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

Two resistors of resistance $100\,\Omega$ and $200\,\Omega$ are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in $100\,\Omega$ to that in $200\,\Omega$ in a given time is:

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 ................ $A$.

In the given circuit,all resistances are of value $R \ \Omega$ each. The equivalent resistance between $A$ and $B$ is:

$A$ 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 ................. $W$.

All resistances in the figure are $1\,\Omega$ each. The value of current '$I$' is $\frac{a}{5}\,A$. The value of $a$ is