Find the effective resistance between $A$ and $B$ in the given circuit.

$A$ 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?

In the given circuit,$a$ is an arbitrary constant. The value of $m$ for which the equivalent circuit resistance is minimum is given by $\sqrt{\frac{x}{2}}$. The value of $x$ is:

$A$ 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 $A$)

In the given network,the equivalent resistance between $A$ and $B$ is .............. $\Omega$.

An electric kettle has two coils. When one of these is switched on,the water in the kettle boils in $6\,min$. When the other coil is switched on,the water boils in $3\,min$. If the two coils are connected in series,the time taken to boil the water in the kettle is ............. $min$.