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

AC güç korunumu ilkesi, kaynak tarafından üretilen karmaşık, gerçek ve reaktif güçlerin, yükler tarafından tüketilen toplam karmaşık, gerçek ve reaktif güçlere eşdeğer olduğunu belirtir.
Bu ilke, basitleştirilmiş bir devre modeli ile gösterilebilir.
Önce devrenin toplam empedansı hesaplanır, ardından toplam kaynak akımı belirlenir.
Kaynağın karmaşık gücü daha sonra bu akımın karmaşık eşleniği ve kaynak voltajı kullanılarak hesaplanır.
Gerçek ve hayali kısımları ayırarak kaynağın aktif ve reaktif gücü elde edilebilir.
Daha sonra, her yükteki voltaj düşüşü hesaplanır.
Karmaşık güç, eşlenik akımın çarpımı ve her bölümdeki voltaj düşüşü alınarak belirlenir. Bundan gerçek ve reaktif güçler çıkarılır.
Hesaplanan tüm güçleri karşılaştırırken, kaynağın gücünün, güç korunumu ilkesini doğrulayan tek tek bölümlerin gücünün toplamına eşit olduğu ortaya çıkar.
Bu ilke, seri veya paralel bağlanan yüklerden bağımsız olarak geçerlidir.

ac devrelerde gücünün korunumu

Conservation of AC Power

Gücün korunması ilkesi hem AC hem de DC devrelere uygulanabilir. Bu prensip, AC gücüne uygulandığında, kaynak tarafından üretilen karmaşık, gerçek ve reaktif güçlerin, yükler tarafından emilen toplam karmaşık, gerçek ve reaktif güçlere eşit olduğunu ileri sürer. İki yük empedansı bir ac kaynağına V paralel olarak bağlandığında, kaynak tarafından sağlanan karmaşık güç şu ilişki kullanılarak hesaplanabilir:

<img alt="Equation 1" src="/files/ftp_upload/15121/15121_Equation_1.svg" style="height: 18px;">

Burada S_1 ve S_2 sırasıyla Z_1 ve Z_2 yüklerine iletilen karmaşık güçleri temsil eder. Bu yükler gerilim kaynağına seri olarak bağlanırsa kaynak tarafından sağlanan karmaşık güç değişmeden kalır. Bu, yüklerin seri veya paralel (veya başka herhangi bir konfigürasyonda) bağlı olup olmadığına bakılmaksızın, kaynak tarafından sağlanan toplam gücün, yük tarafından alınan toplam güce eşit olduğunu gösterir. Genel olarak N yüke bağlı bir kaynak için karmaşık güç şu şekilde verilir:

<img alt="Equation 2" src="/files/ftp_upload/15121/15121_Equation_2.svg" style="height: 15px;">

Bu, bir ağdaki toplam karmaşık gücün, bireysel bileşenlerinin karmaşık güçlerinin toplamı olduğu anlamına gelir. Bu gerçek güç ve reaktif güç için geçerlidir, ancak görünür güç için geçerli değildir. Bu, AC güç tasarrufu ilkesini ifade eder. Buradan, bir ağdaki kaynaklardan gelen gerçek (veya reaktif) güç akışının, ağın diğer bileşenlerine gerçek (veya reaktif) güç akışına eşit olduğu sonucu çıkarılabilir.

AC Devrelerde Gücünün Korunumu

AC güç korunumu ilkesi, kaynak tarafından üretilen karmaşık, gerçek ve reaktif güçlerin toplam komplekse eşdeğer olduğunu belirtir, ...

Education

JoVE Core

Electrical Engineering

Elektrik Mühendisliği

Unit 1

Ünite 1

AC Steady State Power

AC Kararlı Durum Gücü

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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 Elektrik Mühendisliği, devre analizi teknikleriyle birlikte elektrik devrelerinin temel kavramlarını kapsayan, anlaşılması kolay animasyonlu videolar sunar. Operasyonel amplifikatörler ve devre dönüşümü kavramlarını kullanarak birinci dereceden ve ikinci dereceden devreleri içerir. Pratik tasarım örneklerinin ve gerçek dünya uygulamalarının bilim insanlarınca hazırlanan videolar aracılığıyla dahil edilmesi, karmaşık kavramları erişilebilir hale getirerek önemli bir eğitim değeri katmaktadır.

electrical engineering

AC Power in Series and Parallel Circuits

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