In the given figure,switches $S_{1}$ and $S_{2}$ are initially open. What is the equivalent resistance across $a b$ when the switches $S_{1}$ and $S_{2}$ are closed? (in $\Omega$)

$A$ wire of length $l$ and resistance $100 \Omega$ is divided into $10$ equal parts. The first $5$ parts are connected in series while the next $5$ parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is: (in $\Omega$)

Each of the resistors shown in the figure has resistance $R.$ Find the equivalent resistance between $A$ and $B :$

$(a)$ Three resistors $1 \;\Omega, 2 \;\Omega$ and $3 \;\Omega$ are combined in series. What is the total resistance of the combination?
$(b)$ If the combination is connected to a battery of $emf \; 12 \; V$ and negligible internal resistance,obtain the potential drop across each resistor.

$A$ wire of resistance $R$ is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of the equivalent resistance between the two end points of an edge of the triangle to that of the square is

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 ............... $V$.