The equivalent resistance across $A$ and $B$ as shown in the figure is ............. $\Omega$.

$A$ wire of resistance $20 \Omega$ is divided into $10$ equal parts. $A$ combination of two parts are connected in parallel and so on. Now,the resulting pairs of parallel combinations are connected in series. The equivalent resistance of the final combination is . . . . . . $\Omega$.

Five identical resistors are initially arranged as shown in the figure by solid lines. If two identical resistors are added as shown by the dashed lines,the change in the equivalent resistance between the initial and final configurations is ....... $\Omega$.

The equivalent resistance between points $A$ and $B$ in the given network is: (in $Omega$)

Three identical resistors $R_1 = R_2 = R_3 = R$ are connected as shown to a battery of constant e.m.f. $V$. The power dissipated is:

$A$ uniform wire of resistance $20 \,\Omega$ having resistance $1 \,\Omega/m$ is bent into a circle as shown in the figure. If the equivalent resistance between $M$ and $N$ is $1.8 \,\Omega$,then the length of the shorter section is ................ $m$.