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

Four wires of the same diameter are connected in turn between two points,maintained at a constant potential difference. Their resistivities and lengths are: $\rho$ and $L$ (wire $1$),$1.2\rho$ and $1.2L$ (wire $2$),$0.9\rho$ and $0.9L$ (wire $3$),and $\rho$ and $1.5L$ (wire $4$). Rank the wires according to the rates at which energy is dissipated as heat,greatest first.

How many calories of heat will be produced approximately in a $210\, W$ electric bulb in $5$ minutes?

An electric heater of resistance $6 \, \Omega$ is run for $10 \, \text{minutes}$ on a $120 \, \text{V}$ line. The energy liberated in this period of time is:

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:

$1\,\text{unit} =$ ...... electric energy.