Name: power from multiple ac sources
Uploaded: 2024-07-08T13:19:54.000Z
Duration: 1 min 19 s
Channel: JoVE

2つの正弦波電圧源を備えた回路を考えてみましょう。
重ね合わせの原理によれば、両方のソースから生じる合計電流は、各ソースが独立して負う電流の合計です。
また、瞬時電力は、瞬時電流に抵抗を掛けたものの2乗です。
これを 1 つの期間で積分すると、各ソースの平均パワーの合計に等しい平均パワーと、周波数が異なるソースの場合は 0 に等しい 3 番目の項が得られます。
簡略化された方程式は、電力の重ね合わせの原理を表しており、異なる周波数を持つソースによって供給される平均電力は、各ソースによって供給される平均電力の合計に等しいことを示しています。
この原則は、ラジオ放送などの電気通信では非常に重要です。
複数のラジオ局が同時に信号を放送し、それぞれが独立した電磁波源として機能します。
電力重ね合わせの原理によれば、ラジオが受信する総電力は、各ステーションによって送信された電力の合計です。
ラジオを特定の周波数にチューニングすると、ユーザーは複数のステーションから信号を受信しているにもかかわらず、一度に1つのステーションを聞くことができます。

電力の重ね合わせの原理

2つの正弦波電圧源がある回路を考えてみましょう。各電圧源は独立して回路に影響を与えますが、重ね合わせの原理は各電圧源からの応答を加算することで複合効果を理解するのに役立ちます。

<img alt="Figure 1" src="/files/ftp_upload/15124/15124_Figure_1.svg" style="height: 150px;">

重ね合わせの原理によると、両方の電圧源による合計電流は、各電圧源による電流の合計です。両方の電圧源が一緒に動作する場合、それぞれの電流 (i_1 と i_2) が加算されて合計電流になります。また、瞬間電力は瞬間電流の 2 乗に抵抗を掛けた値です。

<img alt="Equation 1" src="/files/ftp_upload/15124/15124_Equation_1.svg" style="height: 20px;">

この概念は電力、つまりエネルギーが使用される速度にも当てはまります。任意の瞬間において、回路の瞬間電力は電流の 2 乗に抵抗を掛けた値です。これを 1 周期にわたって積分すると平均電力が得られます。これは各ソースによる平均電力の合計に等しく、3 番目の項は周波数の異なるソースではゼロになります。

<img alt="Equation 2" src="/files/ftp_upload/15124/15124_Equation_2.svg" style="height: 45px;">

<img alt="Equation 3" src="/files/ftp_upload/15124/15124_Equation_3.svg" style="height: 45px;">

簡略化された方程式は電力重ね合わせの原理を表し、異なる周波数のソースによって配信される平均電力は、各ソースによって配信される平均電力の合計に等しいことを示しています。この原理は、ラジオ放送などの通信において非常に重要です。複数のラジオ局が同時に信号を放送し、それぞれが独立した電磁波源として機能します。電力重ね合わせの原理によると、ラジオが受信する総電力は、各局によって送信される電力の合計です。ラジオを特定の周波数に合わせると、ユーザーは複数の局から信号を受信して いるにもかかわらず、つの局のみを聞くことができます。

2つの正弦波電圧源を備えた回路を考えてみましょう。
重ね合わせの原理によれば、両方のソースから生じる合計電流は合計です...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

AC Steady State Power

交流定常状態電力

KEY TERMS AND CONCEPTS

主要用語と概念

The Power Superposition Principle

power from multiple ac sources

Power from multiple AC sources is found by adding the effects of each source separately. In a circuit with two sinusoidal voltage sources, each source acts independently. The superposition principle says the total current is the sum of the currents produced by each source alone. If those currents are labeled i1 and i2, they combine to give the total current.

Instantaneous power is the power at one moment in time. In this circuit, it equals the square of the instantaneous current times the resistance. To find the average power, this expression is integrated over one period. The result shows that the average power from both sources is the sum of the average powers from each source, and a third term becomes zero when the sources have different frequencies.

