Name: phasors for ac circuit analysis
Uploaded: 2024-04-11T12:48:48.000Z
Duration: 1 min 12 s
Channel: JoVE

Phasors are complex representations of the sinusoids where the magnitude of the phasor equals the amplitude, and the angle equals the phase measured from the positive x-axis.
They simplify the analysis of AC circuits by eliminating the time dependence of the current and voltage, transforming the circuit into its equivalent DC form.
Phasors can be represented in rectangular, polar, or exponential forms by using Euler&#39;s identity.
To obtain the phasor of a sinusoid in the sine form, first convert it into cosine form and then express it as the real part of the complex number.
The phasor of this sinusoid equals the time-independent part of the complex number.
Conversely, the sinusoid of a given phasor is obtained by multiplying the phasor with the time factor and taking its real part.
Phasors can be represented as rotating vectors or sinors in a counterclockwise direction on a complex plane with a constant angular frequency, and the diagrams depicting them are known as phasor diagrams.
The projection of the rotating sinors on the real axis represents the sinusoids.

fasoren

Fasoren zijn een krachtig wiskundig hulpmiddel dat wordt gebruikt om wisselstroomcircuits (AC) te analyseren. Ze bieden een complexe getalweergave van sinusoïden, waarbij de grootte van de fasor gelijk is aan de amplitude van de sinusoïde en de hoek van de fasor de fase vertegenwoordigt gemeten vanaf de positieve x-as. Een van de belangrijke voordelen van het gebruik van fasers is dat ze de analyse van wisselstroomcircuits vereenvoudigen door de tijdsafhankelijkheid van stroom en voltage te elimineren. Door deze transformatie kan een wisselstroomcircuit worden geanalyseerd alsof het de equivalente gelijkstroomvorm (DC) is, waardoor berekeningen eenvoudiger worden. Fasoren kunnen in verschillende vormen worden weergegeven - rechthoekig, polair of exponentieel - door gebruik te maken van de identiteit van Euler, een fundamentele formule in complexe analyse die een diepgaande relatie legt tussen trigonometrische en exponentiële functies. Om de fasor van een sinusoïde in sinusvorm te verkrijgen, moet men deze eerst in cosinusvorm omzetten en deze vervolgens uitdrukken als het reële deel van een complex getal. De fasor van deze sinusoïde is gelijk aan het tijdsonafhankelijke deel van dit complexe getal. Omgekeerd kan de sinusoïde van een bepaalde fasor worden verkregen door de fasor te vermenigvuldigen met een tijdsfactor en het reële deel ervan te nemen. In een grafische context kunnen fasoren worden gevisualiseerd als roterende vectoren, of 'sinoren', die tegen de klok in draaien op een complex vlak met een constante hoekfrequentie. De diagrammen die deze roterende sinoren weergeven, staan bekend als fasordiagrammen. Een sleutelconcept bij het begrijpen van het fasordiagram is dat de projectie van de roterende sinoren op de reële as de sinusoïden vertegenwoordigt. Dit betekent dat de horizontale positie van de sinor op elk moment overeenkomt met de momentane waarde van de sinusoïdale functie die deze vertegenwoordigt.

Fasoren

Phasors are complex representations of the sinusoids where the magnitude of the phasor equals the amplitude, and the angle equals the phase measured from ...

Education

JoVE Core

Electrical Engineering

Elektrotechniek

Unit 1

AC Circuit Analysis

AC-circuitanalyse

KEY TERMS AND CONCEPTS

BELANGRIJKE TERMEN EN CONCEPTEN

Phasors

phasors for ac circuit analysis

Phasors are a mathematical tool for analyzing alternating current, or AC, circuits. They represent sinusoids with complex numbers. The phasor magnitude matches the sinusoid amplitude, and the phasor angle shows the phase measured from the positive x-axis.

Phasors make AC circuit analysis simpler by removing time from the current and voltage expressions. That lets an AC circuit be treated like its equivalent direct current, or DC, form for calculations. Phasors can also be written in rectangular, polar, or exponential form.

Euler’s identity links trigonometric functions and exponential functions, and it helps convert between these phasor forms. To find the phasor of a sinusoid in sine form, the signal is first written in cosine form. It is then expressed as the real part of a complex number, and the phasor is the time-independent part of that number.

A sinusoid can also be recovered from a phasor. The phasor is multiplied by a time factor, and then the real part is taken. In a graph, phasors appear as rotating vectors, or sinors, on the complex plane.

These rotating sinors move counterclockwise with constant angular frequency. The diagrams that show them are called phasor diagrams. The projection of a sinor onto the real axis gives the sinusoid, so the horizontal position at any moment shows the instantaneous value of the wave.

Phasors for AC Circuit Analysis

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Learn how phasors represent AC sinusoids, simplify circuit analysis, and appear as rotating vectors on the complex plane in phasor diagrams.

Phasors for AC Circuit Analysis | 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

Phasors for AC Circuit Analysis

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