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

사인파 입력이 있는 회로의 경우 수동 소자에 전달되는 전력은 전압과 전류를 합한 값과 같습니다.
전압과 전류를 정현파 형태로 표현하고 삼각 항등을 적용하면 두 개의 항으로 순간 전력에 대한 표현이 제공됩니다.
첫 번째 항은 전압과 전류 사이의 위상차에 따라 달라지는 상수이고 두 번째 항은 전압 또는 전류 주파수의 두 배인 정현파 함수입니다.
저항과 리액턴스가 혼합된 회로의 경우 순간 전력은 양수 값과 음수 값 사이에서 진동합니다.
순수 저항 회로에서 전압과 전류는 위상이 같아 일관되게 양의 순간 전력 손실이 발생합니다.
순전히 유도 성 및 용량 성 회로의 경우 전압과 전류 사이의 위상 변이로 인해 순간 전력이 양수 값과 음수 값 사이에서 변동합니다.
인덕터와 커패시터는 인덕터를 통과하는 전류 또는 커패시터 양단의 전압이 변함에 따라 에너지를 주기적으로 저장하고 방출합니다.
에너지 방출 주기 동안 반응 소자는 전원으로 작용하여 회로에 에너지를 다시 공급하여 음의 순간 전력으로 이어집니다.

순간 전력

순간 전력은 주로 정현파 입력을 처리할 때 전기 회로에서 중요합니다. p(t)로 표시되는 순간 전력은 소자에 흐르는 순간 전압(v(t))과 소자에 흐르는 순간 전류(i(t))를 곱한 결과입니다. 이 관계는 수동 기호 규칙을 준수하며 전기 공학의 기본 원칙을 나타냅니다.
<img alt="Equation 1" src="/files/ftp_upload/15117/15117_Equation_1.svg" style="height: 15px;">
순간 전력을 살펴보면 두 가지 용어의 조합으로 표현될 수 있습니다. 일정하게 유지되는 첫 번째 항은 전압과 전류 간의 위상차에 따라 달라집니다. 정현파 진동을 특징으로 하는 두 번째 항은 전압이나 전류의 두 배의 주파수를 나타냅니다.
<img alt="Equation 2" src="/files/ftp_upload/15117/15117_Equation_2.svg" style="height: 30px;">
저항 및 리액턴스 요소를 포함하는 회로에서 순간 전력은 동적이며 양수 값과 음수 값 사이에서 진동합니다. 전압과 전류가 완벽하게 동상인 순수 저항성 회로의 경우 순간 전력은 지속적으로 양으로 소산됩니다.
반대로, 유도성 및 용량성 구성 요소가 지배적인 회로에서는 전압과 전류 사이의 위상 변이로 인해 순간 전력이 양수 값과 음수 값 사이에서 간헐적으로 변동됩니다. 이 현상은 전류가 전자를 통과하고 전압이 후자에 나타날 때 인덕터와 커패시터에 의한 에너지의 주기적 저장 및 방출에 기인할 수 있습니다. 에너지 방출 단계에서 이러한 반응성 요소는 전원 역할을 하여 에너지를 회로에 효과적으로 다시 공급하여 음의 순간 전력이 나타납니다. 전압, 전류 및 전력 역학의 복잡한 상호 작용은 전기 회로를 지배하는 기본 원리를 강조합니다. 효율적인 에너지 관리와 전기 시스템 설계를 위해서는 이러한 원칙을 이해하는 것이 중요합니다.

사인파 입력이 있는 회로의 경우 수동 소자에 전달되는 전력은 전압과 전류를 합한 값과 같습니다.
표현...

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

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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