If the current through a resistor in a circuit increases by $3 \%$, then the power dissipated by the resistor

Water boils in an electric kettle in $20$ minutes after being switched on. Using the same main supply, the length of the heating element should be. . . . . . .to . . . . . .. times of its initial length if the water is to be boiled in $15$ minutes.

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

An electric lamp is marked $60\, W$, $ 230\, V$. The cost of $1\, kilowatt$ hour of power is Rs. $1.25$. The cost of using this lamp for $8$ hours is Rs. ................

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

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