Twelve wires of equal length and equal cross-sectional area form a cube. If the resistance of each wire is $R$,then the effective resistance between the two ends of a diagonal is:

The equivalent resistance between points $A$ and $B$ of an infinite network of resistances each of $1\,\Omega$ connected as shown,is

$A$ battery of $e.m.f.$ $10\, V$ and internal resistance $0.5\, \Omega$ is connected across a variable resistance $R$. The value of $R$ for which the power delivered in it is maximum is given by ......... $\Omega$.

In the given circuit,the internal resistance of the $18\,V$ cell is negligible. If $R_1 = 400\,\Omega$,$R_3 = 100\,\Omega$,and $R_4 = 500\,\Omega$,and the reading of an ideal voltmeter across $R_4$ is $5\,V$,then the value of $R_2$ will be ........... $\Omega$.

In the electrical circuit shown in the figure,the current $i$ through the side $AB$ containing the $20 \; \Omega$ resistor is:

By a cell,a current of $0.9\, A$ flows through a $2\, \Omega$ resistor and $0.3\, A$ flows through a $7\, \Omega$ resistor. The internal resistance of the cell is ............ $\Omega$.