For the network shown in the given figure, if no current flows through the branch AO, the current drawn from the cell, is:

2A

The correct answer is Option (2) → 2A

As no current flows through the branch AO,

$\frac{4}{R}=\frac{2}{2.5}⇒R=5Ω$

Now, equivalent resistance of the circuit is,

$\frac{1}{R_{eq}}=\frac{1}{9}+\frac{1}{4.5}=\frac{1.2}{9}$

$R_{eq}=3Ω$

Total resistance of circuit is,

$R_{total}=R_{eq}+2=5Ω$

and,

$I=\frac{V}{R}=\frac{10}{5}=2A$ [By ohm's law]