Answer
a) $55.6\text{ m}^2$
b) $10.3$ years
Work Step by Step
a) We are given
$E_{home}=40kWh$First, we
We calculate the total panel area needed:
Total solar energy panel area is:
$E_{sun}=×\frac{0.5kW}{m^{2}}×8h=4kW$
Total solar energy per m$^2$ per day:
$E_{panel/m^2}=E_{sun}\times 0.18= 4\cdot 0.18=0.72kWh$
The required panel area is:
$\text{Area}=\frac{E_{home}}{E_{panel/m^2}}=\frac{40}{0.72}\approx 55.6\text{ m}^2$
b) The daily cost is:
$40\cdot 0.10=\$4$
Annual electricity cost:
$4\times 365=\$1460$
We calculate the payback time:
$\frac{15000}{1460}\approx 10.3\text{ years}$
