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

交流功率守恒原理指出，电源产生的复功率、有功功率和无功功率等于负载消耗的总复功率、有功功率和无功功率。
这一原理可以通过简化的电路模型来说明。
首先计算电路的总阻抗，然后确定总电源电流。
然后利用该电流的复共轭和电源电压来计算电源的复功率。
通过分离实部和虚部，可以推导出电源的有功功率和无功功率。
接下来，计算每个负载上的电压降。
通过计算共轭电流与各段电压降的乘积来确定复功率。由此可推导出有功功率和无功功率。
比较所有计算得到的功率后可以明显看出，电源的功率等于各部分功率之和，从而验证了能量守恒原理。
无论串联还是并联的负载，该原理均成立。

交流电守恒

Conservation of AC Power

功率守恒原理适用于交流电路和直流电路。当该原理应用于交流电时，那么就可以认为由电源所产生的复功率、有功功率和无功功率等于负载所吸收的复功率、有功功率和无功功率。当两个负载阻抗与交流电源 V 产生并联时，由电源所提供的复功率则可以使用以下公式来进行计算：
<img alt="Equation 1" src="/files/ftp_upload/15121/15121_Equation_1.svg" style="text-align: center; height: 15px;">
其中，S_1 和 S_2 分别用来表示传递给负载 Z_1 和 Z_2 的复功率。如果这些负载与电压源是串联的，那么由电源所提供的复功率将会保持不变。这表明了，无论负载是串联还是并联（或任何其他配置），电源所提供的总功率都会等于负载接收的总功率。一般来说，对于连接到 N 个负载的电源，复数功率的计算公式为：
<img alt="Equation 2" src="/files/ftp_upload/15121/15121_Equation_2.svg" style="text-align: center; height: 12px;">
这意味着网络中的总复数功率是其各个组件的复功率之和。这适用于有功功率和无功功率，但并不适用于视在功率。这阐明了交流电守恒原理。由此可以推断出，网络中来自电源的有功功率（或无功功率）流等于流入网络其他组件的有功功率（或无功功率）流。

交流功率守恒原理指出，电源产生的复功率、有功功率和无功功率等于总的复功率、有功功率和无功功率。

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

AC Steady State Power

交流稳态功率

KEY TERMS AND CONCEPTS

关键术语与概念

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

Description

Transcript