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

Consider an electrical conductor connected across a potential difference $V$. Let $\Delta q$ be a small charge moving through it in time $\Delta t$. If $I$ is the electric current through it,
$I$. the kinetic energy of the charge increases by $I V \Delta t$.
$II$. the electric potential energy of the charge decreases by $I V \Delta t$.
$III$. the thermal energy of the conductor increases by $I V \Delta t$.
Choose the correct option.

Two heating coils of resistances $10 \Omega$ and $20 \Omega$ are connected in parallel and connected to a battery of emf $12 \text{ V}$ and internal resistance $1 \Omega$. The ratio of the power consumed by them is:

Water in an electric kettle starts boiling in $15 \ min$ after being switched on. If the length of the heating wire is reduced to $2/3$ of its original length,the time taken to boil the same amount of water will be ........... $min$.

If two electric bulbs have $40\, W$ and $60\, W$ rating at $220\, V$,then the ratio of their resistances will be

What amount of heat will be generated in a coil of resistance $R$ due to a charge $q$ passing through it if the current in the coil decreases to zero uniformly during a time interval $\Delta t$?