A family uses 8 \mathrm{~kW} of power. (a) Direct solar energy is incident on the horizontal surface at an average rate of 200 \mathrm{~W} per square meter. If 20 \% of this energy can be converted to useful electrical energy, how large an area is needed to supply 8 kW?(b) Compare this area to that of the roof of a typical house.
A family uses 8 \mathrm{~kW} of power. (a) Direct solar energy is incident on the horizontal surface at an average rate of 200 \mathrm{~W} per square meter. If 20 \% of this energy can be converted to useful electrical energy, how large an area is needed to supply 8 kW?(b) Compare this area to that of the roof of a typical house.

(a) Power used by family is given as p=8 \mathrm{KW}=8000 \mathrm{~W}

Solar energy received per square metre is given as 200 \mathrm{~W} / \mathrm{m}^{2}

Percentage of energy converted to useful electrical energy is given as 20 \%

As solar energy is incident at a rate of 200 \mathrm{Wm}^{-2}, the area required to generate the desired energy will be A

Useful electrical energy produced per second can be calculated as,

=(20 / 100) \mathrm{A} \times 200=8000

A=4000 \mathrm{~W} / 200 \mathrm{Wm}^{-2}=200 \mathrm{~m}^{2}

(b) 14 \mathrm{~m} \times 14 \mathrm{~m} is the area needed is comparable to the roof of a large house of dimension.