Name: finding voltage and impedance in circuit a
Uploaded: 2025-05-22T09:06:14.000Z
Duration: 1 min 18 s
Channel: JoVE

配電線と変圧器を含む家庭用配電システムは、ソースネットワークと見なすことができます。
家の中では、さまざまな電化製品を負荷インピーダンスとして表すことができます。
テブナンの定理は、この複雑な分布システムをテブナンの等価回路に単純化します。
テブナンの等価回路を見つけるには、テブナン電圧とテブナンインピーダンスの2つのパラメータに関する知識が必要です。
それらを決定するプロセスを理解するために、電圧源に接続された簡略化されたRLC回路を考えてみましょう。
テブナンインピーダンスを計算するには、電圧源を短絡回路に交換し、回路の等価インピーダンスを決定します。
テブナン電圧は開回路電圧に等しく、回路の並列分岐両端の電圧降下に相当します。
最初に、回路の閉じたメッシュを流れる電流が計算されます。次に、オームの法則を使用して、平行分岐の両端の電圧降下が決定され、テブナン電圧が得られます。
回路に異なる周波数で動作するソースがある場合、テブナンの等価回路とコンデンサおよびインダクタのインピーダンスは、周波数ごとに個別に決定する必要があります。

テブナンの等価回路

Th&#233venin Equivalent Circuits

配電線と変圧器を含む家庭用配電システムは、一次ネットワークとして機能します。 家庭内の電気機器は負荷インピーダンスとして表すことができます。 この複雑な分配システムを単純化するために、テブナンの定理を適用してテブナンの等価回路を作成できます。 Figure に示すように、AC 回路が 2 つの部分 (回路 A と回路 B) に分割され、1 対の端子で接続されている場合。

<img alt="Figure1" src="/files/ftp_upload/15113/15113_PT_Figure_1.svg" style="text-align: center; height: 140px;">
Figure 1: 2 つの部分に分割された回路 

<img alt="Figure2" src="/files/ftp_upload/15113/15113_PT_Figure_2.svg" style="text-align: center; height: 150px;">
図 2: 回路 A をテブナン等価回路に置き換え

 回路 A をテブナン等価回路 (インピーダンスと直列の電圧源) に置き換えても、回路 B (図 2 を参照) のどの要素の電流も電圧も変わりません。 回路 B 内のすべての回路要素の電流と電圧の値は、回路 B が回路 A またはそのテブナン同等物に接続されているかどうかに関係なく、同じになります。 テブナンの等価回路を見つけるには、テブナン電圧とテブナン インピーダンスの 2 つのパラメータが必要です。 図 3 は、開回路電圧 v_oc を決定するために回路 A の端子間に接続された開回路を示しています。一方、図 4 は、テブナン インピーダンス Z_t が回路 A* の等価インピーダンスであることを示しています。

<img alt="Figure3" src="/files/ftp_upload/15113/15113_PT_Figure_3.svg" style="text-align: center; height: 96px;">
図 3: v_oc を使用したテブナン等価回路。

<img alt="Figure4" src="/files/ftp_upload/15113/15113_PT_Figure_4.svg" style="text-align: center; height: 96px;">
 Figure 4：Z_tを示すテブナン等価回路。 。

回路 A* は独立している電圧源を短絡回路に置き換え電流源を開回路に置き換えることによって、回路 A から形成されます。 一般に、テブナン インピーダンス Z_t は、直列または並列のインピーダンスを等価なインピーダンスに繰り返し置き換えることによって決定できます。

配電線と変圧器を含む家庭用配電システムは、ソースネットワークと見なすことができます。
家の中では、...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

AC Circuit Analysis

交流回路解析

KEY TERMS AND CONCEPTS

主要用語と概念

finding voltage and impedance in circuit a

The household power distribution system can be simplified with Thevenin's theorem. In this system, distribution lines and transformers form the main network. Electrical appliances can be treated as load impedance, which makes the circuit easier to analyze.

An AC circuit can be split into two parts, circuit A and circuit B, with a single pair of terminals between them. Circuit A can then be replaced by its Thevenin equivalent circuit. That equivalent has a voltage source in series with an impedance.

Replacing circuit A with its Thevenin equivalent does not change the current or voltage of any element in circuit B. The values in circuit B stay the same whether it is connected to the original circuit A or to the Thevenin equivalent. This is why the method is useful for studying connected circuits.

Two values are needed to build the Thevenin equivalent circuit. The first is the Thevenin voltage, which is found from the open-circuit voltage across the terminals of circuit A. The second is the Thevenin impedance, Zt, which is the equivalent impedance of circuit A*.

To form circuit A*, all independent voltage sources are replaced with short circuits. All independent current sources are replaced with open circuits. Then series or parallel impedances can be combined repeatedly to find Zt.

Finding Voltage and Impedance in Circuit A

finding-voltage-and-impedance-in-circuit-a

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 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...

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...

node analysis for ac circuits

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...

th&#233venin equivalent circuits

The household power distribution system can be simplified with Thevenin's theorem. In this system, distribution lines and transformers form the main network. Electrical appliances can be treated as load impedance, which makes the circuit easier to analyze. An AC circuit can be split into two parts, circuit A and circuit B, with a single pair of terminals between them. Circuit A can then be replaced by its Thevenin equivalent circuit. That equivalent has a voltage source in series with an...

norton equivalent circuits

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...

op amp ac circuits

Analyzing an Op Amp Audio Filter

An op amp audio filter shapes an amplified sound signal by strongly reducing the lower-frequency parts. In this circuit, the focus is on a basic filter setup used after an amplifier in an audio system. The filter uses an operational amplifier in an inverting arrangement with resistors R1 and R2 and a capacitor C1. The analysis starts with a known input signal and asks for the output signal. To solve it, the capacitor impedance is found first. That requires the angular frequency from the...

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 Thevenin's theorem simplifies household AC circuits by using open-circuit voltage and equivalent impedance to model circuit A.

Finding Voltage and Impedance in Circuit A | JoVE K12

JoVE Core 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Finding Voltage and Impedance in Circuit A

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