Name: power from multiple ac sources
Uploaded: 2024-07-08T13:19:54.000Z
Duration: 1 min 19 s
Channel: JoVE

Рассмотрим схему с двумя синусоидальными источниками напряжения.
Согласно принципу суперпозиции, суммарный ток, возникающий от обоих источников, является суммой токов, приведенных каждому источнику в отдельности.
Кроме того, мгновенная мощность — это квадрат мгновенного тока, умноженного на сопротивление.
Интегрирование этого за один период дает среднюю мощность, которая равна сумме средних мощностей каждого источника, и третий член, равный нулю для источников с разными частотами.
Упрощенное уравнение обозначает принцип суперпозиции мощности, утверждая, что средняя мощность, выдаваемая источниками с разными частотами, равна сумме средней мощности, выдаваемой каждым источником.
Этот принцип имеет решающее значение в телекоммуникациях, таких как радиовещание.
Несколько радиостанций транслируют свои сигналы одновременно, каждая из которых выступает в качестве независимого источника электромагнитных волн.
Согласно принципу суперпозиции мощности, общая мощность, получаемая радиостанцией, представляет собой сумму мощностей, передаваемых каждой станцией.
Настройка радиоприемника на определенную частоту позволяет пользователю слушать одну станцию за раз, несмотря на получение сигналов от нескольких станций.

Принцип суперпозиции мощности

Рассмотрим схему с двумя источниками синусоидального напряжения. Каждый из них влияет на схему независимо, а принцип суперпозиции помогает нам понять совокупный эффект, суммируя отклики от каждого источника.
<img alt="Figure 1" src="/files/ftp_upload/15124/15124_Figure_1.svg" style="height: 150px;">
Согласно принципу суперпозиции, общий ток обоих источников представляет собой сумму токов каждого источника независимо. Когда оба источника работают вместе, их отдельные токи (i1​ и i2​) складываются и дают общий ток. Кроме того, мгновенная мощность равна квадрату мгновенного тока, умноженному на сопротивление.
<img alt="Equation 1" src="/files/ftp_upload/15124/15124_Equation_1.svg" style="height: 20px;">
Эта концепция также применима к мощности, скорости, с которой используется энергия. В любой момент мгновенная мощность в цепи равна квадрату тока, умноженному на сопротивление. Интегрирование этого значения за один период дает среднюю мощность, которая равна сумме средних мощностей каждого источника, а третий член становится нулевым для источников, имеющих разные частоты.
<img alt="Equation 2" src="/files/ftp_upload/15124/15124_Equation_2.svg" style="height: 45px;">
<img alt="Equation 3" src="/files/ftp_upload/15124/15124_Equation_3.svg" style="height: 45px;">
Упрощенное уравнение означает принцип суперпозиции мощности, утверждающий, что средняя мощность, передаваемая источниками, имеющими разные частоты, равна сумме средней мощности, передаваемой каждым источником. Этот принцип имеет решающее значение в телекоммуникациях, таких как радиовещание. Несколько радиостанций одновременно транслируют свои сигналы, каждая из этих радиостанций действует как независимый источник электромагнитных волн. Согласно принципу суперпозиции мощности, общая мощность, принимаемая по радио, представляет собой сумму мощности, передаваемой каждой станцией. Настройка радио на определенную частоту позволяет пользователю слушать одну станцию ​​за раз, несмотря на прием сигналов от нескольких станций.

Рассмотрим схему с двумя синусоидальными источниками напряжения.
Согласно принципу суперпозиции, суммарный ток, возникающий от обоих источников, равен сумме ...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

AC Steady State Power

Мощность переменного тока в установившемся режиме

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 resistance. To find the average power, this expression is integrated over one period. The result shows that the average power from both sources is the sum of the average powers from each source, and a third term becomes zero when the sources have different frequencies.

This idea is called the power superposition principle. It means that the average power delivered by sources with different frequencies is the sum of the average power delivered by each source. The principle is important in telecommunications, including radio broadcasting. Multiple radio stations can broadcast at the same time, and each one acts as an independent source of electromagnetic waves. A radio receives the total power from all of them, but tuning to one frequency lets the listener hear one station at a time.

Power from Multiple AC Sources

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

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 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 superposition adds currents from two sinusoidal sources and why average power from different frequencies can be combined in AC circuits and radio.

Power from Multiple AC Sources | 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 from Multiple AC Sources

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