Question

Define Phasor and Phase angle.

Answer 1

### Phasor:
A phasor is a complex number that represents the magnitude and phase of a sinusoidal waveform (usually a voltage or current). Instead of dealing with the waveform in time (which is a time-varying signal), a phasor simplifies the analysis by representing the sinusoidal signal in the frequency domain.

A phasor has two main parts:

1. Magnitude: The peak value (or amplitude) of the sinusoidal wave.
   

1. Phase: The phase shift, which tells us the starting point of the waveform.
   

Mathematically, a phasor can be represented as:
\[
\mathbf{V}(t) = V_m \cos(\omega t + \phi)
\]
Where:

1. \(V_m\) is the peak (or maximum) value (magnitude) of the wave.
   

1. \(\omega\) is the angular frequency.
   

1. \(\phi\) is the phase angle.
   

  
The phasor itself would then be represented as:
\[
\mathbf{V} = V_m \angle \phi
\]
Where:

1. \(V_m\) is the magnitude.
   

1. \(\phi\) is the phase angle.
   

This representation makes it easier to perform mathematical operations on sinusoidal functions, especially when dealing with AC circuits.

Phase Angle:

The phase angle (\(\phi\)) is the amount of horizontal shift or delay of a sinusoidal wave relative to a reference wave. It is measured in degrees or radians and indicates how much one wave leads or lags behind another wave.

For example:

1. If one sinusoidal signal reaches its peak earlier than another, we say that it "leads" the other wave by a phase angle.
   

1. If one signal reaches its peak later, it "lags" behind the other signal.
   

In a mathematical form, the phase angle is the \(\phi\) in the expression:
\[
V(t) = V_m \cos(\omega t + \phi)
\]

1. Positive phase angle (\(\phi > 0\)) means the wave is shifted to the right (delayed).
   

1. Negative phase angle (\(\phi < 0\)) means the wave is shifted to the left (advanced).
   

So, the phase angle helps describe the timing difference between different sinusoidal signals.