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

Per la maggior parte delle applicazioni pratiche, la potenza istantanea variabile nel tempo non è una grandezza comunemente usata.
Invece, la potenza media viene utilizzata come quantità misurabile. Si calcola integrando la potenza istantanea nel periodo e dividendola per il periodo.
L'espressione per la potenza istantanea viene sostituita e ulteriormente semplificata per ottenere un'espressione nel dominio del tempo per la potenza media.
Il secondo termine è il valore medio della funzione coseno in un periodo ed è zero.
L'espressione finale della potenza media è indipendente dal tempo ed è proporzionale alla differenza di fase tra la tensione e la corrente.
Il termine risultante dalla metà del prodotto di tensione e corrente in forma di fasori comprende sia parti reali che immaginarie.
Confrontando questa espressione fasoriale con l'equazione della potenza media si indica che la parte reale corrisponde alla potenza media.
In un circuito puramente resistivo, la tensione e la corrente in fase portano a una potenza media positiva.
Tuttavia, nei circuiti puramente reattivi, uno sfasamento di novanta gradi tra tensione e corrente si traduce in una potenza media pari a zero.

potenza media

Nelle applicazioni elettriche, il concetto di potenza istantanea variabile nel tempo non viene utilizzato frequentemente. L’attenzione si sposta invece sulla quantità più pratica nota come potenza media. La potenza media viene determinata integrando la potenza istantanea su un periodo di tempo specificato e dividendola successivamente per tale durata.


<img alt="Equation 1" src="/files/ftp_upload/15118/15118_Equation_1.svg" style="height: 42px;">

L'equazione per la potenza istantanea viene semplificata per arrivare a un'espressione nel dominio del tempo per la potenza media. In particolare, il secondo termine, che coinvolge una funzione coseno, ha una media pari a zero su un ciclo completo.


<img alt="Equation 2" src="/files/ftp_upload/15118/15118_Equation_2.svg" style="height: 42px;">

Di conseguenza, l'espressione finale della potenza media è indipendente dal tempo e dipende dalla differenza di fase tra tensione e corrente.


<img alt="Equation 3" src="/files/ftp_upload/15118/15118_Equation_3.svg" style="height: 30px;">

Confrontando questa espressione con la rappresentazione del fasore del prodotto di tensione e corrente, diventa evidente che la parte reale del fasore corrisponde alla potenza media.


<img alt="Equation 4" src="/files/ftp_upload/15118/15118_Equation_4.svg" style="height: 28px;">

Nei circuiti puramente resistivi, dove tensione e corrente sono perfettamente in fase, la potenza media è positiva, indicando un consumo energetico continuo. Al contrario, la potenza media diminuisce fino a zero nei circuiti puramente reattivi caratterizzati da uno sfasamento di novanta gradi tra tensione e corrente. Questo fenomeno è attribuito allo stoccaggio e al rilascio ciclico di energia, dove, in media, non viene consumata energia netta.


È importante riconoscere che mentre la potenza istantanea varia rispetto al tempo, la potenza media rimane costante. Il calcolo della potenza istantanea richiede tensione e corrente nel dominio del tempo, ma la potenza media può anche essere determinata quando tensione e corrente sono rappresentate nel dominio della frequenza utilizzando fasori.

Comprendere la potenza media è fondamentale nelle applicazioni pratiche, poiché facilita la valutazione del consumo energetico e dell'efficienza, soprattutto nei circuiti caratterizzati da diverse combinazioni di componenti resistivi e reattivi.

Potenza Media

Per la maggior parte delle applicazioni pratiche, la potenza istantanea variabile nel tempo non è una grandezza comunemente usata.
Invece, la potenza media viene utilizzata come ...

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

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 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

Power Consumption in AC Circuits

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