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

Para un circuito con una entrada sinusoidal, la potencia entregada a un elemento pasivo es igual al producto del voltaje y la corriente a través de él.
Expresando el voltaje y la corriente en forma sinusoidal y aplicando la identidad trigonométrica se obtiene la expresión de la potencia instantánea con dos términos.
El primer término es una constante que depende de la diferencia de fase entre el voltaje y la corriente, mientras que el segundo término es una función sinusoidal con el doble de la frecuencia del voltaje o la corriente.
Para circuitos con resistencia y reactancia mixtas, la potencia instantánea oscila entre valores positivos y negativos.
En un circuito puramente resistivo, el voltaje y la corriente están en fase, lo que da como resultado una disipación de potencia instantánea consistentemente positiva.
Para circuitos puramente inductivos y capacitivos, el cambio de fase entre el voltaje y la corriente hace que la potencia instantánea fluctúe entre valores positivos y negativos.
Los inductores y condensadores almacenan y liberan energía cíclicamente a medida que cambia la corriente a través del inductor o el voltaje a través del condensador.
Durante el ciclo de liberación de energía, los elementos reactivos actúan como fuente de energía, suministrando energía al circuito, lo que genera una potencia instantánea negativa.

potencia instantánea

La potencia instantánea es importante en los circuitos eléctricos, principalmente cuando se trata de entradas sinusoidales. La potencia instantánea, denotada como p(t), resulta de la multiplicación del voltaje instantáneo (v(t)) a través de un elemento y la corriente instantánea (i(t)) que fluye a través de él. Esta relación sigue la convención de signos pasivos y representa un principio fundamental en ingeniería eléctrica.
<img alt="Equation 1" src="/files/ftp_upload/15117/15117_Equation_1.svg" style="height: 15px;">
Al examinar la potencia instantánea, se puede expresar como una combinación de dos términos distintos. El primer término, que permanece constante, depende de la diferencia de fase entre voltaje y corriente. El segundo término, caracterizado por una oscilación sinusoidal, exhibe una frecuencia dos veces mayor que la del voltaje o la corriente.
<img alt="Equation 2" src="/files/ftp_upload/15117/15117_Equation_2.svg" style="height: 30px;">
En los circuitos que abarcan elementos de resistencia y reactancia, la potencia instantánea es dinámica y oscila entre valores positivos y negativos. En los casos de circuitos puramente resistivos, donde el voltaje y la corriente están perfectamente en fase, la potencia instantánea se disipa consistentemente de manera positiva.
Por el contrario, en circuitos dominados por componentes inductivos y capacitivos, el cambio de fase entre voltaje y corriente conduce a fluctuaciones intermitentes en la potencia instantánea entre valores positivos y negativos. Este fenómeno se puede atribuir al almacenamiento y liberación cíclico de energía por parte de inductores y condensadores a medida que la corriente atraviesa los primeros y aparece voltaje a través de los segundos. Durante la fase de liberación de energía, estos elementos reactivos actúan como fuentes de energía, suministrando energía de manera efectiva al circuito, lo que resulta en la manifestación de potencia instantánea negativa. Esta intrincada interacción de voltaje, corriente y dinámica de potencia subraya los principios fundamentales que gobiernan los circuitos eléctricos. La comprensión de estos principios es fundamental para la gestión eficiente de la energía y el diseño de sistemas eléctricos.

Potencia instantánea

Para un circuito con una entrada sinusoidal, la potencia entregada a un elemento pasivo es igual al producto del voltaje y la corriente a través de él.
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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

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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