Name: ac circuit rules with phasor diagrams
Uploaded: 2024-04-11T12:48:49.000Z
Duration: 1 min 12 s
Channel: JoVE

배전반의 AC 전원 공급 장치가 기기에 병렬로 연결되는 가정용 회로를 생각해 보십시오.
AC 회로를 분석하려면 부하를 등가의 임피던스로 대체하고 전압과 전류를 페이저 형태로 변환하는 작업이 포함됩니다.
이 AC 회로는 Kirchhoff의 전압 및 전류 법칙을 사용하여 분석 할 수 있습니다.
Kirchhoff의 전압 법칙이 회로의 첫 번째 루프에 적용되면 폐쇄 루프의 페이저 전압의 합이 0이됩니다.
정현파 정상 상태에서 이러한 전압은 시간 영역에서 표현될 수 있으며 등가물(phasor)로 변환될 수 있습니다.
주파수 계수는 null이 될 수 없으므로 페이저 전압의 집계는 0과 같습니다.
이제 노드에 Kirchhoff의 전류 법칙을 적용하면 회로 노드로 들어가는 총 전류가 노드에서 나가는 총 전류와 같다고 주장합니다.
페이저 표기법으로 표현하면 노드에서 페이저 전류의 합은 0과 같습니다.
따라서 Kirchhoff의 법칙은 모든 AC 회로에 적용되어 폐쇄 루프의 위상 전압과 노드의 위상 전류 모두에 대해 제로섬을 보장합니다.

위상기를 사용한 키르히호프의 법칙

전기 시스템의 AC 회로를 분석하는 것은 전기 공학의 기본 측면입니다. 이 회로에서는 AC 전원이 배전반에서 공급되어 다양한 가전 제품에 병렬로 연결됩니다. 포괄적인 분석을 수행하기 위해 전기 엔지니어는 DC 회로와 마찬가지로 AC 회로에도 동일하게 적용되는 키르히호프의 전압 및 전류 법칙을 사용합니다.

키르히호프의 전압 법칙(KVL)은 AC 회로의 폐루프 주변의 페이저 전압의 합이 0과 같다고 명시합니다. AC 전압이 시간에 따라 정현파로 변하는 정현파 정상 상태에서 이러한 전압은 시간 영역에서 표현된 다음 페이저 등가물로 변환될 수 있습니다. 이 과정을 통해 폐루프의 페이저 전압 합계가 0으로 유지됩니다.

<img alt="Equation1" src="/files/ftp_upload/15108/15108_PT_Equation_1.svg" style="text-align: center; height: 14px;">

키르히호프의 전류법칙(KCL)은 회로 노드에 적용되어 노드에 들어가는 총 전류가 노드에서 나가는 총 전류와 같다고 주장합니다. 페이저 표기법으로 표현하면 노드의 페이저 전류 합계도 0과 같습니다.

<img alt="Equation2" src="/files/ftp_upload/15108/15108_PT_Equation_2.svg" style="text-align: center; height: 14px;">

이러한 법칙은 AC 회로 분석을 위한 필수 도구이며 엔지니어가 주파수 영역에서 원활하게 작업할 수 있도록 해줍니다. 주거 및 산업 환경에서 전기 회로를 설계하고 문제를 해결하는 데 중요한 온저항 조합, 노드 및 메쉬 분석, 중첩, 소스 변환과 같은 다양한 작업을 용이하게 합니다.

배전반의 AC 전원 공급 장치가 기기에 병렬로 연결되는 가정용 회로를 생각해 보십시오.
AC 회로 분석에는 다음이 포함됩니다.

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

AC Circuit Analysis

교류 회로 분석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Kirchoff's Laws using Phasors

ac circuit rules with phasor diagrams

AC circuit analysis uses Kirchhoff's voltage law and Kirchhoff's current law with phasors. In household wiring, AC power from a distribution panel is sent to appliances connected in parallel. These rules help describe how voltage and current behave in sinusoidal steady state.

Kirchhoff's voltage law, or KVL, says that the sum of phasor voltages around a closed loop in an AC circuit is zero. The voltages can first be written in the time domain and then changed into phasor form. In phasor notation, the loop still balances to zero.

