Three resistances of $1\, \Omega$ each are connected in parallel. Such a connection is then connected in series with a $\frac{2}{3}\, \Omega$ resistor. The resultant resistance will be ........... $\Omega$.

$A$ ring is made of a wire having a total resistance $R_0 = 12\,\Omega$. Find the ratio of the lengths $\frac{\ell_1}{\ell_2}$ of the two arcs between points $A$ and $B$ as shown in the figure,such that the equivalent resistance $R$ of the circuit between these points is $\frac{8}{3}\,\Omega$.

In the figure given,the electric current flowing through the $5\, k\Omega$ resistor is $'x' \, mA.$
The value of $x$ to the nearest integer is .........

What is the equivalent resistance across $A$ and $B$ in the figure shown,if $R = 3\,\Omega$?

$A$ uniform wire of resistance $9 \, \Omega$ is bent in the form of a circle. The effective resistance across the points $A$ and $B$ is ............... $\Omega$. The angle subtended by the arc $AB$ at the center is $120^{\circ}$.

Four wires $AB, BC, CD, DA$ of resistance $4\, \Omega$ each and a fifth wire $BD$ of resistance $8\, \Omega$ are joined to form a rectangle $ABCD$,where $BD$ is a diagonal. The effective resistance between the points $A$ and $B$ is: