Electrical Engineering ⇒ Topic : Parallelogram method

 Parallelogram method. This method is used for the addition of two phasors at a time. The two phasors are represented in magnitude and direction by the adjacent sides of a parallelogram. Then the diagonal of the parallelogram represents the maximum value of the resultant.Consider two alternating currents i1 and i2 flowing in the two branches of a circuit [See Fig. a (i)]. Let they be represented by

                                                                                      figure (a)

                                                      i₁ = I_m1 sin ωt ;  i₂ = I_m2 sin (ωt  + θ ) 

The two phasors Im1 and Im2 are represented by the adjacent sides OA and OB respectively of the parallelogram OACB [See Fig. a (ii)]. The phase difference between the phasors is 0°; I_m2 leading  I_m1. The maximum value of resultant is I_r. It is represented by the diagonal OC and leads the phasor I_m1 by Φ₁ .

The instantaneous value of resultant current is given by

                                      i_r  =  I_r sin (ωt  + Φ)

This method is convenient only when we have to add two phasors. However, if the number of phasors to be added is more than two, this method becomes quite inconvenient.