Page 329 - Basic Electrical Engineering

Figure 3.30 Phasor diagrams of parallel circuit shown in Fig. 3.29

Sum of X component (active component) of branch currents = I cos ϕ +
1
1
I cosϕ + I cosϕ 3
2
3
2
Y component of I (AL) = –I sin ϕ 1
1
1
Y component of I (BM) = +I sin ϕ 2
2
2
Y component of I (ON) = –I sin ϕ 3
3
3
Sum of Y component (reactive component) of branch currents = −I sin ϕ 1
1
+ I sin ϕ − I sin ϕ 3
3
2
2
Active component of resultant current I = I cos ϕ
Reactive component of resultant current I = I sin ϕ

Active and reactive components of resultant current must be equal to the
sum of active and reactive components of branch currents.

∴ I cosϕ = I cosϕ + I cosϕ + I cosϕ 3
2
2
3
1
1
I sinϕ = −I sinϕ + I sinϕ − I sinϕ 3
3
1
2
2
1
Resultant current