Phasor (AC Analysis)

Phasor   is a complex number that represents the amplitude and phase of a sinusoid. Phasor in our understanding is the simplified form of the sinusoidal function. Which means it can be used provided that the angular frequencies if faced with two or more sinusoidal input functions, are all equal. Also it is simpler to input in our calculators, there is a saying that I made up, although it might exist already, that simpler is better. Hoho.

PHASOR:

It has three forms:

 

Although we rarely to never use the exponential form, learning its existence can also help in some type with different specification for different approach and derivation in order to provide the correct solution of circuit models. 

On the other hand, polar form is what we often use in solving because it shows the angle of the sinusoid. Which means we can actually track down if our answers lags or leads the other values. 

There are rules in relating two phasors with each other: 

Time domain and phasor domain: 

Time domain is the general expression of the sinusoid, while phasor domain is a more simplified one. 

Rules for transforming Time domain into Phasor domain:

1. Time domain must be in cosine function
2. Vm or the magnitude of the function must be positive.

- amplitude and phase difference fare two principal concerns in the study of voltage and current sinusoids.
- phasor will be defined form the cosine-function in all our proceeding study. If a voltage or expression is in the form of a sine, it will be changed to cosine (function) by substracting from the phase.

Phasor is also called a complex number, which we are about to take in Advance Mathematics. We are grateful because we can double the learnings we get from both subject and apply each others' learnings with one another, if that make sense.