As shown in the figure,$13$ resistors each of resistance $R$ are connected. The effective resistance between points $A$ and $B$ is:

The total resistance between $x$ and $y$ is ...... $\Omega$.

Three resistances of magnitude $2\,\Omega$,$3\,\Omega$,and $5\,\Omega$ are connected in parallel to a battery of $10\,V$ and of negligible resistance. The potential difference across the $3\,\Omega$ resistance will be ............... $V$.

$A$ cube is formed with ten identical resistances $R$ (thick lines) and two shorting wires (dotted lines) along the arms $AC$ and $BD$ as shown in the figure below. The resistance between point $A$ and $B$ is ........... $\Omega$.

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage,the ratio of heat produced in the same time for parallel to series will be:

$A$ 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?