Mesh Analysis
Sol -
IN LOOP 1
8I₁ - j2I₁ + j4I₁ - j4I₂ = 0
8I₁ + j2I₁ - j4I₂ = 0
( 8 + j2 )I₁ - j4I₂ = 0 - - - (1)
IN LOOP 2
j4( I₂ - I₁ ) + 6( I₂ - I₃ ) - 50 ∠ 30° = 0
j4I₂ - j4I₁ + 6I₂ - 6I₃ = 50 ∠ 30°
( j4 + 6 ) I₂ - j4I₁ - 6I₃ =50 ∠ 30° .....(2)
IN LOOP 3
I₃ = 10
PUT I3 VALUE IN EQU. (2)
( j4 + 6 )I₂ - j4I₁ - 6 (10) = 50 ∠ 30°
( j4 + 6 )I₂ - j4I₁ - 60 = 43.3 + 25j
( j4 + 6 )I₂ - j4I₁ = 103.3 + 25j
Now solve in Matrix method equ. 1 and 2
∆ = ⎥ (8+j2) -j4 ⎥ ⎥ 0 ⎥
⎥ (j4+6) -j4 ⎥ ⎥ 103.3 + j25 ⎥
∆ = (8+j2)(j4+6) + (j4) (-j4)
40 +j44 + 16
= 56+j44
∆I₁ = ⎥ 0 -j4 ⎥
⎥ 103.3 + j25 ( J4+6) ⎥
= 0+ j4 (103.3 + j25 )
= - 100 + j413
Io = ∆I₁ /∆ = -100 + j413.2 ÷ 56 + j44
Io = 2.480 + j5.42
Io= 5.969 ∠ 65.447 A