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

Stellen Sie sich einen Wechselstromkreis mit einer periodischen Spannungsquelle vor, die mit einem Widerstand verbunden ist.
Die durchschnittliche Leistung, die an den Widerstand abgegeben wird, entspricht dem Integral der Momentanleistung über eine Periode dividiert durch die Periode.
Wenn dieser Widerstand an eine Gleichstromquelle angeschlossen ist, ist die durchschnittliche Leistung, die er aufnimmt, das Produkt aus dem Quadrat des Stroms und seinem Widerstand.
Unter Berücksichtigung der Tatsache, dass die durchschnittliche Leistung, die von einer Gleichstromquelle an den Widerstand abgegeben wird, der des periodischen Stroms entspricht, entspricht der Gleichstrom dem Effektivwert des periodischen Stroms.
Der Effektivwert des Stroms ist also die Quadratwurzel des Durchschnitts der quadrierten momentanen Stromwerte.
In ähnlicher Weise kann der Ausdruck für den Effektivwert der Spannung erhalten werden.
Für jedes periodische Signal ist der effektive Wert, der auch als Mittelwert im Quadrat bezeichnet wird, gleich der Quadratwurzel des Mittelwerts des Quadrats des periodischen Signals.
Bei sinusförmigem Strom und sinusförmiger Spannung entspricht der Effektivwert dem Spitzenwert dividiert durch die Quadratwurzel aus zwei.

effektivwert einer periodischen wellenform

Effective Value of a Periodic Waveform

Das Konzept des Effektivwerts, des quadratischen Mittelwerts (RMS), ist entscheidend für das Verständnis von elektrischen Schaltkreisen und der Leistungsabgabe. Diese Idee ergibt sich aus der Notwendigkeit, die Wirksamkeit einer Spannungs- oder Stromquelle bei der Leistungsabgabe an eine ohmsche Last zu messen.

Der Effektivwert eines periodischen Stroms stellt den Gleichstrom (DC) dar, der die gleiche Durchschnittsleistung an einen Widerstand überträgt wie der periodische Strom selbst. Dieses Konzept ist entscheidend bei der Beurteilung von Wechselstromkreisen. Um den Effektivwert des Stroms zu bestimmen, muss man den RMS-Strom ermitteln, der die Quadratwurzel des Mittelwerts der quadrierten Momentanstromwerte über einen Zeitraum ist. Dieser RMS-Wert entspricht dem Gleichstrom, der die gleiche Durchschnittsleistung liefert wie der periodische Strom, wenn er an einen Widerstand angelegt wird.

<img alt="Equation 1" src="/files/ftp_upload/15119/15119_Equation_1.svg" style="text-align: center; height: 60px;">

Ebenso wird der Effektivwert der Spannung auf die gleiche Weise berechnet wie der Strom. Er stellt die RMS-Spannung dar, die für die Beurteilung des Stromverbrauchs in elektrischen Systemen von entscheidender Bedeutung ist.

<img alt="Equation 1" src="/files/ftp_upload/15119/15119_Equation_1.svg" style="text-align: center; height: 60px;">

Der Effektivwert ist ein grundlegendes Konzept, das nicht auf sinusförmige Signale beschränkt ist. Für jede periodische Funktion wird der Effektivwert berechnet, indem das Quadrat der Funktion ermittelt wird, der Mittelwert der Quadrate bestimmt und dann die Quadratwurzel dieses Mittelwerts gezogen wird. In praktischen Anwendungen werden Spannung und Strom häufig in Form ihrer Effektivwerte und nicht in Form ihrer Spitzenwerte ausgedrückt. Dies liegt daran, dass der Durchschnittswert eines sinusförmigen Signals Null ist, wodurch der Effektivwert eine nützlichere Messgröße für die Leistungsanalyse darstellt. Darüber hinaus sind analoge Voltmeter und Amperemeter so konzipiert, dass sie die Effektivwerte von Spannung und Strom direkt ablesen können, was sie zu unverzichtbaren Werkzeugen bei Leistungsmessungen macht.

Effektivwert einer periodischen Wellenform

Stellen Sie sich einen Wechselstromkreis mit einer periodischen Spannungsquelle vor, die mit einem Widerstand verbunden ist.
Die durchschnittliche Leistung, die an den Widerstand abgegeben wird, entspricht dem Integral des ...

Education

Lehre

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

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

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

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 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

Description

Transcript

Tags