since R2 and R3 are in parallel
i2 R2 = i3 R3
i2 (500) = i3 (400)
i3 = 1.25 i2
using KCL :
i1 + i4 = i2 + i3
i1 + i4 = 1.25 i2 + i2
i1 + i4 = 2.25 i2 eq-1
using KVL in loop ABCHA
i1 R1 - V1 + i2 R2 = 0
200 i1- 200 + 500 i2 = 0
i1= (200 - 500 i2 )/200 eq-2
using KVL in loop EDGFE
i3 R3 - V2 + i4 R4 = 0
400 i3- 400 + 300 i4 = 0
i4 = (400 - 400 i3 )/300 eq-3
using eq-1 , eq-2 and eq-3
(200 - 500 i2 )/200 + (400 - 400 i3 )/300 = 2.25 i2
(200 - 500 i2 )/200 + (400 - (400) (1.25) i2)/300 = 2.25 i2
i2 = 0.364 A
i3 = 1.25 i2 = 1.25 x 0.364 = 0.455 A
i1= (200 - 500 i2 )/200 = (200 - 500 (0.364))/200 = 0.09 A
i4 = (400 - 400 i3 )/300 = (400 - 400 (0.455))/300 = 0.727 A
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