$A$ bulb has a specification of $1\, kW$ and $250\, V$. The resistance of the bulb is .................. $\Omega$.

The heat developed in an electric wire of resistance $R$ by a current $I$ for a time $t$ is

Water boils in an electric kettle in $20$ minutes after being switched on. Using the same main supply,the length of the heating element should be . . . . . . to . . . . . . times of its initial length if the water is to be boiled in $15$ minutes.

$A$ bulb rated $100\, W, 220\, V$ is connected to a $110\, V$ supply. What is the power consumed in $W$?

In a $Ag$ voltameter,$2.68 \, g$ of silver is deposited in $10 \, \min$. The heat developed in a $20 \, \Omega$ resistor during the same period 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