Sum of Y component (reactive components) of the branch currents
=−+−
II
I
112233
si
ns
in
sinfff
=−+−II
I
112233
sinsin
sin
fff
Active component of resultant current II
=
cos
f
Reactive component of resultant current II
=
sin
f
The active and reactive components of the resultant current must be equal to the sum of
active and reactive components of the branch currents.
∴=
++
=−
+−
II
II
II
II
cos
sin
ff
ff
fff
1122
33
11223
coscoscos
sinsinsiinf
3
Resultant current III
=+
()
()
cos sin
ff
22
=(coscoscos)(sinsinsi
n)
II II
II
112233
2
1122
33
2
ffff
ff
+++−+−
tan
sinsinsin
coscos
f
f
f
fff
ff
==
−+−
++
I
I
II I
II
sin
cos
1122
33
1122
II
33
cosf
f
fff
fff
=
−+−
++
−
tan
(s
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