In the given circuit diagram a wire is joining points B and D. The current in this wire is

1Ω and 4Ω are in parallel 1(4)1+4=45Ω2Ω and 3Ω are in parallel 2(3)2+3=65Ω45Ω and are in series Reff=45+65=105=2Ω i=VReff=102=5 AApply junction rule at point BLet R1=4Ω,R2=1Ω,R3=3Ω ad R4=2Ω current through R1=4Ω is i1 current through R2=1Ω is i2 current through R3=3Ω is i3 current through R4=2Ω is i4  Current across 4Ω,I1=R2iR1+R2==1(5)1+4=1A Current across 3Ω,I3=R4iR3+R4==2(5)2+3=2A current through BC=i=I3-I1=2−1=1A