Name: ac power and phase shift
Uploaded: 2024-07-08T13:19:51.000Z
Duration: 1 min 22 s
Channel: JoVE

Pour un circuit avec une entrée sinusoïdale, la puissance délivrée à un élément passif est égale au produit de la tension et du courant qui le traversent.
L’expression de la tension et du courant sous une forme sinusoïdale et l’application de l’identité trigonométrique donnent l’expression de la puissance instantanée avec deux termes.
Le premier terme est une constante dépendante de la différence de phase entre la tension et le courant, tandis que le second terme est une fonction sinusoïdale avec deux fois la fréquence de la tension ou du courant.
Pour les circuits à résistance et réactance mixtes, la puissance instantanée oscille entre des valeurs positives et négatives.
Dans un circuit purement résistif, la tension et le courant sont en phase, ce qui permet d’obtenir une dissipation de puissance instantanée toujours positive.
Pour les circuits purement inductifs et capacitifs, le déphasage entre la tension et le courant fait fluctuer la puissance instantanée entre des valeurs positives et négatives.
Les inductances et les condensateurs stockent et libèrent de l’énergie de manière cyclique lorsque le courant traversant l’inductance ou la tension aux bornes du condensateur change.
Au cours du cycle de libération d’énergie, les éléments réactifs agissent comme une source d’énergie, fournissant de l’énergie au circuit, ce qui entraîne une puissance instantanée négative.

puissance instantanée

La puissance instantanée est importante dans les circuits électriques, principalement lorsqu’il s’agit d’une entrée sinusoïdale. La puissance instantanée, notée p(t), résulte de la multiplication de la tension instantanée (v(t)) aux bornes d'un élément et du courant instantané (i(t)) qui le traverse. Cette relation adhère à la convention du signe passif et représente un principe fondamental en génie électrique.

 <img alt="Equation 1" src="/files/ftp_upload/15117/15117_Equation_1.svg" style="height: 15px;">

Lorsqu’on examine la puissance instantanée, elle peut être exprimée comme une combinaison de deux termes distincts. Le premier terme, qui reste constant, dépend de la différence de phase entre la tension et le courant. Le deuxième terme, caractérisé par une oscillation sinusoïdale, présente une fréquence deux fois supérieure à celle de la tension ou du courant.

 <img alt="Equation 2" src="/files/ftp_upload/15117/15117_Equation_2.svg" style="height: 30px;">

Dans les circuits comprenant des éléments de résistance et de réactance, la puissance instantanée est dynamique, oscillant entre des valeurs positives et négatives. Dans le cas de circuits purement résistifs, où la tension et le courant sont parfaitement en phase, la puissance instantanée se dissipe systématiquement positivement.
À l’inverse, dans les circuits dominés par des composants inductifs et capacitifs, le déphasage entre tension et courant entraîne des fluctuations intermittentes de la puissance instantanée entre valeurs positives et négatives. Ce phénomène peut être attribué au stockage et à la libération cycliques d'énergie par les inductances et les condensateurs lorsque le courant traverse les premiers et qu'une tension apparaît aux bornes des seconds. Pendant la phase de libération d'énergie, ces éléments réactifs agissent comme des sources d'énergie, fournissant efficacement de l'énergie dans le circuit, ce qui entraîne la manifestation d'une puissance instantanée négative. Cette interaction complexe de tension, de courant et de dynamique de puissance souligne les principes fondamentaux régissant les circuits électriques. La compréhension de ces principes est essentielle pour une gestion efficace de l’énergie et la conception de systèmes électriques.

Puissance instantanée

Pour un circuit avec une entrée sinusoïdale, la puissance délivrée à un élément passif est égale au produit de la tension et du courant qui le traversent.
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Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

AC Steady State Power

Puissance alternative en régime permanent

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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.

In a purely resistive circuit, voltage and current are in phase. In that case, instantaneous power stays positive and is always dissipated. In circuits with resistance and reactance, the power can swing between positive and negative values.

This change happens because inductors and capacitors store and release energy over time. As current passes through an inductor, or as voltage appears across a capacitor, these elements can give energy back to the circuit during release. That is why negative instantaneous power can appear when reactive elements act like power sources. Understanding these voltage, current, and power relationships is important for efficient energy use and electrical system design.

AC Power and Phase Shift

instantaneous power

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

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 instantaneous power depends on voltage, current, and phase shift in AC circuits, including resistive, inductive, and capacitive behavior.

AC Power and Phase Shift | 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

AC Power and Phase Shift

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