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:

Consider the ladder network shown in the figure. What should be the value of resistance $R$ so that the effective resistance between $A$ and $B$ becomes independent of the number of elements in the combination? ............. $\Omega$

$A$ wire of resistance $R$ is bent to form a square $ABCD$ as shown in the figure. The effective resistance between $E$ and $C$ is ( $E$ is the mid-point of arm $CD$ ).

$A$ straight uniform wire of resistance $36 \Omega$ is bent in the form of a semi-circular loop. The effective resistance between the ends of the diameter of the semi-circular loop is

$A$ wire has a resistance of $12 \, \Omega$. It is bent in the form of an equilateral triangle. The effective resistance between any two corners of the triangle is

In the given circuit,the equivalent resistance between $A$ and $B$ is (in $Omega$)