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
i1 = Im1 sin ωt ; i2 = Im2 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°; Im2 leading Im1. The maximum value of resultant is Ir. It is represented by the diagonal OC and leads the phasor Im1 by Φ1 .
The instantaneous value of resultant current is given by
ir = Ir 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.
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