Problem 2187 - JEE Physics

Question

The sun delivers \(10^{3} \mathrm{Wm}^{-2}\) of electromagnetic flux to earth's surface. The total power that is incident on a roof of dimension \(8 \mathrm{~m} \times 20 \mathrm{~m}\) will be (A) \(4 \times 10^{5} \mathrm{w}\) (B) \(2.56 \times 10^{4} \mathrm{w}\) (C) \(6.4 \times 10^{5} \mathrm{w}\) (D) \(1.6 \times 10^{5} \mathrm{w}\)

Step-by-Step Solution

Answer

The total power incident on the roof with dimensions \(8 \mathrm{m} \times 20 \mathrm{m}\) and the sun delivering \(10^{3} \mathrm{Wm^{-2}}\) of electromagnetic flux is \(\boldsymbol{1.6 \times 10^{5}}\) W.

Step 1: Understanding the relation between flux and power

Electromagnetic flux is the power per unit area received by a surface. We can use this information to determine the total power that is incident on the roof. To do this, we need to multiply the electromagnetic flux by the area of the roof.

Step 2: Calculating the area of the roof

The given dimensions of the roof are: length = 8 m and width = 20 m. To calculate the area of the roof, we will multiply the length by the width as follows: Area = Length × Width Area = 8 m × 20 m Area = 160 \(\mathrm{m^2}\)

Step 3: Calculate the total power incident on the roof

Now that we have the area of the roof, we can calculate the total power incident on the roof. The formula for total power incident is: Power = Electromagnetic flux × Area Recall that the sun delivers \(10^3 \mathrm{Wm^{-2}}\) of electromagnetic flux to the earth's surface. Substitute the values into the formula: Power = \(10^3 \mathrm{Wm^{-2}}\) × 160 \(\mathrm{m^2}\) Power = \(1\times10^3\) W × 160 Power = 160 × \(10^3\) W Power = 1.6 × \(10^5\) W Thus, the total power incident on the roof is \(\boldsymbol{1.6 \times 10^{5}}\) W, making the correct answer choice (D) \(1.6 \times 10^{5} \mathrm{w}\).

Key Concepts

power calculation

Calculating power is an essential part of understanding how much energy is being supplied, used, or converted in any system. When it comes to electromagnetic flux, the power calculation is derived from multiplying this flux by the area on which it is incident. In our case, the sun provides an electromagnetic flux of \(10^3 \mathrm{Wm}^{-2}\). This represents the power received per square meter from the sun's rays.

To find the total power incident on a surface, you simply multiply the electromagnetic flux by the total area of that surface. For example, if you have a roof that is exposed to sunlight, the total power received by it can be calculated with the formula:
- Power = Electromagnetic Flux × Area
This will give you the total power in watts received by the entire surface, which is an important step in understanding how much solar energy can possibly be converted or stored. Calculating power in this manner helps in determining the efficiency of solar panels and other energy conversion devices.

solar energy

Solar energy is one of the most abundant and clean energy sources available on Earth. It originates from the sun and is delivered in the form of light and heat, which can be converted into usable energy through various technologies. Solar energy plays a crucial role in today's world, providing a sustainable and renewable alternative to fossil fuels.

Here are some benefits and applications of solar energy:

• Environmentally friendly and reduces carbon footprint
• Cost-effective over time, as the sun's energy is free
• Used in a variety of ways, including solar heating, photovoltaic systems, and solar thermal electricity
• Decentralized energy source, reducing transmission costs

Solar energy ties closely with power calculation, as understanding the amount of energy your system can capture can lead to better energy management and efficiency.

energy conversion

Energy conversion is the process of changing one form of energy into another, such as converting solar energy into electricity. This is critical for utilizing renewable energy sources, as it turns raw solar input into a usable form that can power homes, businesses, and vehicles.

Technologies used for energy conversion from solar energy include:

• Photovoltaic (PV) cells: These devices convert sunlight directly into electricity using semiconductors.
• Solar thermal collectors: These systems capture solar light to heat a fluid, which can then be used directly or to generate electricity.
• Concentrated solar power (CSP): Utilizes mirrors or lenses to concentrate the sun's energy and convert it to heat, which drives a heat engine connected to a power generator.

Understanding how energy is converted helps in designing efficient systems and choosing the right technology for specific energy needs. It's also a critical factor when calculating the potential and actual output power from a solar energy system.

area calculation

Calculating the area is a straightforward mathematical process but is crucial when determining the total power received by a surface under sunlight. In the context of solar energy, the larger the area exposed to the sun, the more potential energy can be harnessed.

For a rectangular surface like a roof, the area can be easily computed using the formula:
- Area = Length × Width
For example, if a roof has dimensions of 8 meters by 20 meters, the area calculation would be:
\[\text{Area} = 8 \, \mathrm{m} \times 20 \, \mathrm{m} = 160 \, \mathrm{m^2}\]

This calculated area is then used in power calculations, such as determining the total solar power incident on the roof by multiplying it with the electromagnetic flux provided by the sun. Area calculation is not only fundamental for understanding solar power potential but also for planning and designing solar installations effectively.