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.

In the given circuit, the terminal potential difference of the cell is :

The number of electrons flowing per second in the filament of a $$110 \mathrm{~W}$$ bulb operating at $$220 \mathrm{~V}$$ is : (Given $$\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}$$)

The value of unknown resistance $$(x)$$ for which the potential difference between $$B$$ and $$D$$ will be zero in the arrangement shown, is :