An electric fan and a heater are marked as $100 \ W, 220 \ V$ and $1000 \ W, 220 \ V$ respectively. The resistance of the heater is

$A$ resistor develops $300 \,J$ of thermal energy in $15 \,s$,when a current of $2 \,A$ is passed through it. If the current increases to $3 \,A$,the energy developed in $10 \,s$ is........$J.$

$A$ $5\,^{\circ}\text{C}$ rise in temperature is observed in a conductor by passing a current. When the current is doubled the rise in temperature will be approximately ........... $^{\circ}\text{C}$

$4$ bulbs marked $40\, W, 250\, V$ are connected in series with a $250\, V$ mains. The total power consumed is ............. $W$.

$A$ time-varying current $i$ is passed through a resistance $R$ as shown in the figure. The total heat generated in the resistance is

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