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

ניתן להמיר את יחסי המתח-זרם של הנגדים, המשרנים והקבלים מתחום הזמן לתחום הפאזור או התדר באמצעות ייצוג פאזור.
בתחום הזמן, חוק אוהם מספק יחס בין הזרם הזורם דרך נגד לבין המתח שחוצה אותו.
באופן דומה, בייצוג פאזור, המתח והזרם נמצאים בפאזה ועוקבים אחר חוק אוהם.
עבור משרן, קצב שינוי הזרם נותן את המתח לרוחבו. הפונקציה הסינוסואידלית מומרת לפאסור שלה בפורמט קוטבי.
בהשוואה בין פאזורי הזרם והמתח, הזרם מפגר את המתח ב -90 מעלות.
באמצעות זהותו של אוילר, מתקבל יחס זרם-מתח בתחום הפאזור.
באופן דומה, בעת טעינת קבל, קצב שינוי המתח קובע את הזרם העובר דרכו, והפונקציה הסינוסואידלית משמשת לקבלת הפאסור שלו בצורה קוטבית.
ייצוגי הפאזור מצביעים על כך שהזרם מוביל מתח ב-90 מעלות, וניתן לקבל את הקשר בין פאזורי הזרם והמתח על ידי החלפת נגזרת הזמן של המתח.

יחסי פאזור לאלמנטים במעגל

Phasor Relationships for Circuit Elements

<div style="direction:rtl">ייצוג פאזור הוא כלי רב עוצמה המשמש להפיכת יחסי מתח-זרם עבור נגדים, משרנים וקבלים מתחום הזמן לתחום התדר. טרנספורמציה זו מפשטת את הניתוח של מעגלי זרם חילופין (AC). בתחום הזמן, חוק אוהם מספק יחס בסיסי בין הזרם הזורם דרך נגד לבין המתח על פניו:

<img alt="Equation1" src="/files/ftp_upload/15107/15107_PT_Equation_1.svg" style="text-align: center; height: 12px;">

כאשר V הוא המתח, I הוא הזרם, ו-R הוא ההתנגדות. בייצוג פאזור, הקשר הזה מתקיים גם כן, כאשר פאזורי המתח והזרם נמצאים בשלבים ועוקבים אחר חוק אוהם.

עבור משרן, הקשר בין המתח על פניו לזרם הזורם דרכו ניתן על ידי קצב השינוי של הזרם. ניתן להמיר את הפונקציה הסינוסואידאלית המייצגת את הקשר הזה לפאזור שלה בפורמט קוטבי. כאשר משווים את פאזורי הזרם והמתח עבור משרן, ניתן להבחין כי הזרם מפגר את המתח ב-90 מעלות. באמצעות זהות אוילר, נוסחה בסיסית בניתוח מורכב, ניתן לקבל את היחס בין זרם-מתח בתחום הפאזור. באופן דומה, בעת טעינת קבל, הזרם העובר דרכו נקבע על פי קצב השינוי של המתח על פניו. שוב, ניתן להמיר את הפונקציה הסינוסואידאלית המייצגת את הקשר הזה לפאזור שלו בצורה קוטבית. במקרה של קבל, ייצוגי הפאזור מצביעים על כך שהזרם מוביל את המתח ב-90 מעלות. ניתן לקבל את הקשר בין פאזורי הזרם והמתח עבור קבל באמצעות נגזרת הזמן של המתח.</div>

ניתן להמיר את יחסי המתח-זרם עבור נגדים, משרנים וקבלים מתחום הזמן לתחום הפאזור או התדר ...

phasor-relationships-for-circuit-elements

Education

JoVE Core

Electrical Engineering

הנדסה חשמלית

Unit 1

יחידה 1

AC Circuit Analysis

ניתוח מעגלי זרם חילופין (AC)

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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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graphical and analytic representation of sinusoids

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phasors

Phasors for AC Circuit Analysis

Phasors are a mathematical tool for analyzing alternating current, or AC, circuits. They represent sinusoids with complex numbers. The phasor magnitude matches the sinusoid amplitude, and the phasor angle shows the phase measured from the positive x-axis. Phasors make AC circuit analysis simpler by removing time from the current and voltage expressions. That lets an AC circuit be treated like its equivalent direct current, or DC, form for calculations. Phasors can also be written in...

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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...

kirchoff's laws using phasors

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AC Circuit Response: Impedance and Admittance

AC circuit response changes with frequency, and impedance describes how resistors, inductors, and capacitors affect sinusoidal current flow. In phasor form, voltage and current are used to show this behavior in a clear way. Impedance is a key idea in AC circuit analysis because it measures opposition to current in an alternating circuit. These components behave differently in AC than in DC. In DC circuits, inductors act like short circuits and capacitors act like open circuits. In AC circuits,...

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Series and Parallel Impedance Rules

Impedance in series and parallel circuits follows the same rules used for resistors. A string of Christmas lights is a simple example. Each bulb represents one impedance element. In a series connection, the current stays the same through every component. This series behavior matches Kirchhoff’s Voltage Law, or KVL. The total impedance in the circuit is the sum of the individual impedances. The source voltage is then divided among the components based on their values. This is the voltage...

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AC Source Conversion in Circuit Analysis

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Norton Current in AC Circuit Analysis

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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 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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