Problem 75 - Physics for Scientists and Engineers with Modern Physics

Question

A solar cell, \(3.0 \mathrm{~cm}\) square, has an output of \(350 \mathrm{~mA}\) at \(0.80 \mathrm{~V}\) when exposed to full sunlight. A solar panel that delivers close to \(1.3 \mathrm{~A}\) of current at an emf of \(120 \mathrm{~V}\) to an external load is needed. How many cells will you need to create the panel? How big a panel will you need, and how should you connect the cells to one another? How can you optimize the output of your solar panel?

Step-by-Step Solution

Answer

600 cells are needed. The panel size is 0.54 m². Connect 4 groups of 150 series cells in parallel.

Step 1: Calculate Current Requirement per Cell

Each solar cell produces a current of \(350 \mathrm{~mA}\). To meet the requirement of \(1.3 \mathrm{~A}\), calculate how many cells are needed in parallel by dividing the total required current by the current of one cell:\[ \text{Number of parallel cells} = \frac{1.3 \mathrm{~A}}{0.350 \mathrm{~A}} \approx 3.71 \] Since you can’t use a fraction of a cell, you’ll need \(4\) cells in parallel to fulfill the current requirement.

Step 2: Calculate Voltage Requirement per Cell

Each solar cell produces a voltage of \(0.80 \mathrm{~V}\). To meet the requirement of \(120 \mathrm{~V}\), calculate how many cells are needed in series by dividing the total required voltage by the voltage of one cell:\[ \text{Number of series cells} = \frac{120 \mathrm{~V}}{0.80 \mathrm{~V}} = 150 \]You will need \(150\) cells connected in series to fulfill the voltage requirement.

Step 3: Calculate Total Number of Cells and Panel Size

To create the desired output, combine the series and parallel calculations. You'll need \(4\) parallel rows of \(150\) cells each. That’s a total of:\[ 4 \times 150 = 600 \text{ cells} \]Each cell is \(3.0 \text{ cm square} = 9.0 \text{ cm}^2\). So, the size of the panel is:\[ 600 \text{ cells} \times 9.0 \text{ cm}^2 = 5400 \text{ cm}^2 = 0.54 \text{ m}^2 \]The panel will be a rectangle measuring approximately \(90 \text{ cm} \times 60 \text{ cm}\) (for arranging 15 rows).

Step 4: Connect Cells for Optimal Output

To optimize the solar panel output, you should connect the cells in groups of \(150\) in series to match the voltage, then connect \(4\) such groups in parallel to meet the current requirement. This configuration ensures the panel delivers \(1.3 \text{ A at } 120 \text{ V}\).

Step 5: Optimize Solar Panel's Orientation

To further optimize your solar panel output, ensure it is oriented to receive maximum sunlight. Typically, panels should face south in the northern hemisphere and north in the southern hemisphere. Adjusting the angle to match the latitude can also improve efficiency.

Key Concepts

Solar Cell Configuration

When designing a solar panel, it's crucial to understand solar cell configuration. This involves connecting cells in specific arrangements that meet the electrical requirements of a given application.
To achieve a desired electrical output, cells can be connected in series and parallel configurations.

• In a **series configuration**, the solar cells are connected end-to-end, which sums their voltage while maintaining the same current. This is like building a taller stack of batteries to increase the total voltage.
• In a **parallel configuration**, the cells are side-by-side, increasing total current while keeping the voltage the same. This is akin to adding more taps to the same water channel to increase flow rate.

For example, if each cell provides 0.80 V and 350 mA, connecting them in specific patterns achieves higher voltage or current necessary for the load. Remember that for a robust solar panel, both configurations are often combined to meet complex energy demands and ensure efficiency.

Current and Voltage Calculations

Calculating the required current and voltage is foundational in solar panel design. It's all about ensuring the panel meets the load's demand in terms of electricity supply.
Start by determining how many cells are needed to meet these requirements:

• **Current Calculation**: If each solar cell produces 350 mA but you need 1.3 A for your panel, divide the total required current by the current output of one cell. This tells you the number of cells you need in parallel configuration.
• **Voltage Calculation**: Similarly, if the required voltage is 120 V and each cell provides 0.80 V, divide the total needed voltage by the voltage of one cell to find how many cells are required in series configuration.

Once these calculations are done, you arrange the cells in the necessary series and parallel combinations. This ensures the solar panel's output aligns perfectly with the electrical load's requirements.

Optimized Solar Panel Orientation

To maximize the efficiency of a solar panel, optimizing its orientation is key. This involves adjusting the panel's placing and angle to ensure maximum sunlight exposure throughout the day.
Key factors to consider include:

• **Direction Facing**: Panels should generally be positioned facing the equator—south in the northern hemisphere and north in the southern hemisphere. This helps capture the most sunlight during the day.
• **Angle Tilt**: Adjusting the angle can further enhance performance. A rule of thumb is to tilt the panel at the same angle as the geographical latitude of the location. This provides a balance between morning and afternoon sun exposure.

Regularly cleaning the panels and ensuring there are no obstructions can also significantly improve efficiency. By focusing here, the solar panel will perform optimally, delivering the intended power throughout its operational period.