Heat produced in a wire of resistance $R$ due to current flowing at constant potential difference is proportional to

$A$ uniform heating wire of resistance $36 \, \Omega$ is connected across a potential difference of $240 \, V$. The wire is then cut into half and a potential difference of $240 \, V$ is applied across each half separately. The ratio of power dissipation in the first case to the total power dissipation in the second case would be $1:x$,where $x$ 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

By what percentage will the illumination of the lamp decrease if the current drops by $20 \%$ (in $\%$)?

The energy consumed in a $1\, kW$ electric heater in $30$ seconds will be:

From where does electrical power derive? Explain it.