An electric kettle takes $4 \mathrm{A}$ when connected to a circuit of $220 \mathrm{V}$ potential difference.

(ii) Find the time required to melt and boil away one kilogram of ice at $0°\mathrm{C}$ assuming a loss of generated heat by $40$ per cent due to conduction, radiation etc.,

(iii) Also calculate the cost of electrical energy consumed during the time if the cost of one kilowatt-hour of energy is $20$ paise only. Given latent heat of vapourisation of water at $100°\mathrm{C}$ is $540 \mathrm{cal}/\mathrm{gm}$.

(i) Find the time in which the wire will start melting. The change of resistance with temperature of the wire may be neglected.

Given, for copper density $=9\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$, sp. heat $=9\times {10}^{-2}\mathrm{Cal}/\mathrm{kg}°\mathrm{C},$ melting point $=1075°\mathrm{C}$ resistivity $=1.6\times {10}^{-8} \mathrm{\Omega m}$.

(ii) What will this time be if the length of the wire is doubled.

Given, for copper density $=9\times {10}^3 \mathrm{kg}/{\mathrm{m}}^3$, sp. heat $=9\times {10}^{-2}\mathrm{Cal}/\mathrm{kg}°\mathrm{C},$ melting point $=1075°\mathrm{C}$ resistivity $=1.6\times {10}^{-8} \mathrm{\Omega m}$.

An electric bulb when connected across a power supply of $220 \mathrm{V}$, consumes a power $60 \mathrm{W}$.

$\left(A\right)$ If the supply drops to $180 \mathrm{V}$, then what is the power consumed?

$\left(B\right)$ If the supply is suddenly increased to $240 \mathrm{V}$, then what is the power consumed?

In the circuit shown in Fig. $6.18$ the $5 \mathrm{\Omega }$ resistance develops $10.24 \mathrm{cal}/\mathrm{s}$ due to the current flowing through it. Calculate the heat developed per second in the $2\mathrm{\Omega }$ resistance.