Net resistance of the given circuit between $X$ and $Y$ is ............... $\Omega$.

$A$ wire is bent in the form of a circle of radius $2 \ m$. The resistance per unit length of the wire is $\frac{1}{\pi} \ \Omega/m$. $A$ battery of $6 \ V$ is connected between points $A$ and $B$ as shown in the figure. Given $\angle AOB = 90^{\circ}$,find the current flowing through the battery. (in $A$)

The equivalent resistance between points $A$ and $B$ in the given network is ............ $\Omega$.

Two metal wires of identical dimensions are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the metal wires respectively,the effective conductivity of the combination is

$A$ wire has resistance $12\,\Omega$. It is bent in the form of a circle. The effective resistance between the two points on any diameter is equal to ................ $\Omega$.

In the following star circuit diagram, the equivalent resistance between the points $A$ and $H$ will be ..............$r$.