Question

What do you mean by phasor and phasor diagram? Explain.

Answer 1

Phasor A phasor may be defined as a quantity which varies periodically with time and is represented as the projection of a rotating vector.

In d.c. supply the e.m.f. and current are always in same phase but in a.c. circuit having a resistor R or an inductor L or a capacitor C or any combination of these circuit elements, it is found that although the e.m.f. and current have the same frequency, yet they may be out of phase with each other i.e. the peak value of current may not occur, at the same time. This brings the idea of ‘lag’ or ‘lead’ in a.c. circuit.

Let instantaneous value of alternating e.m.f. be given by

E = E₀ sin ωt ............(1)

and I = I₀ sin (ωt - Φ) .........(2)

where Φ is the angle between E and I. (Here the current is said to be lagging behind e.m.f. by a phase Φ)

Here E and I may be considered to be the projections of E₀ and I₀ respectively. Such alternating e.m.f. and currents are called phasors. Angle between these phasors, represents the phase difference between applied alternating e.m.f. and current flowing through the circuit.

Phasor diagram

Diagram which represents alternating e.m.f. and currents (having the same frequency) on the rotating vectors along with phase angle between them is called a phasor diagram.

In order to draw a phasor diagram of alternating e.m.f. and current as given in Eq. 1 & 2. Let us draw two circles having

radii E₀ and I₀ respresented by rotating vectors \(\overrightarrow {OP}\) and \(\overrightarrow {OQ}\) 

 respectively Fig. The projection of E₀ is E and I₀ is I represent the phasor (i.e. instantaneous value of alternating e.m.f. and current respectively) and Φ represents the phase angle by which phasor I lags behind phasor E. 

Thus Fig. is a phasor diagram. Fig. is also a phasor diagram of alternating, e.m.f. and current drawn in a simple way and we can also draw phasor diagram by Fig. if we are interested only in phase relationship.