$A$ 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 $CD$ ).

The equivalent resistance of two resistors connected in series is $6 \ \Omega$ and their parallel equivalent resistance is $\frac{4}{3} \ \Omega$. What are the values of the resistances?

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

Resistors of $10\, \Omega, 5\, \Omega, 7\, \Omega$, and $3\, \Omega$ are connected along the sides $AB, BC, CD$, and $DA$ of a square, respectively. A resistor of $10\, \Omega$ is connected across the diagonal $AC$. What is the equivalent resistance between points $A$ and $B$ in $\Omega$?

An electrical bulb rated $220\,V, 100\,W$ is connected in series with another bulb rated $220\,V, 60\,W$. If the voltage across the combination is $220\,V$,the power consumed by the $100\,W$ bulb will be about $........... W$.

Write the differences between series and parallel connections of resistors.