A family uses 8 kW of power.
Question.
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 $8 \mathrm{~kW}$ ?

(b) Compare this area to that of the roof of a typical house.

solution:

(a) $200 \mathrm{~m}^{2}$

(a) Power used by the family, $P=8 \mathrm{~kW}=8 \times 10^{3} \mathrm{~W}$

Solar energy received per square metre = 200 W

Efficiency of conversion from solar to electricity energy $=20 \%$

Area required to generate the desired electricity = A

As per the information given in the question, we have:

$8 \times 10^{3}=20 \% \times(A \times 200)$

$=\frac{20}{100} \times A \times 200$

$\therefore A=\frac{8 \times 10^{3}}{40}=200 \mathrm{~m}^{2}$

(b) The area of a solar plate required to generate $8 \mathrm{~kW}$ of electricity is almost equivalent to the area of the roof of a building having dimensions $14 \mathrm{~m} \times 14 \mathrm{~m}$.