The equivalent resistance between points $A$ and $B$ in the given network is: (in $\Omega$)

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

$A$ heating coil can heat the water of a vessel from $20\,^oC$ to $60\,^oC$ in $30$ minutes. Two such heating coils are put in series and then used to heat the same amount of water through the same temperature range. The time taken now will be ............ $min$ (neglecting thermal capacity of the coils).

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.

$A$ current of $15\,mA$ flows in the circuit as shown in the figure. The value of the potential difference between the points $A$ and $B$ will be $...\,V$.

If a resistance ${R_2}$ is connected in parallel with the resistance $R$ in the circuit shown,then the possible value of current through $R$ and the possible value of ${R_2}$ will be: