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

Per un circuito con un ingresso sinusoidale, la potenza erogata a un elemento passivo è uguale al prodotto della tensione e della corrente che lo attraversano.
Esprimendo tensione e corrente in forma sinusoidale e applicando l'identità trigonometrica si ottiene l'espressione per potenza istantanea con due termini.
Il primo termine è una costante dipendente dalla differenza di fase tra la tensione e la corrente, mentre il secondo termine è una funzione sinusoidale con il doppio della frequenza della tensione o della corrente.
Per i circuiti con resistenza mista e reattanza, la potenza istantanea oscilla tra valori positivi e negativi.
In un circuito puramente resistivo, la tensione e la corrente sono in fase, con conseguente dissipazione di potenza istantanea costantemente positiva.
Per i circuiti puramente induttivi e capacitivi, lo sfasamento tra la tensione e la corrente fa sì che la potenza istantanea fluttui tra valori positivi e negativi.
Gli induttori e i condensatori immagazzinano e rilasciano ciclicamente energia al variare della corrente attraverso l'induttore o della tensione attraverso il condensatore.
Durante il ciclo di rilascio dell'energia, gli elementi reattivi fungono da fonte di alimentazione, fornendo energia al circuito, portando a una potenza istantanea negativa.

potenza istantanea

La potenza istantanea è importante nei circuiti elettrici, soprattutto quando si tratta di ingresso sinusoidale. La potenza istantanea, indicata come p(t), risulta dalla moltiplicazione della tensione istantanea (v(t)) ai capi di un elemento e della corrente istantanea (i(t)) che lo attraversa. Questa relazione aderisce alla convenzione dei segni passivi e rappresenta un principio fondamentale nell'ingegneria elettrica.


<img alt="Equation 1" src="/files/ftp_upload/15117/15117_Equation_1.svg" style="height: 15px;">

Quando si esamina la potenza istantanea, questa può essere espressa come una combinazione di due termini distinti. Il primo termine, che rimane costante, dipende dalla differenza di fase tra tensione e corrente. Il secondo termine, caratterizzato da un'oscillazione sinusoidale, presenta una frequenza doppia rispetto a quella della tensione o della corrente.


<img alt="Equation 2" src="/files/ftp_upload/15117/15117_Equation_2.svg" style="height: 30px;">

Nei circuiti che comprendono elementi di resistenza e reattanza, la potenza istantanea è dinamica e oscilla tra valori positivi e negativi. Nei casi di circuiti puramente resistivi, dove tensione e corrente sono perfettamente in fase, la potenza istantanea si dissipa costantemente positivamente.

Al contrario, nei circuiti dominati da componenti induttivi e capacitivi, lo sfasamento tra tensione e corrente porta a fluttuazioni intermittenti della potenza istantanea tra valori positivi e negativi. Questo fenomeno può essere attribuito all'accumulo e al rilascio ciclico di energia da parte di induttori e condensatori mentre la corrente attraversa i primi e la tensione appare nei secondi. 


Durante la fase di rilascio dell'energia, questi elementi reattivi agiscono come fonti di energia, restituendo effettivamente energia al circuito con conseguente manifestazione di potenza istantanea negativa. Questa complessa interazione tra tensione, corrente e dinamica di potenza sottolinea i principi fondamentali che governano i circuiti elettrici. La comprensione di questi principi è fondamentale per una gestione efficiente dell’energia e la progettazione dei sistemi elettrici.

Potenza istantanea

Per un circuito con un ingresso sinusoidale, la potenza erogata a un elemento passivo è uguale al prodotto della tensione e della corrente che lo attraversano.
Esprimere...

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

AC Steady State Power

Potenza in regime stazionario CA

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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