Electric power is transmitted over long distances through conducting wires at high voltage because

A heating coil can heat the water of a vessel from $20\,^oC$ to $60\,^oC$ in $30$ minutes. Two such heating coils are put in series and then used to heat the same amount of water through the same temperature range. The time taken now will be ............ $min$ (neglecting thermal capacity of the coils)

The variation of current $(I)$ and voltage $(V)$ is as shown in figure $A$. The variation of power $P$ with current $I$ is best shown by which of the following graph

In a building there are $15$ bulbs of $45\; \mathrm{W}, 15$ bulbs of $100\; \mathrm{W}, 15$ small fans of $10 \;\mathrm{W}$ and $2$ heaters of $1 \;\mathrm{kW}$. The voltage of electric main is $220\; \mathrm{V}$. The minimum fuse capacity (rated value) of the building will be: .......... $A$

In the circuit shown below, the resistances are given (in $\Omega$ ) and the battery is assumed ideal with emf equal to $3.0 \,V$. The resistor that dissipates the most power is

A time varying current $i$ is passed through a resistance $R$ as shown in figure. The total heat generated in the resistance is