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.

phasors

Phasors are a powerful mathematical tool used to analyze alternating current (AC) circuits. They provide a complex number representation of sinusoids, with the magnitude of the phasor equating to the amplitude of the sinusoid and the angle of the phasor representing the phase measured from the positive x-axis.
One of the significant benefits of using phasors is that they simplify the analysis of AC circuits by eliminating the time dependence of the current and voltage. This transformation allows an AC circuit to be analyzed as if it were its equivalent direct current (DC) form, making calculations more straightforward.
Phasors can be represented in different forms - rectangular, polar, or exponential - by using Euler&#39;s identity, a fundamental formula in complex analysis that establishes a deep relationship between trigonometric and exponential functions.
To obtain the phasor of a sinusoid in sine form, one must first convert it into cosine form and then express it as the real part of a complex number. The phasor of this sinusoid equals the time-independent part of this complex number. Conversely, the sinusoid of a given phasor can be obtained by multiplying the phasor with a time factor and taking its real part.
In a graphical context, phasors can be visualized as rotating vectors, or &#39;sinors,&#39; spinning in a counterclockwise direction on a complex plane with a constant angular frequency. The diagrams that depict these rotating sinors are known as phasor diagrams.
A key concept in understanding the phasor diagram is that the projection of the rotating sinors onto the real axis represents the sinusoids. This means that the horizontal position of the sinor at any point in time corresponds to the instantaneous value of the sinusoidal function it represents.

Phasors

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

Unit 1

AC Circuit Analysis

KEY TERMS AND CONCEPTS

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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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...

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key terms and concepts

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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