Name: power consumption in ac circuits
Uploaded: 2024-07-08T13:19:51.000Z
Duration: 1 min 13 s
Channel: JoVE

ほとんどの実用的なアプリケーションでは、時間とともに変化する瞬時電力は一般的に使用される量ではありません。
代わりに、平均電力が測定可能な量として使用されます。これは、期間全体の瞬時パワーを積分し、それを期間で割ることによって計算されます。
瞬時パワーの式を代入し、さらに簡略化して、平均パワーの時間領域式を得る。
2 番目の項は、ある期間の余弦関数の平均値であり、0 です。
平均電力の最終的な表現は時間に依存せず、電圧と電流の位相差に比例します。
電圧と電流の半分の積をフェーザ形式で生成した項は、実数部と虚数部の両方で構成されます。
このフェーザ式を平均電力方程式と比較すると、実数部が平均電力に対応することがわかります。
純粋な抵抗性回路では、同相の電圧と電流が正の平均電力につながります。
ただし、純粋な反応性回路では、電圧と電流の間の位相シフトが90度になると、平均電力はゼロになります。

平均電力

実際の電気アプリケーションでは、時間によって変化する瞬間電力の概念はあまり使用されません。代わりに、焦点は平均電力と呼ばれる、より実用的な量に移ります。平均電力は、指定された期間にわたって瞬間電力を積分し、その後その期間で割ることによって決定されます。

<img alt="Equation 1" src="/files/ftp_upload/15118/15118_Equation_1.svg" style="height: 42px;">

瞬間電力の式は、平均電力の時間領域式に到達するように簡略化されます。特に、コサイン関数を含む 2 番目の項は、完全なサイクルにわたって平均するとゼロになります。

<img alt="Equation 2" src="/files/ftp_upload/15118/15118_Equation_2.svg" style="height: 42px;">

その結果、平均電力の最終的な式は時間に依存せず、電圧と電流の位相差に依存します。

<img alt="Equation 3" src="/files/ftp_upload/15118/15118_Equation_3.svg" style="height: 30px;">

この式を電圧と電流の積の位相器表現と比較すると、位相器の実部が平均電力に対応することが明らかになります。

<img alt="Equation 4" src="/files/ftp_upload/15118/15118_Equation_4.svg" style="height: 28px;">

電圧と電流が完全に同位相である純抵抗回路では、平均電力は正であり、継続的な電力消費を意味します。逆に、電圧と電流の位相が 90 度ずれている純リアクタンス回路では、平均電力は 0 に減少します。この現象は、エネルギーの周期的な蓄積と放出に起因しており、平均すると、正味電力は消費されません。

瞬間電力は時間に応じて変化しますが、平均電力は一定であることを認識することが重要です。瞬間電力を計算するには、時間領域での電圧と電流が必要ですが、電圧と電流を位相器を使用して周波数領域で表すと、平均電力も決定できます。

平均電力を理解することは、特に抵抗コンポーネントとリアクティブなコンポーネントのさまざまな組み合わせを備えた回路において、電力消費と効率の評価を容易にするため、実際のアプリケーションでは非常に重要です。

ほとんどの実用的なアプリケーションでは、時間とともに変化する瞬時電力は一般的に使用される量ではありません。
代わりに、平均電力は...

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

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 not change with time and depends on the phase difference between voltage and current.

The same result appears in the phasor form of voltage and current. The real part of the phasor product matches the average power. In a purely resistive circuit, voltage and current are in phase, so the average power is positive and the circuit keeps consuming power.

In a purely reactive circuit, voltage and current are ninety degrees apart. In that case, the average power drops to zero because energy is stored and then released in a cycle. Instantaneous power still changes with time, but average power stays constant. It can be calculated from time-domain signals or from phasors in the frequency domain. This makes average power useful for judging power use and efficiency in circuits with resistive and reactive parts.

Power Consumption in AC 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 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

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 average power describes power consumption in AC circuits, why phase difference matters, and why reactive circuits can have zero net power.

Power Consumption in AC 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

Power Consumption in AC Circuits

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