An electric kettle has two filaments. The first filament boils a certain amount of water in $10 \text{ minutes}$ and the second filament boils it in $15 \text{ minutes}$. If both filaments are connected in parallel,the water will boil in .............. minutes.

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.

In the given figure,the $emf$ of the cell is $2.2 \, V$ and the internal resistance is $0.6 \, \Omega$. Calculate the power dissipated in the whole circuit (in $W$).

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?

$A$ straight wire of resistance $18 \Omega$ is bent in the form of an equilateral triangular loop. The effective resistance between any two vertices of the triangle is (in $\Omega$)

$A$ wire of resistance $R$ is bent into a triangular pyramid as shown in the figure,with each segment having the same length. The resistance between points $A$ and $B$ is $R / n$. The value of $n$ is