In the given star circuit,find the equivalent resistance between $A$ and $H$. (in $r$)

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.

Two resistance wires on joining in parallel the resultant resistance is $\frac{6}{5} \ \Omega$. One of the wires breaks,the effective resistance is $2 \ \Omega$. The resistance of the broken wire is ............ $\Omega$.

Two bulbs,one of $200 \ V, 60 \ W$ and the other of $200 \ V, 100 \ W$,are connected in series to a $200 \ V$ supply. The power consumed will be ................ $W$.

Two heater wires of equal length are first connected in series and then in parallel. The ratio of heat produced in the two cases is

The current $I_{1}$ (in $A$) flowing through the $1\; \Omega$ resistor in the following circuit is: