Name: rms value for ac power measurement
Uploaded: 2024-07-08T13:19:51.000Z
Duration: 1 min 7 s
Channel: JoVE

周期的な電圧源が抵抗に接続されたAC回路を考えてみましょう。
抵抗器に供給される平均電力は、ある期間の瞬時電力を周期で割った積分に等しくなります。
この抵抗器がDC電源に接続されている場合、吸収する平均電力は電流の2乗とその抵抗の積です。
DC電源から抵抗器に供給される平均電力が周期電流によって供給される電力と同等であることを考慮すると、直流電流は周期電流の実効値に等しくなります。
したがって、電流の実効値は、二乗された瞬時電流値の平均の平方根です。
同様に、電圧の実効値に対する式を求めることができる。
周期的な信号の場合、実効値 (二乗平均平方根値とも呼ばれる) は、周期的な信号の 2 乗の平均の平方根に等しくなります。
正弦波の電流と電圧の場合、RMS値はピーク値を2の平方根で割った値に等しくなります。

周期波形の実効値

Effective Value of a Periodic Waveform

実効値の概念、つまり二乗平均平方根 (RMS) 値は、電気回路と電力供給を理解する上で非常に重要です。この概念は、抵抗負荷に電力を供給する電圧または電流源の有効性を測定する必要性から生まれました。

周期電流の実効値は、周期電流自体と同じ平均電力を抵抗器に伝える直流電流 (DC) を表します。この概念は、AC 回路を評価する際に重要です。電流の実効値を決定するには、RMS 電流を見つける必要があります。これは、一定期間の瞬時電流値の二乗の平均の平方根です。この RMS 値は、抵抗器に適用されたときに周期電流と同じ平均電力を供給する DC に対応します。

<img alt="Equation 1" src="/files/ftp_upload/15119/15119_Equation_1.svg" style="height: 60px;">

同様に、電圧の実効値は電流と同じ方法で計算されます。これは、電気システムの電力消費を評価するために不可欠な RMS 電圧を表します。

<img alt="Equation 2" src="/files/ftp_upload/15119/15119_Equation_2.svg" style="height: 60px;">

RMS 値は基本的な概念であり、正弦波信号に限定されません。周期関数の場合、RMS 値は関数の二乗を求め、二乗の平均を求め、その平均の平方根を取ることによって計算されます。実際のアプリケーションでは、電圧と電流はピーク値ではなく RMS 値で表現されることがよくあります。これは、正弦波信号の平均値がゼロであることから、RMS 値が電力分析のより有用な指標となるためです。これに加えて、アナログ電圧計と電流計は電圧と電流の RMS 値を直接読み取るように設計されているため、電力測定に不可欠なツールとなっています。

周期的な電圧源が抵抗に接続されたAC回路を考えてみましょう。
抵抗器に供給される平均電力は、...

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

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 result is the DC current that would produce the same average power in a resistor.

The same method is used for voltage. The effective value of voltage is the RMS voltage, and it is used to judge power use in electrical systems. The RMS idea also works for any periodic function, not only sinusoidal signals.

For any periodic waveform, the RMS value comes from squaring the function, averaging the squared values, and then taking the square root. In practice, voltage and current are often given as RMS values instead of peak values. That is useful because the average value of a sinusoidal signal is zero, while the RMS value still shows its power effect.

Analog voltmeters and ammeters are designed to read RMS values directly. That makes them useful tools for measuring voltage and current in power circuits.

RMS Value for AC Power Measurement

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

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 RMS, or effective value, compares AC voltage and current to DC power in resistive loads, and why it is used in electrical measurements.

RMS Value for AC Power Measurement | 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

RMS Value for AC Power Measurement

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