Two wires '$A$' and '$B$' of the same material have lengths in the ratio $1 : 2$ and radii in the ratio $2 : 1$. If the two wires are connected in parallel to a battery,the ratio of heat produced in wire '$A$' to that in wire '$B$' will be:

Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature,$100 \ W$,$60 \ W$ and $40 \ W$ bulbs have filament resistances $R_{100}$,$R_{60}$ and $R_{40}$,respectively,the relation between these resistances is

$A$ house is served by a $220 \, V$ supply line in a circuit protected by a $9 \, A$ fuse. What is the maximum number of $60 \, W$ lamps in parallel that can be turned on simultaneously?

In the figure shown,the power generated in $y$ is maximum when $y = 5\,\Omega$. Then $R$ is

$A$ $10\, \Omega$ electric heater operates on a $110\, V$ line. Calculate the rate at which it develops heat in $watts$.

$A$ household supply is $220 \, V$ with a fuse of $9 \, A$. What is the maximum number of $60 \, W$ bulbs that can be connected in parallel and operated simultaneously?