Phasor Algebra: Operations, Rules and Applications | 相量的代数运算规则详解

📚 Phasor Algebra: Operations, Rules and Applications | 相量的代数运算规则详解

When two alternating voltages are connected in series, or when waves from different sources meet at a point, the resultant cannot be found by adding their amplitudes arithmetically. The phase difference between them must be respected. A phasor is a rotating vector that encodes both amplitude and phase; it reduces sinusoidal addition to vector (or complex-number) algebra. This article reviews the algebraic operations on phasors — addition, subtraction, scalar multiplication, multiplication and division — and shows how they apply to impedance and power in IB-level AC circuits.

当两个交变电压串联，或者不同波源的波在同一点相遇时，合成结果并不能通过简单相加振幅来得到，还必须考虑它们之间的相位差。相量是一种旋转矢量，同时记录振幅与相位；它把正弦量叠加问题转化为矢量（即复数）代数问题。本文系统复习相量的代数运算——加减、标量乘、乘除——并说明它们如何应用于IB物理阶段的交流电路阻抗与功率分析。

1. What Is a Phasor? | 相量是什么？

For a sinusoidal quantity x(t) = A cos(ωt + φ), the phasor is written as X = A e^(jφ). It stores only the amplitude A and the initial phase φ; the common factor e^(jωt) is deliberately omitted. The same phasor can be expressed in three equivalent forms: rectangular X = a + jb, polar X = A∠φ, and exponential X = A e^(jφ). In IB Physics the polar form is the one you normally draw on a phasor diagram.

对于正弦量 x(t)

Published by TutorHao | IB Physics Revision Series | aleveler.com

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