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

AC 전력 절약의 원리에 따르면 소스에서 생성된 복잡, 실제 및 무효 전력은 부하에서 소비하는 총 복잡, 실제 및 무효 전력과 동일합니다.
이 원리는 단순화된 회로 모델을 통해 설명할 수 있습니다.
회로의 총 임피던스가 먼저 계산된 다음 총 소스 전류를 결정합니다.
그런 다음 소스의 복잡한 전력은 이 전류와 소스 전압의 복잡한 켤레를 사용하여 계산됩니다.
실수 부분과 허수 부분을 분리함으로써 소스의 활성 및 무효 전력을 도출할 수 있습니다.
다음으로, 각 부하의 전압 강하가 계산됩니다.
복잡한 전력은 각 섹션에 걸쳐 공액 전류와 전압 강하의 곱을 취하여 결정됩니다. 이로부터 실제 및 반응 능력이 추론됩니다.
계산된 모든 거듭제곱을 비교할 때 소스의 거듭제곱이 개별 섹션의 거듭제곱의 합과 같다는 것이 분명해지며, 이는 전력 보존 원리를 확인합니다.
이 원리는 직렬 또는 병렬로 연결된 부하에 관계없이 적용됩니다.

ac 전원 보존

Conservation of AC Power

전력 보존 원리는 AC 회로와 DC 회로 모두에 적용됩니다. 이 원리를 AC 전원에 적용하면 소스에서 생성된 복소수, 실수 및 무효 전력이 부하에 의해 흡수된 전체 복소수, 실수 및 무효 전력과 동일하다고 주장됩니다. 두 개의 부하 온저항이 AC 소스 V에 병렬로 연결된 경우 소스에서 제공되는 복소 전력은 다음 관계를 사용하여 계산할 수 있습니다.
<img alt="Equation 1" src="/files/ftp_upload/15121/15121_Equation_1.svg" style="height: 18px;">
여기서 S_1과 S_2는 각각 부하 Z_1과 Z_2에 전달되는 복소 전력을 나타냅니다. 이러한 부하가 전압 소스와 직렬로 연결되면 소스에서 공급되는 복합 전력은 변경되지 않습니다. 이는 부하가 직렬 또는 병렬(또는 다른 구성)로 연결되었는지 여부에 관계없이 소스에서 제공하는 총 전력이 부하에서 수신하는 총 전력과 동일하다는 것을 의미합니다. 일반적으로 N개의 부하에 연결된 소스의 경우 복소 전력은 다음과 같이 계산됩니다.
<img alt="Equation 2" src="/files/ftp_upload/15121/15121_Equation_2.svg" style="height: 15px;">
이는 네트워크의 총 복합 전력이 개별 구성 요소의 복합 전력의 합임을 의미합니다. 이는 유효 전력과 무효 전력에는 적용되지만 피상 전력에는 적용되지 않습니다. 이는 AC 전력 보존의 원리를 명확히 설명합니다. 이를 통해 네트워크 소스로부터의 실제(또는 무효) 전력 흐름이 네트워크의 다른 구성 요소로 유입되는 실제(또는 무효) 전력 흐름과 동일하다는 것을 추론할 수 있습니다.

AC 전원 보존

AC 전력 보존의 원리는 소스에 의해 생성된 복잡하고 실제적이며 무효 전력이 전체 복합체와 동일하다는 것을 나타냅니다.

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

AC Steady State Power

교류 정상 상태 전력

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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