$A$ 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 ................ $m$.

Four wires of equal length and of resistances $10 \ \Omega$ each are connected in the form of a square. The equivalent resistance between two opposite corners of the square is ............. $\Omega$. (in $\Omega$)

$A$ letter $'A'$ is constructed of a uniform wire with resistance $1.0\,\Omega/cm$. The sides of the letter are $20\,cm$ and the cross-piece in the middle is $10\,cm$ long. The apex angle is $60^{\circ}$. The resistance between the ends of the legs is close to ................ $\Omega$.

Two known resistances of $R \ \Omega$ and $2R \ \Omega$ and one unknown resistance $X \ \Omega$ are connected in a circuit as shown in the figure. If the equivalent resistance between points $A$ and $B$ in the circuit is $X \ \Omega$, then the value of $X$ is . . . . . . $\Omega$.

The voltage across the $10 \, \Omega$ resistor in the given circuit is $x$ volt. The value of $x$ to the nearest integer is..........

Resistors of $4\, R, 16\, R, 64\, R, \dots \infty$ are connected in series. Find their equivalent resistance.