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Phasor Diagram | What is Phasor Diagram

Phasor Diagram | What is Phasor Diagram :- It is a diagram that represents alternating current and voltage of the same frequency as a vector (phasor) and shows the phase angle relationship between them. To understand a phasor diagram, it is necessary to know the following quantities :

Phase and phase difference and
Concept of lagging and leading

(1). Phase and phase difference

Phase :

Phase is that quantity which gives the knowledge of the instantaneous value of alternating current or alternating voltage and the position of the quantity at that particular time (i.e. whether the quantity is in the positive half cycle or in the negative half cycle).
In simple terms, if there is a sine (sin) or cosine (cos) wave, it has a cyclic nature. Any point on this cycle can be measured as the phase of the wave.
Phase is expressed in degrees (°) or radians. In one complete cycle, the phase of a periodic wave is 360° or 2π radians.
For example, in I = I₀ sin (ωt + ϕ), the term (ωt + ϕ) is called the phase angle, and ϕ is called the initial phase.
The initial phase ϕ does not depend on time and remains constant, whereas the phase angle (ωt + ϕ) depends on time.
If a sine wave is at its maximum value, then its phase angle will be 90° or (π/2) radians.

Phase difference

Phase difference is the difference in the phase angles of two or more waves.
When two alternating waves (such as AC current or voltage) have the same frequency but their peaks and troughs occur at different times, there is a phase difference between them.
A phase difference indicates how much one alternating wave leads or lags behind another wave. This difference is measured in degrees or radians.
For example, if the phase difference between two waves is 90°, one wave will be at its peak value while the other wave will have zero value at that moment (i.e., its cycle will be just beginning).

(2). Concept of lagging and leading

The concepts of lagging and leading are used to understand the phase difference between voltage and current in an AC circuit. They indicate whether the current in an alternating circuit is ahead of the voltage or behind it.

Phasor

A phasor is a vector that rotates in the counter-clockwise direction with a constant angular velocity [The angular frequency ω of the alternating quantity (voltage or current) is the angular velocity of the phasor.]. The length of the phasor is equal to the peak value of the alternating voltage or alternating current, and the instantaneous values of the alternating voltage or current are represented by a component of the phasor.

When the phasor completes one full rotation in the counterclockwise direction, the tip of the phasor rotates through an angle of 360° or 2π radians, which represents one complete cycle of an alternating quantity. Every point in the phasor’s rotation corresponds to the instantaneous value of the alternating voltage or current at a particular time. For example, when the phasor lies on the y-axis (vertical direction), it represents the maximum voltage or current (the peak value), and when it lies on the x-axis (horizontal direction), it represents zero voltage or current.

Example 1.

The equation for the instantaneous current in an alternating current circuit is $\displaystyle I=4sin\left[ 100\pi \ t\ +\ \frac{\pi }{3} \right]$ amperes. Calculate the following :