The ratio of the equivalent resistance of the network (shown in figure) between the points $a$ and $b$ when the switch is open and when the switch is closed is $x : 8$. The value of $x$ is ..... .

$A$ uniform ring of conducting wire of radius $r$ has resistance $R$. $A$ and $B$ are two points on the ring which subtend an angle $\theta$ at the centre of the ring. The equivalent resistance between points $A$ and $B$ is:

$n$ equal resistors are first connected in series and then connected in parallel. What is the ratio of the maximum to the minimum resistance?

The effective resistance of a parallel connection that consists of four wires of equal length,equal area of cross-section,and same material is $0.25\, \Omega$. What will be the effective resistance if they are connected in series? (In $\Omega$)

The equivalent resistance of three unequal resistors connected in parallel is $1 \ \Omega$. If the ratio of two of them is $1:2$ and all resistance values are integers,what is the value of the largest resistor in ohms?

You are given $10$ resistors each of resistance $2 \ \Omega$. First,they are connected to obtain the possible minimum resistance. Then,they are connected to obtain the possible maximum resistance. The ratio of maximum and minimum resistance is . . . . . . .