Sinusoids: A sinusoid is a mathematical function that describes a smooth, periodic oscillation. It is represented by a sine or cosine waveform and is characterized by its amplitude, frequency, and phase. In AC systems, voltage and current waveforms are typically sinusoidal.

Amplitude: The amplitude of a sinusoid represents the peak value or maximum magnitude of the waveform. It determines the range of values that the sinusoid reaches during each cycle.

Frequency: The frequency of a sinusoid represents the number of complete cycles it completes in one second. It is measured in hertz (Hz). The frequency determines the rate at which the waveform oscillates.

Phase: The phase of a sinusoid indicates the shift or displacement of the waveform from a reference point. It is measured in degrees or radians and determines the position of the waveform relative to a particular point in time.

Phasors: Phasors are a mathematical representation of sinusoidal quantities in complex number form. A phasor consists of a magnitude (amplitude) and an angle (phase) and is typically represented using complex numbers. Phasors simplify the analysis of AC circuits by converting time-domain sinusoidal functions into algebraic operations.

For example, a sinusoidal voltage V(t) = Vm * sin(ωt + θ) can be represented by a phasor V = Vm * ∠θ, where Vm is the peak amplitude, ω is the angular frequency, t is time, and θ is the phase angle.

Phasors enable us to perform algebraic operations such as addition, subtraction, multiplication, and division on sinusoidal quantities, making calculations in AC circuits more manageable.

Sinusoidal Steady-State Analysis: Sinusoidal steady-state analysis is a technique used to analyze the behavior of AC circuits under steady-state sinusoidal conditions. It assumes that the circuit has reached a stable condition, and all voltages and currents have settled into their periodic sinusoidal patterns.