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

Considérons un circuit alternatif avec une source de tension périodique connectée à une résistance.
La puissance moyenne délivrée à la résistance est égale à l’intégrale de la puissance instantanée sur une période divisée par la période.
Lorsque cette résistance est connectée à une source CC, la puissance moyenne qu’elle absorbe est le produit du courant au carré et de sa résistance.
Si l’on considère que la puissance moyenne fournie par une source CC à la résistance est équivalente à celle fournie par le courant périodique, le courant continu est égal à la valeur effective du courant périodique.
Ainsi, la valeur effective du courant est la racine carrée de la moyenne des valeurs de courant instantané au carré.
De même, l’expression de la valeur effective de la tension peut être obtenue.
Pour tout signal périodique, la valeur effective, également connue sous le nom de valeur quadratique moyenne, est égale à la racine carrée de la moyenne du carré du signal périodique.
Pour un courant et une tension sinusoïdaux, la valeur efficace est égale à la valeur de crête divisée par la racine carrée de deux.

valeur effective d'une forme d'onde périodique

Effective Value of a Periodic Waveform

Le concept de valeur efficace, la valeur efficace (RMS), est crucial pour comprendre les circuits électriques et la fourniture de puissance. Cette idée découle de la nécessité de mesurer l’efficacité d’une source de tension ou de courant pour alimenter une charge résistive.
La valeur efficace d'un courant périodique représente le courant continu (DC) qui transmet à une résistance la même puissance moyenne que le courant périodique lui-même. Ce concept est crucial lors de l’évaluation des circuits AC. Pour déterminer la valeur efficace du courant, il faut trouver le courant RMS, qui est la racine carrée de la moyenne des carrés des valeurs instantanées du courant sur une période. Cette valeur RMS correspond au DC qui délivre la même puissance moyenne que le courant périodique lorsqu'il est appliqué à une résistance. 
<img alt="Equation 1" src="/files/ftp_upload/15119/15119_Equation_1.svg" style="height: 60px;">
De même, la valeur efficace de la tension est calculée de la même manière que le courant. Elle représente la tension efficace, essentielle pour évaluer la consommation électrique des systèmes électriques. 
<img alt="Equation 2" src="/files/ftp_upload/15119/15119_Equation_2.svg" style="height: 60px;">
La valeur RMS est un concept fondamental qui ne se limite pas aux signaux sinusoïdaux. Pour toute fonction périodique, la valeur RMS est calculée en trouvant le carré de la fonction, en déterminant la moyenne des carrés, puis en prenant la racine carrée de cette moyenne. Dans les applications pratiques, la tension et le courant sont souvent exprimés en termes de valeurs efficaces plutôt que de valeurs de crête. En effet, la valeur moyenne d'un signal sinusoïdal est nulle, ce qui fait de la valeur RMS une mesure plus utile pour l'analyse de puissance. De plus, les voltmètres et ampèremètres analogiques sont conçus pour lire directement les valeurs efficaces de la tension et du courant, ce qui en fait des outils indispensables dans les mesures de puissance.

Valeur effective d'une forme d'onde périodique

Considérons un circuit alternatif avec une source de tension périodique connectée à une résistance.
La puissance moyenne délivrée à la résistance est égale à l’intégrale de la ...

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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

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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

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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...

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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...

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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...

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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...

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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...

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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 Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

RMS Value for AC Power Measurement

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