Question

Define phasors in AC circuit analysis.

Answer 1

In AC (alternating current) circuit analysis, a phasor is a complex number representation of a sinusoidal waveform that simplifies the analysis of AC circuits. It helps convert the time-domain analysis of AC circuits into the more manageable and convenient domain of complex numbers.

A phasor has two components: magnitude and phase angle. It is represented as:


=

max
∠

V=V
max
    ​

∠θ

where:


V is the phasor representing the AC voltage or current.

max
V
max
    ​

 is the maximum amplitude (peak value) of the sinusoidal waveform.

θ is the phase angle, which represents the phase difference between the sinusoidal waveform and a reference sinusoid (usually taken as the reference voltage waveform).

Key points to remember about phasors:

Phasors simplify the analysis of AC circuits by replacing time-varying sinusoidal functions with constant complex numbers.
Addition and subtraction of phasors in the complex domain correspond to the addition and subtraction of their corresponding sinusoidal functions in the time domain.
Phasor analysis is particularly useful when dealing with resistors, capacitors, and inductors in series or parallel configurations, as it allows straightforward calculation of impedance and other AC circuit parameters.
To convert phasor quantities back to the time domain, one can use the inverse phasor transformation, which involves taking the real part of the complex phasor.

Phasor analysis is a powerful tool for AC circuit analysis and is widely used in electrical engineering to solve complex circuits efficiently and accurately.