Question

A solar cell that is 15% efficient in converting solar to electric energy produces an energy flow of 1.00 kW/`\text(m)^2` when exposed to full sunlight. The cell has an area of 30.0 `\text(cm)^2`. (a) What is the power output of the cell, in watts?

Two sections:

• What is the power output of the cell, in watts?
• If the power calculated in part (a) is produced at 0.45 V , how much current does the cell deliver?

Answer 1

Here's what I got.

Explanation:

Start by calculating the energy flow of the solar cell in kilowatts per square centimeter, `"kW cm"^(-2)`. Use the fact that

`color(blue)(ul(color(black)("1 m"^2 = 10^4"cm"^2)))`

to find

`1.00 "kW"/color(Red)(cancel(color(black)("m"^2))) * (1color(Red)(cancel(color(black)("m"^2))))/(10^4"cm"^2) = 1.00 * 10^(-4) "kW cm"^(-2)`

Now, you know that the total surface of the solar cell is equal to `"30.0 cm"^2`. Use this to calculate the total power processed by the cell from the incoming solar energy

`30.0 color(Red)(cancel(color(black)("cm"^2))) * (1.00 * 10^(-4)"kW")/(1color(Red)(cancel(color(black)("cm"^2)))) = 3.00 * 10^(-3)"kW"`

The cell is said to have an efficiency of `15%`, which basically means that for every `"100 kW"` of processed solar power, i.e. the power input, only `"15 kW"` are converted to electric power, i.e. the power output.

In your case, this efficiency will produce a power output of

`3.00 * 10^(-3)color(Red)(cancel(color(black)("kW input"))) * "15 kW output"/(100color(Red)(cancel(color(black)("kW input")))) = 4.5 * 10^(-4)"kW"`

Finally, to convert this to watts, use the fact that

`color(blue)(ul(color(black)("1 kW" = 10^3"W")))`

You will end up with

`4.5 * 10^(-4) color(Red)(cancel(color(black)("kW"))) * "1 W"/(10^3color(Red)(cancel(color(black)("kW")))) = color(darkgreen)(ul(color(black)("0.45 W")))`

The answer is rounded to two sig figs, the number of sig figs you have for the efficiency of the solar cell.

For part (b), use the fact that

`color(blue)(ul(color(black)(P = I * V)))`

Here

• `P` is electric power
• `I` is electric current
• `V` is voltage

Rearrange to solve for `I`

`P = I * V implies I = P/V`

Keeping in mind that in terms of units you have

`color(blue)(ul(color(black)("1 W" = "1 A" * "1 V")))`

plug in your values to find

`I = (0.45color(red)(cancel(color(black)("V"))) * "A")/(0.45color(red)(cancel(color(black)("V")))) = color(darkgreen)(ul(color(black)("1.0 A")))`