Question

A solar cell that is \(15 \%\) efficient in converting solar to electric energy produces an energy flow of \(1.00 \mathrm{kW} / \mathrm{m}^{2}\) when exposed to full sunlight. (a) If the cell has an area of \(40.0 \mathrm{cm}^{2}\), what is the power output of the cell, in watts? (b) If the power calculated in part (a) is produced at \(0.45 \mathrm{V},\) how much current does the cell deliver?

Short answer

The power output of the cell is 0.60 Watts and the current that the cell delivers is 1.33 Amperes.

Step-by-step solution

Power Output Calculation

The power input to the cell per unit area is given. To find the total power input to the cell, the power input per unit area needs to be multiplied by the total area of the cell. The cell's area is given in cm², but we need it in m² for the calculations. Convert cm² to m² using the conversion \(1 m^{2} = 10^{4} cm^{2}\). Hence, \(40.0 cm^{2} = 4.0 \times 10^{-3} m^{2}\). Next, calculate the total power input by multiplying it with the power per unit area, which is \(1.00 kW/m^{2} = 1.00 \times 10^{3} W/m^{2}\). Thus, the total power input \(P_{in} = 1.00 \times 10^{3} W/m^{2} \times 4.0 \times 10^{-3} m^{2} = 4.0 W\). Lastly, the power output \(P_{out}\) can be found by multiplying the total power input \(P_{in}\) with the efficiency (15%), which is \(P_{out} = 0.15 \times P_{in} = 0.15 \times 4.0 W = 0.60 W\).

Current Calculation

For the second part of the problem, we're asked to find the current delivered by the cell. Using Ohm's law which states that the current \(I\) is equal to the power \(P\) divided by the voltage \(V\), \(I = P/V\). The power \(P\) is given from step 1 as 0.60 W, while the voltage \(V\) is given as 0.45 V. Hence, the current \(I = 0.60 W / 0.45 V = 1.33 A\).

Key concepts

Power Output

Solar cells harness sunlight and convert it into electrical energy. The power output of a solar cell depends on its efficiency and the amount of sunlight it receives. In this exercise, we are given a solar cell with a known efficiency and a specific sunlight energy input.
The power input to the solar cell is calculated based on the energy flow per square meter. Given as 1.00 kW/m², this represents the energy received by each square meter of the cell. To calculate the total power input to our solar cell, we have to first convert its area from cm² to m². Given an area of 40.0 cm², this is converted to 4.0 x 10^-3 m².
After conversion, the total power input is calculated by multiplying the energy flow (1.00 x 10³ W/m²) by the area (4.0 x 10^-3 m²), resulting in a power input of 4.0 W. Now, using the efficiency (15%), the power output is determined by the formula:

• Power Output = Efficiency x Power Input
• Power Output = 0.15 x 4.0 W

This calculation gives us a power output of 0.60 W.

Current Calculation

To find out how much current the solar cell delivers, we need to understand the relationship between power, voltage, and current. This relationship is described by a fundamental principle known as Ohm's law.
The exercise tells us that the power output of the solar cell is 0.60 W, with a voltage of 0.45 V. Using the formula for current, which is derived from Ohm's law, we can determine the current as follows:

• Current (I) = Power (P) / Voltage (V)
• Current (I) = 0.60 W / 0.45 V

By conducting this division, we learn the current output from the solar cell is 1.33 A. This means the solar cell can deliver a current of 1.33 Amperes when functioning under these conditions.

Ohm's Law

Ohm's law is a fundamental principle in the world of electricity that describes how voltage, current, and resistance relate to one another. Understanding this law is crucial for calculating various parameters in electrical circuits, including the one in our solar cell exercise.
The law is expressed with the equation:

• V = I x R

where V is voltage, I is current, and R is resistance. In the context of power output, another form of this equation proves handy:

• P = I x V

This alternative equation allows us to express the power (P) of a circuit as a product of its current (I) and voltage (V). This is exactly how we are able to compute the current delivered by the solar cell. By rearranging the equation to solve for current, we utilize:

• I = P/V

This helped us determine that the solar cell’s ability to produce power under the given voltage results in a delivered current of 1.33 A. Thus, Ohm's law not only underpins this particular calculation but is foundational for understanding and working with any electric circuits.