Find the equivalent resistance between $P$ and $Q$. (If each wire has a resistance $R$)

There are $n$ similar conductors each of resistance $R$. The resultant resistance comes out to be $x$ when connected in parallel. If they are connected in series,the resistance comes out to be

$A$ heater $A$ gives out $300 \ W$ of heat when connected to a $200 \ V$ $d.c.$ supply. $A$ second heater $B$ gives out $600 \ W$ when connected to a $200 \ V$ $d.c.$ supply. If a series combination of the two heaters is connected to a $200 \ V$ $d.c.$ supply,the heat output will be ................. $W$.

By which of the following single load resistance should the load bridge be replaced so that the power to the load remains unchanged (in $\Omega$)? (Given $r = 3 \ \Omega$ for each resistor in the bridge)

The equivalent resistance between $A$ and $B$ is $6 \Omega$. The value of $R_1$ is (in $\Omega$)

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.