Phasori

Phasori are a mathematical tool used primarily in electrical engineering and physics to represent sinusoidal quantities. A phasor is essentially a complex number that represents the amplitude and phase of a time-varying sinusoid. Instead of dealing with differential equations that describe the behavior of AC circuits over time, phasor analysis allows engineers to transform these equations into algebraic equations. This simplifies the analysis considerably, especially for circuits with multiple components.

A phasor is typically denoted by an arrow or a bold letter. For a sinusoidal voltage or current of the form $V(t) = V_m \cos(\omega t + \phi)$, its corresponding phasor representation, often denoted as $\mathbf{V}$, would be a complex number $V_m e^{j\phi}$, where $V_m$ is the amplitude (or RMS value, depending on convention) and $\phi$ is the phase angle. The angular frequency $\omega$ is implicitly understood in the phasor domain and is not explicitly part of the phasor itself, but it is crucial for converting back to the time domain.

In AC circuit analysis, components like resistors, inductors, and capacitors are represented by their impedance in the phasor domain. Resistors have a real impedance, while inductors and capacitors have imaginary impedances that depend on the frequency. By applying Kirchhoff's laws in the phasor domain, complex circuit problems can be solved using simple algebraic manipulations, making it a powerful technique for understanding and designing AC systems.