di variazione della corrente fornisce la tensione attraverso di esso. La funzione sinusoidale viene convertita nel suo fasore in formato polare.
Confrontando i fasori di corrente e tensione, la corrente è in ritardo rispetto alla tensione di 90 gradi.
Utilizzando l'identità di Eulero, si ottiene la relazione corrente-tensione nel dominio dei fasori.
Allo stesso modo, quando si carica un condensatore, la velocità di variazione della tensione determina la corrente che lo attraversa e la funzione sinusoidale viene utilizzata per ottenere il suo fasore in forma polare.
Le rappresentazioni dei fasori indicano che la corrente precede la tensione di 90 gradi e la relazione tra i fasori di corrente e tensione può essere ottenuta sostituendo la derivata temporale della tensione.

relazioni tra fasori per gli elementi del circuito

La rappresentazione dei fasori è un potente strumento utilizzato per trasformare la relazione tensione-corrente per resistori, induttori e condensatori dal dominio del tempo, al dominio della frequenza. Questa trasformazione semplifica l'analisi dei circuiti in corrente alternata (CA).

Nel dominio del tempo, la legge di Ohm fornisce una relazione fondamentale tra la corrente che scorre attraverso un resistore e la tensione ai suoi capi:

<img alt="Equation1" src="/files/ftp_upload/15107/15107_PT_Equation_1.svg" style="text-align: center; height: 12px;">

dove V è la tensione, I è la corrente e R è la resistenza. Nella rappresentazione dei fasori, anche questa relazione è vera, con i fasori di tensione e corrente che sono in fase e seguono la legge di Ohm.

Per un induttore, la relazione tra la tensione ai suoi capi e la corrente che lo attraversa è data dalla velocità di variazione della corrente. La funzione sinusoidale che rappresenta questa relazione, può essere convertita nel suo fasore in formato polare. Confrontando i fasori di corrente e di tensione per un induttore, si può osservare che la corrente è in ritardo di 90 gradi rispetto alla tensione. Utilizzando l'identità di Eulero, una formula fondamentale nell'analisi complessa, è possibile ottenere la relazione corrente-tensione nel dominio dei fasori.

Allo stesso modo, quando si carica un condensatore, la corrente che lo attraversa è determinata dalla velocità di variazione della tensione ai suoi capi. Ancora una volta, la funzione sinusoidale che rappresenta questa relazione, può essere convertita nel suo fasore in forma polare. Nel caso di un condensatore, la rappresentazione dei fasori indica che la corrente anticipa la tensione di 90 gradi. La relazione tra i fasori di corrente e di tensione per un condensatore, può essere ottenuta utilizzando la derivata temporale della tensione.

Relazioni tra Fasori per gli Elementi del Circuito

La relazione tensione-corrente per i resistori, gli induttori e i condensatori può essere trasformata dal dominio del tempo al dominio del fasore o della frequenza ...

phasor-relationships-for-circuit-elements

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

AC Circuit Analysis

Analisi dei circuiti in CA

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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.

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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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