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.

$A$ $12 \text{ HP}$ motor has to be operated $8 \text{ hours/day}$. How much will it cost at the rate of $50 \text{ paisa/kWh}$ in $10$ days? (in $Rs.$)

$A$ circular wire has a current density $J = (2 \times 10^{10} \text{ A/m}^2) r^2$, where $r$ is the radial distance from the center and the wire radius is $2 \text{ mm}$. The potential difference applied across the wire is $50 \text{ V}$. How much energy (in Joules) is converted to thermal energy in $100 \text{ s}$ (in $\pi$)?

Two electric lamps of $40\, W$ each are connected in parallel. The power consumed by the combination will be ........... $W$.

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 $\Delta t$?

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.