Math Problem Statement

Solar​ (photovoltaic) cells convert sunlight directly into electricity. If solar cells were​ 100% efficient, they would generate about 1000 watts of power per square meter of surface area when exposed to direct sunlight. With lower​ efficiency, they generate proportionally less power. For​ example, 10% efficient cells generate 100 watts of power in direct sunlight. Suppose you want to supply 1 kilowattnothing of power to a house by putting solar panels on its roof. For solar cells with the average power of 46 watts per square meter of solar​ panels, how many square meters of solar panels would you​ need? Assume you can make use of the average power from the solar cells​ (by, for​ example, storing energy in batteries until it is​ needed). How many square meters of solar pannels would you need?

Solution

To determine how many square meters of solar panels are needed to generate 1 kilowatt of power, we can use the following steps:

Given:

  • The solar cells generate 46 watts per square meter.
  • You need to generate 1 kilowatt (or 1000 watts) of power.

Step 1: Set up the equation

To find how many square meters of solar panels (AA) are required, divide the total power needed (1000 watts) by the power generated per square meter (46 watts per square meter).

A=Total Power NeededPower per Square Meter=1000 watts46 watts/m2A = \frac{\text{Total Power Needed}}{\text{Power per Square Meter}} = \frac{1000 \text{ watts}}{46 \text{ watts/m}^2}

Step 2: Calculate

A=10004621.74m2A = \frac{1000}{46} \approx 21.74 \, \text{m}^2

Final Answer:

You would need approximately 21.74 square meters of solar panels to generate 1 kilowatt of power with solar cells that generate 46 watts per square meter.

Would you like further details on this, or do you have any other questions?

Here are 5 related questions to deepen your understanding:

  1. What factors affect the efficiency of a solar panel?
  2. How do different weather conditions impact the power output of solar panels?
  3. What are the advantages of storing solar energy in batteries?
  4. How does the orientation and tilt of solar panels affect their efficiency?
  5. How does solar panel degradation over time impact power generation?

Tip: Always consider the geographical location when estimating solar power generation, as sunlight availability varies across different regions.

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Math Problem Analysis

Mathematical Concepts

Ratio and Proportion
Unit Conversion

Formulas

Area (A) = Total Power Needed / Power per Square Meter
A = 1000 watts / 46 watts per square meter

Theorems

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Suitable Grade Level

Grades 9-11