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

저항기, 인덕터 및 커패시터에 대한 전압-전류 관계는 위상 표현을 사용하여 시간 영역에서 위상 또는 주파수 영역으로 변환할 수 있습니다.
시간 영역에서 옴의 법칙은 저항을 통해 흐르는 전류와 저항을 통과하는 전압 사이의 관계를 제공합니다.
유사하게, 페이저 표현에서 전압과 전류는 위상이 같고 옴의 법칙을 따릅니다.
인덕터의 경우 전류 변화율은 인덕터에 전압을 제공합니다. 사인파 함수는 극성 형식의 위상으로 변환됩니다.
전류 페이저와 전압 페이저를 비교하면 전류는 전압보다 90도 지연됩니다.
오일러의 아이덴티티를 사용하여 페이저 영역의 전류-전압 관계를 얻습니다.
유사하게, 커패시터를 충전할 때 전압의 변화율은 커패시터를 통과하는 전류를 결정하고 정현파 함수는 극성 형태의 페이저를 얻는 데 사용됩니다.
페이저 표현은 전류가 전압을 90도 리드한다는 것을 나타내며 전류와 전압 페이저 간의 관계는 전압의 시간 도함수를 대체하여 얻을 수 있습니다.

회로 요소의 위상기 관계

페이저 표현은 저항기, 인덕터 및 축전기의 전압-전류 관계를 시간 영역에서 주파수 영역으로 변환하는 데 사용되는 강력한 도구입니다. 이러한 변환은 교류(AC) 회로 분석을 단순화합니다.

시간 영역에서 옴의 법칙은 저항기를 통해 흐르는 전류와 저항기를 통과하는 전압 사이의 기본적인 관계를 제공합니다.

<img alt="Equation1" src="/files/ftp_upload/15107/15107_PT_Equation_1.svg" style="text-align: center; height: 12px;">

여기서 V는 전압, I는 전류, R은 저항입니다. 페이저 표현에서 이 관계는 전압 및 전류 페이저가 동상이고 옴의 법칙을 따르는 경우에도 적용됩니다.

유도자의 경우, 인덕터에 걸리는 전압과 흐르는 전류 사이의 관계는 전류 변화율로 표시됩니다. 이 관계를 나타내는 정현파 함수는 극 형식의 페이저로 변환될 수 있습니다. 유도자의 전류 및 전압 페이저를 비교할 때 전류가 전압보다 90도 지연되는 것을 볼 수 있습니다. 복잡한 해석의 기본 공식인 오일러의 항등식을 사용하여 페이저 영역의 전류-전압 관계를 얻을 수 있습니다.

마찬가지로, 축전기를 충전할 때 이를 통과하는 전류는 축전기 양단의 전압 변화율에 따라 결정됩니다. 다시 말하지만, 이 관계를 나타내는 정현파 함수는 극 형태의 페이저로 변환될 수 있습니다. 축전기의 경우 페이저 표현은 전류가 전압보다 90도 앞서 있음을 나타냅니다. 축전기의 전류와 전압 페이저 사이의 관계는 전압의 시간 도함수를 사용하여 얻을 수 있습니다.

저항기, 인덕터 및 커패시터에 대한 전압-전류 관계는 시간 도메인에서 페이저 또는 주파수 도메인으로 변환될 수 있습니다.

phasor-relationships-for-circuit-elements

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

AC Circuit Analysis

교류 회로 분석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

ac-circuit-phasors-resistor-inductor-capacitor

sinusoidal sources

AC Waveform Basics and Phase

Alternating current, or AC, changes direction and magnitude over time, unlike direct current, or DC, which flows in one direction with constant polarity. AC is the main form of electricity used for modern power transmission and distribution because it can travel long distances efficiently. In homes, power supplies use sinusoidal sources to deliver electricity. A sinusoidal source creates a voltage that rises and falls in a smooth wave-like pattern. This waveform is called a sinusoid, which is...

graphical and analytic representation of sinusoids

graphical-and-analytic-representation-of-sinusoids

Measuring Sinusoid Phase on an Oscilloscope

Measuring sinusoid phase on an oscilloscope helps compare two sinusoidal voltages with the same amplitude and period. An oscilloscope is an instrument used to display and analyze waveforms. The process starts by reading the peak-to-peak value, which is twice the amplitude of the sinusoid. This shows the maximum voltage swing of the waveform. Next, the period and angular frequency are measured. The period is the time for one complete cycle. Angular frequency, often written as omega, is the rate...

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...

phasor arithmetics

Phasor Rules for AC Circuit Analysis

Phasor rules make AC circuit analysis easier by linking sinusoids to their matching phasors. A phasor is a complex-number form of a sinusoidal signal. This connection helps explain how alternating current changes with time. Differentiation and integration work in both the time domain and the phasor domain. If you take the derivative of a sinusoid in time, its phasor is multiplied by jω, where j is the imaginary unit and ω is the angular frequency. If you integrate a sinusoid in time, its...

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

AC Circuit Rules with Phasor Diagrams

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impedances and admittance

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,...

impedance combination

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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Impedance Matching with Mesh Currents

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AC Source Conversion in Circuit Analysis

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th&#233venin equivalent circuits

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Norton Current in AC Circuit Analysis

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Analyzing Mixed-Frequency Linear Circuits

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op amp ac circuits

Analyzing an Op Amp Audio Filter

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design-example-capacitance-multiplier-circuit

Capacitance Multiplier Circuit for Larger Capacitance

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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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