The equivalent circuit is shown in figure
Resistance in arm ` AB= 1Omega`
Resistance in arm FG
` = (1 xx 1)/(1 +1) + ( 1xx 1)/(1+1)= 1/2 +1/2=1 Omega`
Resistance in arm DC = `1 Omega`
As resistance of these arms are in parallel, their equivalent resistance is
`1/R_(e) = 1/1 +1/1+1/1 =3/1`
or `R_(e) = 1/3`
Total resistance of circuit,
`R= R_(e) + r =1/3 +2/3 =1 Omega`
`:.` Current `I= in/R=1/1 =1A`