Name: ac power in series and parallel circuits
Uploaded: 2024-07-08T13:19:51.000Z
Duration: 1 min 15 s
Channel: JoVE

AC電力保存の原則は、ソースによって生成される複素電力、実電力、および無効電力は、負荷によって消費される複素電力、実電力、および無効電力の合計と同等であることを示しています。
この原理は、簡略化された回路モデルを通じて説明できます。
回路の合計インピーダンスが最初に計算され、次に合計ソース電流が決定されます。
次に、ソースの複素電力は、この電流とソース電圧の複素共役を使用して計算されます。
実数部と虚数部を分離することで、発生源の有効電力と無効電力を導き出すことができます。
次に、各負荷の電圧降下を計算します。
複素電力は、共役電流と各セクション間の電圧降下の積を取ることによって決定されます。これから、実数と無効電力が演繹されます。
計算されたすべての電力を比較すると、ソースの電力が個々のセクションの電力の合計に等しいことが明らかになり、電力保存の原理が確認されます。
この原理は、直列または並列に接続された負荷に関係なく当てはまります。

ac 電力の保存

Conservation of AC Power

電気量保存の法則は、AC 回路と DC 回路の両方に適用できます。この原理を AC 電源に適用すると、電源によって生成される複素電力、実電力、無効電力は、負荷によって吸収される複素電力、実電力、無効電力の合計に等しいとされます。2つの負荷インピーダンスがAC電源Vに並列に接続されている場合、電源によって提供される複素電力は、次の関係を使用して計算できます。

<img alt="Equation 1" src="/files/ftp_upload/15121/15121_Equation_1.svg" style="height: 18px;">

ここで、S_1 と S_2 は、それぞれ負荷 Z_1 と Z_2 に供給される複素電力を表します。これらの負荷が電圧源と直列に接続されている場合、電源によって供給される複素電力は変わりません。これは、負荷が直列に接続されているか並列に接続されているか(またはその他の構成)に関係なく、電源によって提供される合計電力は、負荷によって受信される合計電力に等しいことを示しています。一般に、N個の負荷に接続された電源の場合、複素電力は次のように表されます

<img alt="Equation 2" src="/files/ftp_upload/15121/15121_Equation_2.svg" style="height: 15px;">

これは、ネットワーク内の総複素電力が、個々のコンポーネントの複素電力の合計であることを意味します。これは、有効電力と無効電力には当てはまりますが、皮相電力には当てはまりません。これは、AC 電力保存の原理を明確に示しています。このことから、ネットワーク内の電源からの有効 (または無効) 電力フローは、ネットワークの他のコンポーネントへの有効 (または無効) 電力フローと等しいと推測できます。

AC 電力の保存

AC電力保存の原則は、ソースによって生成される複素電力、実電力、および無効電力は、総複素数、...

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

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 supplied by the source stays the same. This shows that the total power from the source does not depend on the load arrangement.

The same idea extends to a network with N loads. The total complex power is the sum of the complex powers of the individual components. The rule also applies to real power and reactive power, but not to apparent power. This is the principle of AC power conservation, and it means the real or reactive power leaving sources in a network equals the real or reactive power absorbed by the other components.

AC Power in Series and Parallel Circuits

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 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

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 AC power is shared in series and parallel circuits, and why total complex, real, and reactive power stay conserved across a network.

AC Power in Series and Parallel Circuits | 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

AC Power in Series and Parallel Circuits

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