The equivalent resistance between the points $a$ and $b$ of the electrical network shown in the figure is:

$A$ wire of resistance $12 \, \Omega$ is bent to form an equilateral triangle. What is the equivalent resistance between any two corners of the triangle?

$A$ 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 $A$ and $D$ is ............. $\Omega$.

Three resistances,each of $1\,\Omega$,are joined in parallel. Three such combinations are put in series,then the resultant resistance will be ............. $\Omega$.

When two conducting wires are connected in series,the equivalent resistance is $14\, \Omega$,and when they are connected in parallel,the equivalent resistance is $3.43\, \Omega$. The resistance of the wire with the higher value is ................. $\Omega$.

Resistors $R, 2R, 4R, 8R, ..... \infty$ are connected in parallel. What is their equivalent resistance?