Fázory

Fázory, also known as phasor diagrams, are graphical representations used in electrical engineering and physics to analyze alternating current (AC) circuits and other systems involving sinusoidal quantities. A pházor is a rotating vector in a complex plane, where its length represents the amplitude (maximum value) of the sinusoidal quantity, and its angle represents the phase of the quantity at a given time.

The complex plane consists of a real axis and an imaginary axis. The pházor itself is typically drawn starting from the origin. The real part of the pházor can be related to the cosine component of the sinusoid, and the imaginary part to the sine component, or vice-versa, depending on the convention used. The angle of the pházor with respect to the real axis indicates the phase shift relative to a reference sinusoid.

Pházors are particularly useful for simplifying the analysis of AC circuits containing resistors, inductors, and capacitors. In these circuits, voltages and currents are sinusoidal and can vary in phase. By representing these quantities as pházors, AC circuit analysis becomes similar to DC circuit analysis, involving vector addition and subtraction rather than complex calculus. For instance, the impedance of an inductor is represented as jωL, and that of a capacitor as 1/(jωC), which are complex numbers that can be readily incorporated into pházor calculations.

When performing operations like addition or subtraction of sinusoidal quantities with the same frequency, their corresponding pházors are added or subtracted as vectors. The resultant pházor represents the amplitude and phase of the combined sinusoidal quantity. This graphical method allows for a quick and intuitive understanding of the relationships between different voltages and currents in an AC circuit, especially when dealing with phase shifts.