$A$ wire of resistance $R$ is bent to form a square $ABCD$ as shown in the figure. The effective resistance between $E$ and $C$ is ( $E$ is the mid-point of arm $CD$ ).

Write the differences between series and parallel connections of resistors.

In an aluminium $(Al)$ bar of square cross-section,a square hole is drilled and is filled with iron $(Fe)$ as shown in the figure. The electrical resistivities of $Al$ and $Fe$ are $2.7 \times 10^{-8} \ \Omega m$ and $1.0 \times 10^{-7} \ \Omega m$,respectively. The electrical resistance between the two faces $P$ and $Q$ of the composite bar is

First,a set of $n$ equal resistors of $R$ each are connected in series to a battery of $emf$ $E$ and internal resistance $R$. $A$ current $I$ is observed to flow. Then,the $n$ resistors are connected in parallel to the same battery. It is observed that the current increases $10$ times. What is $n$?

Three unequal resistances are connected in parallel. Two of these resistances are in the ratio $1:2$. The equivalent resistance of these three resistors connected in parallel is $1 \Omega$. What is the highest resistance value among these three resistances if no resistance is fractional (in $\Omega$)?

$A$ regular hexagon is formed by six wires each of resistance $r \Omega$ and the corners are joined to the centre by wires of the same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be: