$A$ lamp is rated at $240 \ V, 60 \ W$. When in use,the resistance of the filament of the lamp is $20$ times that of the cold filament. The resistance of the lamp when not in use is: (in $\Omega$)

$A$ 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........... .

If the power in the external resistance $R$ is maximum,then which of the following statements are correct?
$(i) R = r$
$(ii)$ Power in $R$ is $\frac{E^2}{4R}$
$(iii)$ Input power is $\frac{E^2}{2R}$
$(iv)$ Efficiency is $50\%$

Two electric bulbs have resistances in the ratio $1 : 2$. If they are connected in parallel to a constant voltage source,the ratio of power dissipated in them will be:

$A$ $6.0\,V$ battery is connected to two light bulbs as shown in the figure. Light bulb $1$ has a resistance of $3\,\Omega$ while light bulb $2$ has a resistance of $6\,\Omega$. The battery has negligible internal resistance. Which bulb will glow brighter?

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