Name: ac power in series and parallel circuits
Uploaded: 2024-07-08T13:19:51.000Z
Duration: 1 min 15 s
Channel: JoVE

Das Prinzip der AC-Leistungserhaltung besagt, dass die von der Quelle erzeugten komplexen, realen und Blindleistungen der gesamten komplexen, realen und Blindleistung entsprechen, die von den Verbrauchern verbraucht wird.
Dieses Prinzip lässt sich durch ein vereinfachtes Schaltungsmodell verdeutlichen.
Zuerst wird die Gesamtimpedanz der Schaltung berechnet, gefolgt von der Bestimmung des gesamten Quellenstroms.
Die komplexe Leistung der Quelle wird dann aus dem komplexen Konjugat dieses Stroms und der Quellenspannung berechnet.
Durch die Trennung von Real- und Imaginärteil kann die Wirk- und Blindleistung der Quelle abgeleitet werden.
Als nächstes wird der Spannungsabfall an jeder Last berechnet.
Die komplexe Leistung wird bestimmt, indem das Produkt aus dem konjugierten Strom und dem Spannungsabfall über jeden Abschnitt genommen wird. Daraus werden die Real- und Blindleistung abgeleitet.
Beim Vergleich aller berechneten Potenzen wird deutlich, dass die Leistung der Quelle gleich der Summe der Potenz der einzelnen Abschnitte ist, was das Prinzip der Leistungserhaltung bestätigt.
Dieses Prinzip gilt unabhängig von den in Reihe oder parallel geschalteten Verbrauchern.

erhaltung der wechselstromleistung

Conservation of AC Power

Das Prinzip der Leistungserhaltung ist sowohl auf Wechselstrom- als auch auf Gleichstromkreise anwendbar. Dieses Prinzip besagt, wenn es auf Wechselstrom angewendet wird, dass die von der Quelle erzeugte komplexe, reale und Blindleistung gleich der gesamten komplexen, realen und Blindleistung ist, die von den Lasten aufgenommen wird. Wenn zwei Lastimpedanzen parallel an eine Wechselstromquelle V angeschlossen sind, kann die von der Quelle bereitgestellte komplexe Leistung mithilfe der Beziehung berechnet werden:

<img alt="Equation 1" src="/files/ftp_upload/15121/15121_Equation_1.svg" style="text-align: center; height: 15px;">

wobei S_1 und S_2 die komplexen Leistungen darstellen, die an die Lasten Z_1 bzw. Z_2 geliefert werden. Wenn diese Lasten in Reihe mit der Spannungsquelle angeschlossen sind, bleibt die von der Quelle gelieferte komplexe Leistung unverändert. Dies legt nahe, dass unabhängig davon, ob die Lasten in Reihe oder parallel (oder in einer anderen Konfiguration) angeschlossen sind, die von der Quelle bereitgestellte Gesamtleistung gleich der von der Last empfangenen Gesamtleistung ist. Im Allgemeinen ist die komplexe Leistung für eine Quelle, die an N Lasten angeschlossen ist, gegeben durch

<img alt="Equation 2" src="/files/ftp_upload/15121/15121_Equation_2.svg" style="text-align: center; height: 12px;">

Dies bedeutet, dass die gesamte komplexe Leistung in einem Netzwerk die Summe der komplexen Leistungen seiner einzelnen Komponenten ist. Dies gilt für Wirkleistung und Blindleistung, aber nicht für Scheinleistung. Dies drückt das Prinzip der Wechselstrom-Energieeinsparung aus. Daraus lässt sich folgern, dass der Wirk- (oder Blind-)Leistungsfluss von Quellen in einem Netzwerk dem Wirk- (oder Blind-)Leistungsfluss in die anderen Komponenten des Netzwerks entspricht.

Erhaltung der Wechselstromleistung

Das Prinzip der AC-Leistungserhaltung besagt, dass die komplexen, realen und reaktiven Leistungen, die von der Quelle erzeugt werden, der Gesamtkomplexleistung ...

Education

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JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

AC Steady State Power

Stationäre Leistung im Wechselstromkreis

KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

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 supplied by the source stays the same. This shows that the total power from the source does not depend on the load arrangement.

The same idea extends to a network with N loads. The total complex power is the sum of the complex powers of the individual components. The rule also applies to real power and reactive power, but not to apparent power. This is the principle of AC power conservation, and it means the real or reactive power leaving sources in a network equals the real or reactive power absorbed by the other components.

AC Power in Series and Parallel 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

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 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 AC power is shared in series and parallel circuits, and why total complex, real, and reactive power stay conserved across a network.

AC Power in Series and Parallel 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

AC Power in Series and Parallel Circuits

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