Page 14 - NETWORK ANALYSIS

8
Mesh Analysis

Loop I2

By applying Kirchhoff Voltage Law (KVL);

o
(10 + j5) I2 – j5 I1 = – (10 ∠90 )

– j5 I1 + (10 + j5) I2 1 = – j10 ------------------------------- (2)

Converting mesh equations into matrix form;

j1 −j5 I 20 ∠45
1
[ ] [ ] = [ ]
−j5 (10 + j5) I 2 −j10

To find ∆:

j1 −j5
[ ]
−j5 (10 + j5)

∆ = (j1) (10+j5) – (−j5) ( −j5) = (20 + j10)

To find ∆I1:

20∠ 45 −j5
[ ]
−j10 (10 + j5)

∆ I1 = (20∠45)(10 + 5) − (− 5)(− 10) = (120.711 + j212.132)

∆ I1 (120.711+j212.132)
I1 = = = ( . + . )
∆ (20+j10)

To find ∆I2:

j1 20 < 45
[ ]
−j5 −j10

∆ I2 = (j1)(−j10) − (20 < 45)(−j5) = (−60.711 + j70.711)

∆ I2 (−60.711 + j70.711)
I2 = = = (− . + . )
∆ (20+j10)