In the circuit shown, the currents in 4  Ω and 8  Ω resistances are

Since battery is in parallel with 4  Ω resistance, it carries currentI=104=2.5AIn open loop a1a d e g,Va1+10−10=0⇒Va1=0Thus, all resistances, i.e, 2  Ω,  2  Ω,  1  Ω  and 8  Ω,  connected between a1 and g, carry zero current.