If ${R_1}$ and ${R_2}$ are respectively the filament resistances of a $200$ $watt$ bulb and $100$ $watt$ bulb designed to operate on the same voltage, then

The energy consumed in $1\, Kwatt$ electric heater in $30$ seconds will be

The capacitor $C$ is initially without charge.$X$ is now j oined to $Y$ for a long time, during which $H_1$ heat is produced in the resistance $R$. $X-Y$ connection is removed and $X$ is now joined to $Z$ for a long time, during which heat $H_2$ is produced in $R$.

If power in $3\,\Omega $ is $27\,W$ then what is the power in $2\,\Omega $  ................ $\mathrm{W}$

Two wires with resistances $R$ and $2R$ are connected in parallel, the ratio of heat generated in $2R$ and $R$ is

A wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to current, the temperature of the wire is raised by $\Delta T$ in a time $t$. A number $N$ of similar cells is now connected in series with a wire of the same material and cross-section but of length $2\, L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time $t$. the value of $N$ is