Kirchhoff's current law, or KCL, applies at a node, which is a connection point in a circuit. It states that the total current entering the node equals the total current leaving it. When written as phasor currents, the sum at the node is also zero.

Using phasors makes AC circuit analysis easier in the frequency domain. Engineers use these laws for impedance combination, nodal analysis, mesh analysis, superposition, and source transformation. These tools are important for designing and troubleshooting electrical circuits in residential and industrial settings.

AC Circuit Rules with Phasor Diagrams

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

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...

kirchoff's laws using phasors

AC circuit analysis uses Kirchhoff's voltage law and Kirchhoff's current law with phasors. In household wiring, AC power from a distribution panel is sent to appliances connected in parallel. These rules help describe how voltage and current behave in sinusoidal steady state. Kirchhoff's voltage law, or KVL, says that the sum of phasor voltages around a closed loop in an AC circuit is zero. The voltages can first be written in the time domain and then changed into phasor form. In phasor...

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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AC Circuit Node Method in an Angioplasty Model

AC circuit node analysis is used to study an angioplasty system with a catheter turbine. The system helps remove plaque deposits from coronary arteries. Its electrical model is similar to a dual-node RLC circuit driven by a current-controlled voltage source. The analysis begins by collecting the input source voltage, inductance, and capacitance values. These measurements are used to find the driving voltage for the catheter shaft. The circuit is then viewed in the frequency domain, where...

mesh analysis for ac circuits

Impedance Matching with Mesh Currents

Impedance matching in radio communication uses resistor, capacitor, and inductor circuits to help signals move efficiently between a transmitter and a receiver. The circuit must balance the input and output signals before the current in the capacitor can be found. This makes the problem a good example of AC circuit analysis for high school students. The first step is to identify the input voltage and the output signal. The angular frequency is then taken from the time-domain form of the input...

source transformation for ac circuits

AC Source Conversion in Circuit Analysis

AC source conversion is a circuit analysis method used in the frequency domain. It changes a voltage source in series with an impedance into a current source in parallel with the same impedance, or it converts a current source back into a voltage source. The source values must keep the correct relationship during each change. This method helps solve for an unknown voltage in a circuit that includes a current source and components such as resistors, capacitors, and inductors. Each of these...

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Finding Voltage and Impedance in Circuit A

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Norton Current in AC Circuit Analysis

Norton’s theorem helps simplify complex AC circuits by replacing a two-terminal linear network with a smaller equivalent circuit. That equivalent circuit uses an impedance in parallel with a constant current source. The method lets students break one complicated circuit into two parts and analyze them more easily. To build the Norton equivalent, the source is replaced by its internal impedance. The result is the Norton impedance, which is the same as the Thévenin impedance. This parallel...

superposition theorem for ac circuits

Analyzing Mixed-Frequency Linear Circuits

Analyzing mixed-frequency linear circuits starts with the principle of superposition. In a linear circuit, the total output from several inputs is the sum of the outputs from each input acting alone. Here, the inputs are the voltages from independent voltage sources and the currents from independent current sources. When one source is kept active, every other independent source is set to zero. A 0-V voltage source becomes a short circuit, and a 0-A current source becomes an open circuit. This...

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Analyzing an Op Amp Audio Filter

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design example: capacitance multiplier circuit

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Capacitance Multiplier Circuit for Larger Capacitance

A capacitance multiplier circuit creates a larger effective capacitance from a small physical capacitor. In integrated circuit technology, this approach is useful when a small capacitor is not enough. The circuit can multiply capacitance by as much as 1000, so a 10-pF capacitor can act like a 100-nF capacitor. The design uses two op-amps. The first op-amp works as a voltage follower, which helps isolate the generated capacitance from the loading caused by the second stage. The second op-amp...

key terms and concepts

Learn how Kirchhoff's voltage and current laws apply to AC circuits with phasors, including loop and node analysis in sinusoidal steady state.

AC Circuit Rules with Phasor Diagrams | 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 Rules with Phasor Diagrams

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