Phasors and their corresponding sinusoids are interrelated, offering unique insights into the behavior of alternating current (AC) circuits. One way to understand this relationship is through the operations of differentiation and integration in both the time and phasor domains.

When the derivative of a sinusoid is taken in the time domain, it transforms into its corresponding phasor multiplied by j-omega (jω) in the phasor domain, where j is the imaginary unit, and ω is the angular frequency. Conversely, when a sinusoid is integrated in the time domain, it translates into its corresponding phasor divided by j-omega in the phasor domain. These transformations provide a means to find steady-state solutions for the sinusoid without knowing the initial variable values.

Next, consider two phasors, each represented in rectangular and polar forms. To add or subtract these two phasors, their rectangular forms are used (which express the phasor as a complex number with real and imaginary parts). The real part of the resultant phasor is the sum (for addition) or difference (for subtraction) of the real parts of the two original phasors, and its imaginary part is the sum or difference of the imaginary parts of the individual phasors.

When multiplying or dividing any two phasors, their polar forms are used (expressing the phasor as a magnitude and an angle). The magnitude of the resultant phasor is the product (for multiplication) or quotient (for division) of the magnitudes of the two original phasors, and the angle of the resultant phasor is the sum or difference of the angles of the individual phasors.

Lastly, the complex conjugate of a phasor - which is obtained by changing the sign of its imaginary part - can be expressed in both rectangular and polar forms. This operation is crucial in many applications, including the computation of power in AC circuits.

In conclusion, phasors serve as a powerful mathematical tool in the study of AC circuits, simplifying analysis and solving problems that would be significantly more complex in the time domain.

Tags
PhasorSinusoidAlternating Current ACDifferentiationIntegrationAngular FrequencyRectangular FormPolar FormComplex NumberMagnitudeAngleComplex ConjugateAC Circuit AnalysisSteady state Solutions

Del capítulo 6:

article

Now Playing

6.4 : Phasor Arithmetics

AC Circuit Analysis

120 Vistas

article

6.1 : Fuentes sinusoidales

AC Circuit Analysis

238 Vistas

article

6.2 : Representación gráfica y analítica de los sinusoides

AC Circuit Analysis

271 Vistas

article

6.3 : Fasores

AC Circuit Analysis

310 Vistas

article

6.5 : Relaciones de fasores para elementos de circuito

AC Circuit Analysis

324 Vistas

article

6.6 : Leyes de Kirchoff usando fasores

AC Circuit Analysis

216 Vistas

article

6.7 : Impedancias y Admisión

AC Circuit Analysis

381 Vistas

article

6.8 : Combinación de impedancia

AC Circuit Analysis

183 Vistas

article

6.9 : Análisis de nodos para circuitos de CA

AC Circuit Analysis

187 Vistas

article

6.10 : Análisis de malla para circuitos de CA

AC Circuit Analysis

236 Vistas

article

6.11 : Transformación de fuentes para circuitos de CA

AC Circuit Analysis

325 Vistas

article

6.12 : Circuitos equivalentes #233venin

AC Circuit Analysis

117 Vistas

article

6.13 : Circuitos equivalentes de Norton

AC Circuit Analysis

218 Vistas

article

6.14 : Teorema de superposición para circuitos de CA

AC Circuit Analysis

447 Vistas

article

6.15 : Circuitos de CA de amplificador operacional

AC Circuit Analysis

99 Vistas

See More

JoVE Logo

Privacidad

Condiciones de uso

Políticas

Investigación

Educación

ACERCA DE JoVE

Copyright © 2025 MyJoVE Corporation. Todos los derechos reservados