The best solar panels currently available are about 13% efficient in converting sunlight to electricity. A typical home will use about 40. kWh of electricity a day. Assuming 8 hours of useful sunlight per day, calculate the minimum solar panel surface area necessary to provide all of a typical home's electricity.
Energy rate of sun = 1.0 kilowatt per square meter of surface area.
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To calculate the minimum solar panel surface area necessary to provide all of a typical home's electricity, we need to follow these steps:
Step 1: Calculate the total electricity usage of the home in kilowatt-hours (kWh) per day. In this case, the typical home uses 40 kWh of electricity per day.
Step 2: Calculate the amount of electricity generated by a solar panel in kilowatt-hours per day. This can be done by multiplying the solar panel's efficiency by the energy rate of the sun and the number of hours of useful sunlight per day.
Efficiency = 13% = 0.13 (in decimal form)
Energy rate of sun = 1.0 kilowatt per square meter
Hours of useful sunlight per day = 8 hours
Electricity generated per solar panel = Efficiency * Energy rate of sun * Hours of useful sunlight per day
Step 3: Calculate the minimum number of solar panels required to meet the home's electricity needs. This can be done by dividing the total electricity usage of the home by the electricity generated per solar panel.
Minimum number of solar panels = Total electricity usage of the home / Electricity generated per solar panel
Step 4: Calculate the minimum solar panel surface area necessary by multiplying the minimum number of solar panels by the surface area of a single solar panel.
To calculate the surface area of a single solar panel, we need to use the energy rate of the sun provided: 1.0 kilowatt per square meter.
Surface area of a single solar panel = Electricity generated per solar panel / Energy rate of sun
Now, we can calculate the minimum solar panel surface area.
Let's perform the calculations:
Step 1: Total electricity usage of the home = 40 kWh/day
Step 2: Electricity generated per solar panel = 0.13 * 1.0 * 8 = 1.04 kWh/day
Step 3: Minimum number of solar panels = 40 kWh/day / 1.04 kWh/day ≈ 38.46
Step 4: Surface area of a single solar panel = 1.04 kWh/day / 1.0 kilowatt/square meter = 1.04 square meters
Minimum solar panel surface area = 38.46 * 1.04 square meters ≈ 40.00 square meters
Therefore, the minimum solar panel surface area necessary to provide all of a typical home's electricity is approximately 40.00 square meters.