What is the equivalent resistance between points $A$ and $B$ in the given circuit?

$A$ 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 $A$)

$A$ man has some identical resistors,each with a resistance $R = 10 \, \Omega$ and a maximum current rating of $1 \, \text{A}$. He needs to create a circuit with an equivalent resistance of $5 \, \Omega$ that can handle a total current of $4 \, \text{A}$. What is the minimum number of such resistors required?

$(a)$ Three resistors $2 \; \Omega$,$4 \; \Omega$,and $5 \; \Omega$ are combined in parallel. What is the total resistance of the combination?
$(b)$ If the combination is connected to a battery of $emf \; 20 \; V$ and negligible internal resistance,determine the current through each resistor,and the total current drawn from the battery.

$A$ uniform conductor of resistance $R$ is cut into $20$ equal pieces. Half of them are joined in series and the remaining half of them are connected in parallel. If the two combinations are joined in series,the effective resistance of all the pieces is

In the network shown in the figure,the equivalent resistance between points $X$ and $Y$ will be . . . . . . $\Omega$. The value of each resistor is $2 \Omega$.