An electrical cable consists of a single copper wire of radius $9 \ mm$. Its resistance is $5 \ \Omega$. If this cable is replaced by $6$ copper wires,each of radius $3 \ mm$,then the total resistance of the cable will be ............. $\Omega$.

$A$ 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 $...\,V$.

An electric heater and an electric bulb are rated $500\, W, 220\, V$ and $100\, W, 220\, V$ respectively. Both are connected in series to a $220\, V$ $a.c.$ mains. The current in the circuit when both are connected in series is ................ $A$.

$A$ uniform wire of resistance $9 \, \Omega$ is bent in the form of a circle. The effective resistance across the points $A$ and $B$ is ............... $\Omega$. The angle subtended by the arc $AB$ at the center is $120^{\circ}$.

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 circuit,the equivalent resistance between $A$ and $B$ is ....... $\Omega$.