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 ........... $min$.

$A$ heater coil is cut into two parts of equal length and one of them is used in the heater. The ratio of the heat produced by this half coil to that by the original coil is

An electric fan and a heater are marked as $100 \ W, 220 \ V$ and $1000 \ W, 220 \ V$ respectively. The resistance of the heater is

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.

$A$ resistor dissipates $192 \, J$ of energy in $1 \, s$ when a current of $4 \, A$ is passed through it. Now,when the current is doubled,the amount of thermal energy dissipated in $5 \, s$ is $..... \, J$.

The heat produced per unit time,on passing electric current through a conductor at a given temperature,is directly proportional to . . . . . . .