The equivalent resistance between the points $P$ and $Q$ in the network given here is equal to ................ $\Omega$ (given $r = \frac{3}{2} \Omega$).

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.

$A$ ring is made of a wire having a resistance $R_0 = 12\,\Omega$. Find the positions of points $A$ and $B$ such that the equivalent resistance of the circuit shown is $8/3\,\Omega$.

Three electric bulbs of $200\,W, 200\,W$ and $400\,W$ are shown in the figure. The resultant power of the combination is ................ $W$.

Two wires $A$ and $B$ are made of the same material and have the same mass. The radius of wire $A$ is twice the radius of wire $B$. If wires $A$ and $B$ are connected in parallel,the equivalent resistance will be:

From the combination of resistors with resistance values $R_1 = R_2 = R_3 = 5 \ \Omega$ and $R_4 = 10 \ \Omega$,which of the following combinations is the best circuit to get an equivalent resistance of $6 \ \Omega$?