Alternating Current Analysis 249
The matrix loop equation is indicated as follows:
82 3 0
385 5
057210
0
01
2
3
j
j
jI
I
I
⋅
and the currents I 1 , I 2 , and I 3 are evaluated as indicated as follows:IV
I
ZIV
I
ZIV
I
11 ^121231det( )
det( )det( )
det( ) det(
33 )
det( )Z
wheredet( )Z.j
j
j
82 3 0
385 5
0572315 16 2
∠det( )I..j(^1) j
85 5
57 2
41 1 24 9
∠
det( )I ( ).
(^2) j
1
35
07 2
21 8 16
∠
det( )I
j
3
38 5
05
15 0
∠
I 1 10 0
41 1 24 9
315 16 2
143 87
∠
∠
∠
∠
..
.
..A
I 2 10 0
21 8 16
315 16 2
0 693 32 2
∠
∠
∠
∠
.
.
..A
I 3 10 0
15 0
315 16 2
0 476 16 2
∠
∠
∠
∠
.
..A
I 1 I 2 I 3
3 Ω 5 Ω
2 Ω
−j 2 Ω
5 Ω −j 2 Ω j^5 Ω
V 1 = 10∠ 0 °VFIGURE 3.22
Phasor network of R.3.57.