The current passing through the battery in the given circuit is: (in $A$)

Three resistors $1 \Omega, 2 \Omega$ and $3 \Omega$ are connected to form a triangle. Across the $3 \Omega$ resistor,a $3 \text{ V}$ battery is connected. The current through the $3 \Omega$ resistor is: (in $\text{ A}$)

What is the equivalent resistance between $A$ and $B$ in the given infinite network?

What is the total current $I$ (in $A$) drawn from the battery in the given circuit?

$A$ student was trying to construct the circuit shown in the figure below marked $(a)$,but ended up constructing the circuit marked $(b)$. Realising her mistake,she corrected the circuit,but to her surprise,the output voltage (across $R$) did not change. The value of resistance $R$ is ............ $\Omega$

Find the current in the $6\,\Omega$ resistance.