What is the equivalent resistance between $A$ and $B$ in the given circuit?

Find the equivalent resistance across the terminals of the source of $e.m.f.$ $24\, V$ for the circuit shown in the figure.

$6 \Omega$ and $12 \Omega$ resistors are connected in parallel. This combination is connected in series with a $10 \text{ V}$ battery and a $6 \Omega$ resistor. What is the potential difference between the terminals of the $12 \Omega$ resistor (in $\text{ V}$)?

$A$ 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

Let there be $n$ resistors $R_1, \dots, R_n$ with $R_{\max} = \max \{R_1, \dots, R_n\}$ and $R_{\min} = \min \{R_1, \dots, R_n\}$. Show that when they are connected in parallel,the resultant resistance $R_p < R_{\min}$ and when they are connected in series,the resultant resistance $R_s > R_{\max}$. Interpret the result physically.

$A$ wire is connected to a battery between the points $M$ and $N$ as shown in figure $(1)$. The same wire is bent in the form of a square and then connected to the battery between the points $M$ and $N$ as shown in figure $(2)$. Which of the following quantities increases?