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

Para la mayoría de las aplicaciones prácticas, la potencia instantánea variable en el tiempo no es una cantidad comúnmente utilizada.
En su lugar, se utiliza la potencia media como cantidad medible. Se calcula integrando la potencia instantánea a lo largo del período y dividiéndola por el período.
La expresión de potencia instantánea se sustituye y se simplifica aún más para obtener una expresión en el dominio del tiempo para la potencia media.
El segundo término es el valor promedio de la función del coseno durante un período y es cero.
La expresión final de la potencia media es independiente del tiempo y es proporcional a la diferencia de fase entre el voltaje y la corriente.
El término resultante de la mitad del producto de voltaje y corriente en forma de fasor comprende partes reales e imaginarias.
La comparación de esta expresión fasorial con la ecuación de potencia promedio indica que la parte real corresponde a la potencia promedio.
En un circuito puramente resistivo, el voltaje y la corriente en fase conducen a una potencia promedio positiva.
Sin embargo, en circuitos puramente reactivos, un cambio de fase de noventa grados entre el voltaje y la corriente da como resultado una potencia promedio cero.

potencia promedio

En aplicaciones eléctricas prácticas, el concepto de potencia instantánea variable en el tiempo no se utiliza con frecuencia. En cambio, la atención se centra en la cantidad más práctica conocida como potencia promedio. La potencia promedio se determina integrando la potencia instantánea durante un período de tiempo específico y posteriormente dividiéndola por esa duración.

<img alt="Equation 1" src="/files/ftp_upload/15118/15118_Equation_1.svg" style="height: 42px;">
La ecuación de la potencia instantánea se simplifica para llegar a una expresión en el dominio del tiempo para la potencia promedio. En particular, el segundo término, que involucra una función coseno, tiene un promedio de cero durante un ciclo completo.
<img alt="Equation 2" src="/files/ftp_upload/15118/15118_Equation_2.svg" style="height: 42px;">
Como resultado, la expresión final de la potencia promedio es independiente del tiempo y depende de la diferencia de fase entre voltaje y corriente.
<img alt="Equation 3" src="/files/ftp_upload/15118/15118_Equation_3.svg" style="height: 30px;">
Al comparar esta expresión con la representación fasorial del producto del voltaje y la corriente, resulta evidente que la parte real del fasor corresponde a la potencia promedio.
<img alt="Equation 4" src="/files/ftp_upload/15118/15118_Equation_4.svg" style="height: 28px;">
En circuitos puramente resistivos, donde el voltaje y la corriente están perfectamente en fase, la potencia promedio es positiva, lo que significa un consumo de energía continuo. Por el contrario, la potencia promedio disminuye a cero en circuitos puramente reactivos caracterizados por un cambio de fase de noventa grados entre voltaje y corriente. Este fenómeno se atribuye al almacenamiento y liberación cíclicos de energía, donde, en promedio, no se consume energía neta.
Es importante reconocer que si bien la potencia instantánea varía con respecto al tiempo, la potencia promedio permanece constante. Calcular la potencia instantánea requiere voltaje y corriente en el dominio del tiempo, pero la potencia promedio también se puede determinar cuando el voltaje y la corriente se representan en el dominio de la frecuencia usando fasores.
Comprender la potencia promedio es vital en aplicaciones prácticas, ya que facilita la evaluación del consumo y la eficiencia de energía, especialmente en circuitos que presentan diversas combinaciones de componentes resistivos y reactivos.

Potencia promedio

Para la mayoría de las aplicaciones prácticas, la potencia instantánea variable en el tiempo no es una cantidad comúnmente utilizada.
En su lugar, la potencia media se utiliza como ...

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

AC Steady State Power

Potencia de corriente alterna en estado estacionario

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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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