This idea is called the power superposition principle. It means that the average power delivered by sources with different frequencies is the sum of the average power delivered by each source. The principle is important in telecommunications, including radio broadcasting. Multiple radio stations can broadcast at the same time, and each one acts as an independent source of electromagnetic waves. A radio receives the total power from all of them, but tuning to one frequency lets the listener hear one station at a time.

Power from Multiple AC Sources

instantaneous power

AC Power and Phase Shift

Instantaneous power in an electrical circuit comes from the voltage across an element and the current through it. It is written as p(t) and follows the passive sign convention. For sinusoidal input, this product helps show how power changes at each moment. When instantaneous power is expanded, it has two parts. One part is constant and depends on the phase difference between voltage and current. The other part is a sinusoidal term that varies at twice the frequency of the voltage or current. <br...

average power

Power Consumption in AC Circuits

Power consumption in AC circuits is often described with average power. In practical electrical work, the changing value of instantaneous power is less useful than the average over a time period. Average power is found by integrating instantaneous power over that time and then dividing by the duration. The time-domain expression for average power comes from simplifying the equation for instantaneous power. In that form, one cosine term averages to zero over a complete cycle. The result does...

effective value of a periodic waveform

RMS Value for AC Power Measurement

The RMS value, or effective value, helps measure how much power a periodic voltage or current can deliver. It is the direct current, or DC, value that gives the same average power to a resistor as the periodic signal does. This idea is especially important in AC circuits. To find the effective value of current, calculate the root mean square, or RMS, current. First square the instantaneous current values over one period. Then find the mean of those squared values and take the square root. The...

complex power

Power Triangle in AC Circuits

Power triangle and complex power help describe how an AC load uses energy. Engineers use complex power to capture the combined effect of parallel loads. It gives a full picture of the power consumed by a specific load. Complex power is found by multiplying voltage by the complex conjugate of current. Using rms values, it is written with the rms voltage phasor and the complex conjugate of the rms current phasor. It can also be written in terms of load impedance. The magnitude of complex power...

conservation of ac power

AC Power in Series and Parallel Circuits

AC power in series and parallel circuits follows a power preservation rule. In AC circuits, the complex power, real power, and reactive power produced by the source are equal to the total complex, real, and reactive powers absorbed by the loads. When two load impedances are connected in parallel to an AC source V, the source power can be written as the sum of the complex powers delivered to loads Z1 and Z2. If those same loads are connected in series with the voltage source, the complex power...

power factor

Power Factor and AC Load Behavior

Power factor describes how voltage and current behave in an AC load. It is the ratio of average, or active, power to apparent power. The power factor angle is the phase difference between voltage and current, and the cosine of that angle gives the power factor. It also matches the angle of the load impedance. Power factor shows how much apparent power becomes real, or average, power. Its value ranges from zero to one. When a load is purely resistive, voltage and current are in phase. In that...

power factor correction

Reducing Reactive Power in AC Loads

Power factor correction helps AC systems use electrical power more efficiently. In a factory circuit, transmitted power includes apparent power, which is made of active power and reactive power. Power factor is the ratio of real power, measured in kW, to apparent power, measured in kVA. It shows how much of the supplied power becomes useful work. A low power factor often happens when an inductive load draws too much reactive power. This creates a lagging power factor. It can also cause large...

the power superposition principle

Power from multiple AC sources is found by adding the effects of each source separately. In a circuit with two sinusoidal voltage sources, each source acts independently. The superposition principle says the total current is the sum of the currents produced by each source alone. If those currents are labeled i1 and i2, they combine to give the total current. Instantaneous power is the power at one moment in time. In this circuit, it equals the square of the instantaneous current times the...

the maximum power transfer theorem

Matching Load Impedance for Maximum Power

Maximum power transfer in an AC circuit depends on matching the load impedance to the Thevenin equivalent of the source network. The load draws current, and the circuit delivers power to that load. To analyze the current, the voltages, currents, network impedance, and load impedance are written in rectangular form. The average power delivered to the load comes from the square of the current multiplied by the load resistance. To find the condition for maximum power, the power is differentiated...

key terms and concepts

Learn how superposition adds currents from two sinusoidal sources and why average power from different frequencies can be combined in AC circuits and radio.

Power from Multiple AC Sources | 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

Power from Multiple AC Sources

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