$A$ wire of resistance $R$ is cut into $8$ equal pieces. From these pieces,two equivalent resistances are made by connecting four of these pieces in parallel in each set. Then,these two sets are connected in series. The net effective resistance of the combination is

$A$ copper wire of resistance $R$ is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have a resistance

$A$ straight uniform wire of resistance $36 \Omega$ is bent in the form of a semi-circular loop. The effective resistance between the ends of the diameter of the semi-circular loop is

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

$(a)$ Three resistors $2 \; \Omega$,$4 \; \Omega$,and $5 \; \Omega$ are combined in parallel. What is the total resistance of the combination?
$(b)$ If the combination is connected to a battery of $emf \; 20 \; V$ and negligible internal resistance,determine the current through each resistor,and the total current drawn from the battery.

The equivalent resistance of a series combination of two resistors is $s$. When they are connected in parallel,the equivalent resistance is $p$. If $s = np$,then the minimum value for $n$ is (Round off to the nearest integer).