A Study on the Phase Difference of Electrical Circuits from the Perspective of Two-Dimensional Isotropic Harmonic Oscillation

Abstract

We studied the effect of voltage drop and phase delay caused by passive elements, such as resistors, inductors, and capacitances, after the application of an external driving voltage to an RLC electric circuit. A two-dimensional isotropic harmonic oscillator of mechanics was analyzed to investigate the effect of delay on the magnitude and phase of the system voltage compared with the external driving force. The phase difference showed dependence on the driving frequency. The angle ψ between the major axis of the ellipse and the x-axis in the two-dimensional XY plane graph was obtained. We investigated the Lissajar patterns in the oscilloscope. In addition, it can be divided into linear, circular, and elliptical polarizations based on the frequency, phase, and amplitude from the viewpoint of light polarization. The Jones matrix was investigated by the corresponding harmonic oscillator analysis of mechanics and Jones vector in the polarization of light.