$A$ wire of resistance $R$ is cut into $n$ equal parts. These parts are then connected in parallel. The equivalent resistance of the combination will be

Obtain the expression for the equivalent resistance for $3$ resistors connected in parallel and also write the expression of equivalent resistance for connection of $n$ resistors.

The equivalent resistance across $A$ and $B$ as shown in the figure is ............. $\Omega$.

For the circuit shown in the figure,the equivalent resistance between $A$ and $B$ is ............. $\Omega$.

Two resistors are connected $(a)$ in series $(b)$ in parallel. The equivalent resistance in the two cases are $9 \ \Omega$ and $2 \ \Omega$ respectively. Then the resistances of the component resistors are

$A$ wire of resistance $R$ is bent to form a circular ring. Find the equivalent resistance between two points $X$ and $Y$ on its circumference. (The angle $XOY = \alpha$ is given.)