[(i) 2 Ω Ω , (ii) 1.5 A]

Sol.(i) Let R AB = x. Then, we can break one chain and connect a resistance of magnitude x in place of it.Thus, the circuit remains as shown in figure.

Now, 2 Ω Ω and x are in parallel. So, their combined resistance is

Or R AB = 1 +

But R AB is a assumed to x. Therefore,

x = 1 +

Solving this equation, we get

x = 2 Ω Ω

Hence proved.

(ii) Net resistance of circuit R = 1 + = 2 Ω Ω

Current through battery i = = 3A

This current is equally distributed in 2 Ω Ω and 2 Ω Ω resistances. Therefore, the desired current is or 1.5 A.