You are given a resistance wire of length $50\, cm$ and a battery of negligible resistance. In which of the following cases is the largest amount of heat generated?

Consider two circuits, $(A)$ and $(B)$, each having two resistors. One of them has a positive temperature coefficient of resistance, $+\alpha$, while the other one has a negative temperature coefficient of resistance, $-\alpha$. The current through these circuits are denoted by $I_A$ and $I_B$. At initial temperature, the resistance of the two resistors is $R_0$. As the temperature is increased, the correct option that describes the variation of current in these circuits 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.

The equivalent resistance between $A$ and $B$ is $:-$

The equivalent resistance between ends $A$ and $B$ is

Three resistances of equal values are arranged in four different configurations as shown below. Power dissipation in the increasing order is