The equivalent resistance between the points $a$ and $b$ of the electrical network shown in the figure is:

$A$ wire of resistance $R$ is bent into a circular ring of radius $r$. The equivalent resistance between two points $X$ and $Y$ on its circumference,where the central angle $XOY$ is $\alpha$ (in radians),is given by:

Different combinations of $3$ resistors of equal resistance $R$ are shown in the figures. The increasing order for power dissipation is:

The equivalent resistance between $A$ and $B$ is $......$

The equivalent resistance between the adjacent corners of a regular $n$-sided polygon made of a uniform wire of total resistance $R$ is:

Four identical resistors are connected in series with a battery,dissipating $20 \ W$ of power. What will be the power dissipated if the same resistors are connected in parallel to the same battery (in $W$)?